CE
Computer time
- Code is now running on Cori, in addition to Anvil
- Enough time for 1 run on Anvil (need to finish quota by June 30), and maybe another run on Cori
- Plan to apply for more time on Cori
Reduction of ambient pressure and density
Method 1 from last post: Starting from t=0 with low ambient pressure and density
- Abandoned this method
- Eventually get Hypre error for tabular EOS run
- Need to set MinDensity = ambient density, which is very inefficient
- Get artifacts in ambient medium that slow code and force extra unwanted refinement
Method 3 from last post: Restarting from frame 86 of old runs and modifying ambient
- Got this to work well with ideal gas EOS run
- Does not quite work yet for tabular EOS run
- If modify density, momentum and energy, then at some point pressure and temperature decrease to very low values, leading to artifacts and unwanted extra refinement
- If modify density and pressure, then code eventually crashes due to protections detecting NANs (energy)
- If modify density and momentum alone, code eventually crashes
- If modify density alone, code slows down catastrophically
Discussion
- Solutions for reducing ambient in tabular EOS run
- Strategy for paper
CE
Computer time
- We need to perform 2 simulations
- We may only be able to complete ~1 simulation using Anvil
- DOE allocation?
Reduction of ambient pressure and density
Method 1 from last post: Starting from t=0 with low ambient pressure and density
- Continued Run 026 (ideal gas) and Run 027 (MESA EOS), from last blog post
- Run 026 took about ~1.75 hours per frame up to 19 frames
- Run 027 took about ~2.5 hours per frame up to 34 frames
- crashed shortly after frame 34
- might have been caused by extra refinement (up to level 3) outside of desired level 4 refinement sphere
- I tried defining a shape like the level 4 refinement sphere but with "DEREFINE_OUTSIDE"
- I also tried setting Refinement%Tolerance=-1d0
- Both of these changes had no effect
- Finally, in physics.data, changed refineVariableFactor to 0d0,0d0,0d0,0d0,0d0,0d0,0d0,0d0,0d0,0d0,0d0 from 1d0,1d0,1d0,1d0,1d0,1d0,1d0,1d0,1d0,1d0,1d0, to force derefinement outside of refinement object 1, and evolved from frame 34 to 35.
- Prevents from crashing and speeds up simulation from 2.5 hours to 1.5 hours per frame
- Is this method fine? If so, should I
- continue from frame 35?
- restart from frame 19 (when unwanted refinement was either absent or marginally present)?
- restart from beginning of simulation?
- Is this method fine? If so, should I
- Prevents from crashing and speeds up simulation from 2.5 hours to 1.5 hours per frame
- might have been caused by extra refinement (up to level 3) outside of desired level 4 refinement sphere
- crashed shortly after frame 34
- Checked separation curve up to 19 days and it seems okay:
- Visualization up to 19 days looks okay but artifacts present, especially in Run 027 — harmless?
Method 3 from last post: Restarting from frame 47 of old runs and modifying ambient
- Found that setting iSelfGravity=2 (non-momentum-conserving self-gravity) was the key to getting rid of the artifacts
- Also speeds up simulation such that it is about half as fast as the original simulation at frame 47 to 47.1
- However, when I try changing back to iSelfGravity=1 (momentum-conserving self-gravity) artifacts at boundary of level 1 grid appear (though artifacts at boundary of level 0 grid that I was seeing before — when iSelfGravity was left unchanged from 1 during the ambient modification — do not appear)
- Figures show density, pressure and temperature, comparing frame 47 (left panel; original Run282, iSelfGravity=1), 47.1 (middle panel; low ambient, iSelfGravity=2) and 47.2 (right panel; iSelfGravity=1):
- Is there a way around this?
- If not, then how bad would it be to use iSelfGravity=2 for the remainder of the simulation?
Discussion
- Method 1 working well now? Artifacts present in ambient but seem harmless
- Decision about refineVariableFactor
CE
Reduction of ambient pressure and density
- Note that pressure needs to be reduced to minimize ambient energy density
- Density needs to be reduced to minimize ambient mass
Review of literature
- In the table below, "UG" stands for uniform grid, and "MM" for moving mesh
- Note: In Ohlmann+16a relaxation runs, the ambient density and pressure are much higher: 2e-10 g/cc and set to "roughly match the surface pressure of the star". He also says that the pressure gradient at the surface is not fully resolved, so the star expands a bit (leading to artificial motions in the ambient medium that do not affect the star) and then stabilizes during the relaxation run.
Paper | Type | Code | Refine criteria | Relaxation run | rho_amb (g/cc) | P_amb (dyn/cm2) |
---|---|---|---|---|---|---|
Chamandy+2018, 2019 | AMR | AstroBEAR | Pressure gradient, density (effectively) | no relaxation run, except for ModelB of paper I: velocity damping ramped down during 17.5 d ~ 5 freefall times | 6.67e-9 or 1e-9 | 1e5 dyn/cm2, comparable to outer layer of star |
Ricker+Taam 2008, 2012 | AMR | Flash | 2nd deriv of rho (RT08), 2nd deriv of P, T (RT12) | 1 dynamical time (13 d) with velocity damping | 1e-9 | pressure of the outermost layer of the star |
Passy+ 2012 | SPH/ UG | Enzo(UG) | N/A | Velocity damping followed by no damping over a few dynamical times | 1e-4 times lowest density of star | Not stated |
Ohlmann+ 2016a | MM | AREPO | density and size relative to softening length | Velocity damping (5 sound-crossing times) followed by no damping (5 sound crossing times) | 1e-16 g/cc | ~1e-4 erg/cc (calculated based on my priv. comm. with S.O.) |
Prust+Chang 2019 | MM | MANGA | Damp spurious velocities and energies | 1e-13 g/cc | T_amb = 1e4 K |
Possible strategies
- Simply reduce ambient pressure and density.
- This would cause pressure scale height at primary surface to decrease and it would no longer be resolved with standard resolution.
- Since the standard resolution in the bulk of the envelope was chosen to resolve the pressure scale height at the surface, might as well reduce it (from envelope maxlevel = 4 to, e.g., envelope maxlevel = 3)
- This seems to be the strategy of other groups, who seem to have low resolution in the envelope (except near the cores). Our resolution is probably still high by comparison.
- Since the scale height will not be resolved, this will lead to artifacts (pressure waves owing to numerical diffusion)
- This will lead to high temperature regions or steep pressure gradients in the ambient medium, leading to spurious motions that slow down the code
- This can be averted to some extent by setting MinDensity, which is the floor density in the simulation
- This will lead to high temperature regions or steep pressure gradients in the ambient medium, leading to spurious motions that slow down the code
- Since the standard resolution in the bulk of the envelope was chosen to resolve the pressure scale height at the surface, might as well reduce it (from envelope maxlevel = 4 to, e.g., envelope maxlevel = 3)
- This would cause pressure scale height at primary surface to decrease and it would no longer be resolved with standard resolution.
- First perform a relaxation run, and then follow the method of #1 above (as done by Ohlmann)
- This is done by some other groups.
- This could help to eliminate spurious motions in the ambient medium that slow down the code
- We have argued in Paper 1 that performing a relaxation run with velocity damping does not make a big difference to the evolution
- It is computationally expensive
- Grid effects become severe during the relaxation run since the primary is not moving with respect to the grid
- For this reason our relaxation run was only half as long as that of Ohlmann+2016 (we did not include the phase without damping)
- In Ohlmann+2016, the relaxation run is peformed with high ambient pressure (Ohlmann, private communication). This ambient pressure is then removed for the simulation. To implement this, we need a way to change the ambient pressure without changing the star.
- That last point leads nicely into this 3rd option. Use our current simulations which resolve the pressure gradients at the surface, but at the appropriate time, when the secondary has already spiralled in (some time after first periastron passage), use the ambient tracer to reduce the ambient pressure and temperature
- This can be done suddenly or gradually
- Implementing it in the code seems to be straightforward
- Total energy of the simulation would not be conserved
- There can still be artificial effects of the ambient before this time.
- If box is enlarged considerably then initial ambient mass will be very large
- This may be harmless but one would have to justify it.
- If box is enlarged considerably then initial ambient mass will be very large
- Give the primary a hydrostatic atmosphere, which transitions to a uniform ambient medium at some large radius
- Explored in a previous blog post (Run 199) and again below
- It fails catastrophically, for reasons that are still not clear
Performing the Runs
- Runs performed on Anvil using 16 nodes (2048 cores)
- No queue time!
- Total allocation on Anvil is 3,312,000 SUs = core-hours
- 16 nodes = 2048 cores
- We have already used 7% of the allocation for testing.
- Want to redo the ideal gas and tabular EOS runs (Runs 282 and 277 — it is not necessary to redo 283)
- If each simulation is 500 frames (as before) and each frame takes an average of 2.5 hours on 16 nodes, we have enough left for 1.2 simulations. So we may need to ask for a supplement.
Strategy #1 from above
- Frame rate kept same as Run 282 (2e4 s) (recall Run 282 lasted for 500 frames = 115 days)
- Simulations were run up to frame 2
- In table below, "eml" stands for envelope maxlevel for refinement of bulk of envelope (innermost 6Rsun is refined at maxlevel 5), "wt" stands for wall time, and "fr" stands for frame
- MinDensity is the density protection setting in physics.data
- The first run, Run002, is the same as Run282
- Runs started from scratch (lRestart=F)
- For each run, first image shows density rho, second shows pressure P in dyn/cm2, and P/rho. In Run027 (tabular EOS), the third image replaces P/rho by temperature T in K.
- Run time is principally determined by MinDensity (compare 007 and 011)
- Reducing the pressure does not greatly affect the run time (compare 012 and 018 or compare 007, 009 and 020)
- Reducing the pressure does not drastically change the level of artifacts present (compare 007 and 009)
- Increasing the box size while reducing the base resolution proportionately does not greatly affect the run time (compare 020 and 022)
- Ideal gas runs are faster than tabular EOS runs by a factor of 2 (compare 026 and 027)
Strategy #4 from above
I again tried to perform a run with an exponential hydrostatic atmosphere transitioning to a uniform ambient at large radius. This run is very similar to Run 199 of previous posts. There are severe artifacts.
Strategy #3 from above
- Shock-like structure moving in from boundary at supersonic velocity
- Ambient not getting modified correctly in ghost zones?
Discussion
- Strategy #1 seems promising, but how much do artifacts affect the inspiral?
- Setting MinDensity equal to ambient density helps to speed up the simulation (apparently by avoiding very high temperatures)
- Smaller ambient density slows the code (why?). Good compromise is 6.63e-12 g/cc, which is 0.001x the lowest density in the initial primary star
- Wall time is very insensitive to changing the ambient pressure. But very low ambient pressure (1e-5 dyn/cm2) caused the code to crash. Good compromise is 1e-1 dyn/cm2.
- Wall time is insensitive to box size Lbox, provided base resolution delta_0 scales with Lbox. However, code crashed for Lbox=3.2e14 cm (do not know why). Also, grid effects are slightly amplified for a larger box (with coarser base resolution). A good compromise is Lbox=1.6e14 cm, which is 2x the box size of Runs 282 and 277. This will allow us to simulate up to 500 frames (115 days) with very little envelope material leaving the grid.
Conclusions
- For a reasonable wall time, sufficient ambient reduction and minimization of artifacts, parameter values of Run 026/027 seem optimal.
- Now need to test whether these runs reproduce the higher resolution runs (Runs 282/277) sufficiently accurately over the first ~40 days when effects of the ambient on envelope gas are still negligible.
CE
Computing
Anvil
- Baowei has gotten the code working on Anvil (Purdue University)
- No queue (as of now)
- Maximum 16 nodes/2048 cores, 96 hours
- More than twice as efficient as Frontera with 64 nodes/3584 cores, in terms of node-hours per frame
- Implies that the code does much better with more cores/node and less nodes, for the same number of cores.
- Anvil has AMD nodes, so nice that our code runs with AMD nodes (before we always used Intel)
- Allocation ends June 30, so need to ask for extension.
Computer time
- Extension for Anvil
- Renew XSEDE (now under a different scheme)?
- Renew Frontera?
New Analysis
Energy terms (star gas only, excludes ambient), evolution with time
- The black and grey lines show that the envelope gas is being energized by the ambient after 40-50 days — problematic
- Is the ambient energizing bound or unbound gas? If unbound, not a big problem. If bound, then implies that our estimates for the unbound mass are higher than they should be.
- Ans: mainly unbound gas, but some bound gas too. The proof is that total energy of particles+bound gas rises, even though it must be transferring energy to unbound gas so should be losing energy rather than gaining:
- Is the ambient energizing bound or unbound gas? If unbound, not a big problem. If bound, then implies that our estimates for the unbound mass are higher than they should be.
Energy terms, bound envelope gas
Unbound mass with factors of two in particle-gas PE
Unbound mass without factors of two in particle-gas PE
So what to do?
- Admit the limitation and write up the paper as "part I". Focus on the bound gas.
- Here is a skeleton paper, with figures: http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos_11Apr2022.pdf
- Redo the simulations with smaller ambient density and pressure
- Requires some experimentation to get it working
- Assuming we can get it to work, requires a few months of running and analysis, but computer time is available and pipeline is ready
CE
Research Plans and Ideas
Papers based on existing simulations
Paper Idea | Description | Simulations | Status | Comments |
---|---|---|---|---|
Drag Force II | Model drag force at late times | Runs 183, 263, 277, 282 | Sims completed | Sim 263 is like published AGB Run 183 but with particles of equal mass, to simplify modeling (Escala+2004) |
Time-dependent energy formalism | Extend/generalize energy formalism using insight from simulations | Run 183, perhaps others as well | Stalled because initial evolution is hard to reconcile with the new formalism | Should be possible to get around this or just exclude early times |
CE planet II | Extend C+21 model | Runs 259 (AGB+10MJup planet), 268 (AGB+0.08Msun, ideal gas), 269 (AGB+0.08Msun, MESA EOS) | Notes and presentations but no write-up yet | Simulations were not really successful, but Run 259 is first of its kind so worth presenting for its intrigue |
Ideas for new simulations
Simulation | Type | Description | Development needed | Comments |
---|---|---|---|---|
Neutron star jet | New regimes/ Parameter space exploration | companion is a NS launching a powerful jet | Ideally would improve accretion/jet model (AstroBEAR already allows for this). | High velocity jet makes run expensive. Ideally would do one run with existing RGB primary and one with a massive primary. |
Envelope ejection? | Improve numerics | Extend a simulation all the way to envelope ejection | Reduce ambient, expand box, increase resolution | Need to try running with a lower ambient energy density and compare to existing runs to see what we can get away with, need to look at energy conservation more carefully. Requires lots of computer time which we do not currently have. |
Vary initial separation | Parameter space exploration/ New regimes | Compare sims with different initial separations, try to obtain RLOF phase | Unclear, perhaps not much | Expensive because of longer periods. Preliminary sims were done long ago: suggests that higher a_i leads to higher eccentricity during plunge-in. Existing work: Reichardt, De Marco, Iaconi, Tout & Price 2019 |
BD/planet companions | New regimes | Improve efforts to simulate RGB/AGB with BD/planet companion | Not much, perhaps | Expensive because of long orbital time. Only (modern) existing work: Kramer, Schneider, Ohlmann+ 2020 |
Include MHD | New physics | Include MHD in our best fiducial RGB run and see what happens | Setup should not be too complicated, but bugs are likely | Makes sense considering that our group has expertise in MHD. Only existing work: Ohlmann+2016b, Ondratschek, Roepke, Schneider+ 2021(preprint) |
Include radiative transfer | New physics | Include flux-limited diffusion (already implemented into AstroBEAR) | Needs lots of testing and learning the theory, need to put in MESA opacity tables and figure out how to use them | Only existing work is a conference proceedings: Ricker+2019, the effect for our fiducial model is likely to be rather negligible. Realistic convection likely requires radiative transfer? |
High mass regime (NS-NS merger progenitors) | New regimes | CE involving 8Msun primary and NS secondary | Will likely require higher resolution. | Larger range of scales so probably more challenging. May be expensive. One existing self-consistent global sim: Moreno+2022(preprint) |
CEE involving two giant stars | New regimes | Binary pair is evolving to RGB at almost same time so get a CE involving envelopes of both stars | Should not require much | Would be expensive. No existing simulation? But see: Schneider+2019 |
Triple systems | New regimes | Introduce a second companion (multiple orbital configurations are possible) | Not much, probably | Triples may be quite important (according to S. Toonen). Limited number of existing simulations: Glanz+Perets 2021 |
CE
New Analysis
2D plots showing Spatial and Temporal dependence
Helium
Hydrogen
Conclusions:
- Helium seems more important than hydrogen.
- Recombination at first but then stagnates. Heating from inspiral balances cooling by expansion?
Ionization and Recombination (Volume-integrated, showing evolution with time)
Results
Conclusions:
- Helium recombination HeIII —> HeII and HeII —> HeI are the dominant transitions
- However, after t = 25 days, there is no net release of recombination energy
Energy terms (Star gas only, excludes ambient), evolution with time
All energy terms, not accounting for fluxes out of box:
Zoom-in on change in the recombination energy:
Conclusions:
1st Figure:
- In both tabular EOS and gamma=5/3 runs, particle energy decreases at a steady (and still substantial) rate after t ~= 57 days, implying that the inpsiral does NOT stall.
- Differences between runs are very small (<10%) implying that ionization and recombination do not play a very important role up until this point in the evolution
- The release of recombination energy between about t = 6 days and t = 25 days leads to a slightly higher thermal energy compared to gamma=5/3 run (the two energy changes roughly balance one another, which makes sense).
- EOS case manages to reduce gas-particle PE terms (by puffing up envelope?) after t ~= 45 days. From t ~= 45 days to t ~= 80 days, we also see a reduction in the thermal energy in the tabular EOS run as compared to the gamma=5/3 run, which is consistent with a puffing up. But this effect has faded by the end of the simulation at t ~= 80 days. This coincides with a transition from a deeper inspiral (compared to gamma=5/3 run) to a shallower inspiral (see also separation results, below).
2nd Figure:
- The peak amount of recombination energy released is about 10%, which happens at t ~= 24 days
- Thereafter, the net recombination energy relased reduces and drops to only 1% by the end of the simulation at t ~= 80 days.
- The evolution of the recombination energy agrees well with the expectation from the ionization/recombination analysis above (using tracers and the Saha equation) FOR THE FIRST 20 DAYS. After that the tracer/Saha analysis predicts that almost 0 recombination energy is released whereas the plot of recombination energy (i.e. internal minus thermal) says that the net release of recombination energy between t ~= 20 days and t ~= 80 days is negative.
- It is important to understand the reasons for this discrepancy
Inter-particle Separation, evolution with time
Separation curve:
Conclusions:
- Mean separation continues to decrease at the ends of both simulations (though at an ever-decreasing rate of decrease)
- There is very little difference between the runs. Suprisingly, the difference between the MESA EOS run (with radiation energy removed — blue curve) and the tabular EOS run with internal energy replaced by thermal energy (green curve) is larger than the difference between MESA EOS and gamma=5/3 (red) curves.
- Comparing MESA EOS (blue) and gamma=5/3 (red) curves, the MESA EOS run shows slightly smaller separation between t ~= 25 days and t ~= 70 days and slighly larger separation thereafter
Envelope Unbinding (Volume-integrated), evolution with time (showing Star tracer mass only)
With factors of two in particle-gas potential energy terms:
Without factors of two in particle-gas potential energy terms:
Conclusions:
- Using the "internal energy" criteria (which makes no sense) would imply that the unbound mass is much higher, as found by other authors (top curve in both plots, and other authors use the equivalent of the second plot)
- Using another criteria for unbound which is more reasonable, the MESA EOS run does lead to a higher unbound mass, of order 10% larger, peaking somewhere between t ~= 25 and t~= 40 days.
- By the end of the MESA EOS simuation at t ~= 80 days, the difference is basically 0
- The MESA EOS simulation with internal energy replaced with thermal energy (green/yellow) is much more similar to the gamma=5/3 run, as would be expected. But this run generally falls between the other two. This suggests that the recombination energy is actually slighly less important than the difference between blue and red curves would suggest.
- Note that after t ~= 50 days, significant mass from the original primary is leaving the box, about the same in both runs (about 5% by t=85 days).
- Generally speaking, the unbound mass is growing steadily by the end of both simulations (irrespective of what criterion for unbound is used)
Energy conservation, evolution with time
- Energy is conserved to within ~2%, where the denominator chosen for this calculation is indicated on the plot
- If one ignores the energy loss from reducing the softening radius, it is more like ~4% for the gamma=5/3 run and <1% for the MESA EOS run
- The energy conservation inside the sphere with radius Lbox/2 (centered on the origin) is probably better: the gravitational potential due to mass outside this sphere is NOT included in the code, so envelope mass leaving this sphere reduces the gravitational PE inside the sphere, leading to an energy increase. This is likely the cause of the increase seen at the end of the simulations.
Status of runs
- Run 277: MESA EOS (analyzed up to frame 344 or 77 days, completed up to frame 377 or 87 days)
- Run 282: Ideal gas gamma=5/3 EOS (analyzed up to frame 374 or 87 days, completed up to frame 407 or 94 days)
- Run 283: MESA EOS with recombination energy removed from EOS tables (completed up to frame 218 or 50 days on Frontera)
- Run 276: MESA EOS with maxlevel increased by 1 compared to Run 277 (for convergence study — completed up to frame 47 or 11 days on Frontera)
- Run 28?: MESA EOS with maxlevel reduced by 1 compared to Run 277 (for convergence study — not yet started on Frontera)
- Run 271: MESA EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 235 or 54 days and will not extend)
- Run 143 (fiducial run of past papers): Ideal gas gamma=5/3 EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 173 or 40 days and will not extend)
Next steps
- Energy terms — include flux in total energy of primary gas tracer
- Anvil
- Continue to extend Runs 277 and 282 — but for how long?
- Extend Run 276 (high res run)
- Make progress on paper write-up
- Explore overlapping ionization species regions to get a sense of how important they might be (< 10% difference?)
- Calculate total angular momentum and check angular momentum conservation
- PostProcessing to check energy conservation within sphere of radius Lbox/2 — expect it to be better than that in full box
CEE
EOS paper
Skeleton of paper with draft intro and methods sections: http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos.pdf.
Relevant papers
3D simulations:
- Reichardt, De Marco, Iaconi+ 2020
- Conclude that final separation unaffected by EOS (ideal or MESA) BUT actually in one of their simulations there is quite a large difference, with the tabular EOS producing a larger final separation by 16%.
- Find that recombination energy release greatly increases the unbound mass
- Unbound mass curves almost independent of EOS up until first periastron passage, and diverge thereafter, with tabular EOS resulting in roughly 50% more unbound mass in both sets of simulations, using a definition of unbound that includes thermal energy but not recombination or radiation energy (Fig. 2)
- Find that released helium recombination energy is thermalized (released at too high an optical depth to radiate away)
- In contrast, find that about half of released hydrogen recombination energy would be radiated away
- Provide references for early papers: Lucy 1967, Roxburgh 1967, Han, Podsiadlowski & Eggleton 1994 and Harpaz 1998
- Provide good summary of the recent literature and controversy over whether released recombination energy would radiate away
- Point out in Sec. 2.0 that the helium mass fraction can vary quite a bit from on star to another, and this could potentially affect the results a lot
- Provide useful information about the MESA EOS in Sec. 2.1 (we could refer to this summary in our paper to avoid having to repeat it)
- End of Sec. 4.1 talk about ionization fronts staying at roughly constant radius, as opposed to e.g. moving inwards "counter to some expectations".
- Fig 4 and 5 showing spatial and time dependence are particularly useful (I have done a similar thing but I did not do a spherical average, ignored overlapping a regions, and also had an extra plot for the tracers. Also, so far I was not planning to include the unbound mass plot for the ideal gas EOS run.)
- Fig 6 is also interesting, purpoting to show the release of recombination energy (which is negative for ionization). However, I think it is flawed because it implicitly assumes that the gas does not move radially
- Sec. 5 tries to estimate how much of the released recombination energy might be lost by convection+radiation (since the simulation cannot include those effects)
- Lau, Hirai, Gonzalez-Bolivar+ 2022
- Simulate CEE involving a 12 Msun RSG primary (focus on case with q=0.25)
- Compare 3 sims: (1) Full EOS; (2) ideal gas; (3) ideal gas + radiation energy and pressure (but no recombination at all)
- Find that the Run (1) unbinds about 114% more mass than Run (3) and 233% more mass than Run (2) (assuming KE+PE+TE energy density definition for unbound)
- Find that recombination energy of helium contributes importantly to envelope unbinding, whereas recombination energy of hydrogen is mostly released into gas that has already become unbound
- Find that the "final" separation in Run (1) is 34% larger than that of Run (2) and the final separation of Run (3) is 14% larger than that in Run (2)
- Simulations are not very well converged with resolution (Fig. 9)
- Also not converged with respect to softening length at late times (Fig. B1)
- Fig. 13: Present spherically averaged color plots of ionization state at a given radius and time —> focus on regions where two ionization states (e.g. HeII and HeIII) coexist, as these regions are where gas is "actively recombining". Density of unbound gas is overplotted.
- These plots also show contours for the tau=1, 10, 100 surfaces (spherically averaged)
- Includes much discussion about the possibility of losses of recombination energy due to convection and radiation (Secs. 4.1 and 4.4)
- Sand, Ohlmann, Schneider+ 2020
- Simulations use OPAL EOS and ideal gas EOS
- Compare ideal gas and OPAL sims and find that ideal gas unbinds ~20% and OPAL ~90% by end of the simulations (about 22% vs 78%, respectively, at time corresponding to the end of the ideal gas simulation), according to the bulk KE + PE density criterion for unbound gas
- Show that the evolution of the released recombination energy during the simulation resembles the unbound mass evolution
- The difference in unbound mass becomes larger after about 400 days, whereas the first periastron passage is at about 600 days.
- Get convection (at some level)
- "recombination energy acts behind the spiral shocks where the gas cools, boosting the expansion"
- Determine tau=1 surface in postprocessing and equate this with location of photosphere (not stated whether they use MESA opacity tables to do this)
- Find that most of the hydrogen ionization happens below the photosphere, but this number goes from 99% at t=296 days to 94% at t=1000 days to 80% at the end of the simulation (t=2500 days)
- Similar results for runs with 2x smaller or 1.5x larger companion mass
- "We find that the spiral-in is deeper by 17%–23% when not including recombination energy compared to the final separations in the simulations that include recombination energy. This can be explained by the fact that without recombination energy release the expansion of the envelope is slower and the transfer of orbital energy terminates later when little mass is within the orbit of the cores."
- "We cannot follow the evolution for longer with confidence with our current numerical methods, because the energy-error rate exceeds the recombination-energy-release rate in the system and we can no longer decide whether a further envelope unbinding is physical or caused by numerical errors"
- Kramer, Schneider, Ohlmann+ 2020
- Simulations use OPAL EOS and one comparison simulation with ideal gas EOS
- Sec. 3.3: The run with 0.08 Msun companion and 1 Msun primary (tip of RGB) unbinds about 78% of the envelope (OPAL) compared to 7% (ideal gas)
- "Companions of even lower masses can certainly not eject the envelope when only tapping the orbital energy reservoir" — seems overly restrictive since simulations could evolve for much longer
- Moreno, Schneider, Roepke+ 2021(preprint)
- Simulations use OPAL EOS
- Emphasize the "internal energy" criterion which tells them the envelope is almost completely unbound at the end of the simulation
- Claim that recombination energy is very important for unbinding the envelope but provide no evidence for this statement
- Ivanova & Nandez 2016
- Identify some differences between 1D and 3D simulations
- Strive to understand the transition between early phase (3D models) and late phase (1D models)
- "The steady recombination outflow may dispel most of the envelope in all slow spiral-in cases, making the existence of a long-term self-regulated phase debatable, at least for low-mass giant donors."
- Find that in some cases their can be a "recombination runaway" where recombination leads to expansion leads to cooling leads to more recombination
- In other cases get a "steady recombination outflow"
- Then can get "shell-triggered ejection" which is partly powered by recombinaton energy (see also Clayton+2017)
- Nandez & Ivanova 2016
- "We can clarify that there is no recombination energy stored in the ejected material at the end of the simulations."
- "The role of the recombination energy for the CEE with a low-mass RG donor is not that it is necessary for the overall energy budget, as none of the considered systems were expected to merge by the standard energy formalism, but because the recombination occurs exactly at the time when the shrunk binary is no longer capable of transferring its orbital energy to the expanded envelope."
- Modify energy formalism to include recombination energy and energy taken away by the ejecta
- Nandez, Ivanova & Lombardi 2015
- "Taking [recombination energy] into account helps to avoid the formation of the circumbinary envelope found in previous studies"
- Use misleading definition of unbound that includes all internal energy density — classify > 0 energy density as "ejecta"
- Find that for the ideal gas + radiation EOS, 50% of the envelope becomes unbound but for the MESA EOS the entire envelope is ejected
- "Indeed, ionized material forms the circumbinary envelope initially. Recombination then takes place there, while the circumbinary envelope continues to expand. This results in the ejection of the circumbinary envelope and effectively of all the CE material."
- "If instead the recombination energy had been released too early, the simulations would have ended up with unexpelled circumbinary envelope as in previous studies"
- Chapter 9 of Ohlmann 2016 (phd thesis)
- Their setup very similar to the one we are using (2 Msun RGB with R = 48 Rsun + 1 Msun companion and initial separation similar to ours, but they have 95% corotation to begin with)
- Contains a critique of Nandez+2015
- Very little difference in the separation curves between ideal gas and OPAL EOS simulations
- More mass is unbound (KE+PE density unbound criteria) in the simulation with the OPAL EOS (Fig. 9.3 — compare blue and yellow curves)
- Includes spatial analysis of where recombination energy is released and whether it contributes to unbinding (Fig. 9.5)
- As in our simulation their high ambient temperature causes material near the surface to be ionized from t=0
- Shows spatial evolution of ionization states in Fig. 9.6
- Prust & Chang 2019
- Study a system almost identical to our own (looking at two cases: 95% corotation or no initial spin like us) — their initial separation is slightly greater than us (52 Rsun compared to 48 Rsun), and they mention that their star is slightly bigger compared to Ohlmann+16a (the latter is almost identical to ours)
- For internal energy density criterion, they get some ~65% of the envelope mass ejected by the end of the simulations (240 days)
- For the KE+PE density criterion, they find that the it is only about 8% ejected (but rising) by 240 days: Unlike Ohlmann+16a but like us, they find a decreasing trend (before a rising trend) — see their Fig. 6
- They do not try an ideal gas (gamma=5/3) model
- Their final separation (no initial corotation) is 3.2 Rsun at 240 days — apparently still decreasing slowly by the end of the simulation (see Fig. 7)
1D simulations
- Ivanova, Justham & Podsiadlowski 2015
- Importance of helium vis-a-vis hydrogen recombination energy
- Detailed study of usefulness of recombination energy in unbinding envelope in their 1D simulations
- Find that ~90% of helium recombination energy is used to unbind the envelope, while for hydrogen it is less clear
Analytical modeling
- Ivanova+ 2013
- Argue that much of the hydrogen recombination energy does not get released until after envelope ejection
- Argue that the subsequent release of this energy can explain LRNe
- Argue that the luminosity comes from the recombination front, i.e. photosphere ~= recombination front
- For the latter they cite Popov (1991) (see text after eq 7 in Popov 1991, in that model R_i is the radius of the front, dimensionless radius of the front is x_i). See also Kasen+Woosley(2009).
- The location of this recombination front is expected to be "almost constant," in contrast with the CE ejecta, which moves out at a speed which is of order the escape speed
- This also implies importance of helium vis-a-vis hydrogen recombination energy in assisting envelope ejection (see Lau+22)
Papers focusing on whether recombination energy is lost owing to radiation or convection+radiation before it can contribute to unbinding
- Soker & Harpaz 2003
- Sabach, Hillel, Schreier & Soker 2017
- Grichener, Efrat & Soker 2018
- Soker, Grichener & Sabach 2018
- Ivanova 2018
Other recent CE papers not directly relevant
- Ondratschek, Roepke, Schneider+ 2021(preprint)
- "able to follow the evolution to complete envelope ejection" — 99% unbound by "kinetic energy criterion"
- Law-Smith, Everson, Ramirez-Ruiz+ 2020(preprint)
- Clayton, Podsiadlowski, Ivanova+ 2017
- Sequel to Ivanova+2015, now extending simulations to include episodic dynamical mass ejections
- Ricker, Timmes, Taam & Webbink 2019
Status of runs
Summary:
- Run 277: MESA EOS (completed up to frame 322 or 75 days on Frontera)
- Run 282: Ideal gas gamma=5/3 EOS (completed up to frame 343 or 79 days on Frontera)
- Run 283: MESA EOS with recombination energy removed from EOS tables (completed up to frame 218 or 50 days on Frontera)
- Run 276: MESA EOS with maxlevel increased by 1 compared to Run 277 (for convergence study — completed up to frame 47 or 11 days on Frontera)
- Run 28?: MESA EOS with maxlevel reduced by 1 compared to Run 277 (for convergence study — not yet started on Frontera)
- Run 271: MESA EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 235 or 54 days and will not extend)
- Run 143 (fiducial run of past papers): Ideal gas gamma=5/3 EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 173 or 40 days and will not extend)
Next steps
- Energy terms graph and compare the two methods of computing the released recombination energy and check that they agree at all times
- Combine tracer figures and make colors non-overlapping
- Normalized energy (red/blue) plot for Run 282
- Continue to extend Runs 277, 282 and 283
- Make progress on paper write-up
- Explore overlapping ionization species regions to get a sense of how important they might be (< 10% difference?)
- Calculate total angular momentum and check angular momentum conservation
CEE
Conferences
- Will submit blurb for the upcoming LANL meeting (date still not finalized), as requested of all participants by the organizer, Chris Fryer.
Jet paper
- Submitted to MNRAS and astro-ph by Amy
EOS paper
Meeting?
A meeting before the end of Feb seems like a good idea. Times?
Writing
Made progress on Intro and Methods sections
Status of runs
- 277 and 282 are now running on Frontera
- Run 283 was not running properly (slow and chombos huge) ⇒ resubmitted using old executable (Baowei) and old module settings
Summary:
- Run 277: MESA EOS (completed up to frame 288 or 67 days on Frontera)
- Run 282: Ideal gas gamma=5/3 EOS (completed up to frame 295 or 68 days on Frontera)
- Run 283: MESA EOS with recombination energy removed from EOS tables (completed up to frame 218 or 50 days on Frontera)
- Run 276: MESA EOS with maxlevel increased by 1 compared to Run 277 (for convergence study — completed up to frame 47 or 11 days on Frontera)
- Run 28?: MESA EOS with maxlevel reduced by 1 compared to Run 277 (for convergence study — not yet started on Frontera)
- Run 271: MESA EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 235 or 54 days and will not extend)
- Run 143 (fiducial run of past papers): Ideal gas gamma=5/3 EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 173 or 40 days and will not extend)
New analysis
Energy terms
We can calculate the released recombination energy two ways:
- Using the Saha equation and tracers to see how the ionic state has changed, calculate the corresponding energy released, and integrate over all gas (see notes from last post),
- Assume an ideal gas (with mean particle mass mu and temperature T taken from the simulation) and integrate to get the total thermal energy and subtract this from the internal energy to get the recombination energy. The negative of the net change in the recombination energy is equal to the released recombination energy.
We want to show that these two methods give approximately the same number (at every time).
I was able to roughly show this for the 7x higher ambient density run 271. However, with the new run 277, the ambient is at a high temperature and contains a lot of recombination energy. Therefore, it becomes more important to exclude the ambient gas when calculating the recombination energy by method 2 above. This calculation is in progress.
There is one small caveat. The potential energy term involving self-gravity of the gas makes use of the potential Phi due to all the gas (excluding particles). We made changes to the code to recalculate Phi excluding the ambient in postprocessing. This is expected to reduce the magnitude of the gas self-gravity potential energy term by 1%. However, it reduces it by 30%, so there must be a bug.
Unbound mass
For the same reason, ideally we would recompute the unbound mass using the correct Phi that does not include the ambient, but this would make such a small difference it may not be worth it (could be mentioned in a footnote). Consider that the unbound mass is perhaps already underestimated because we are including self-gravity of unbound envelope gas, which is maybe too conservative (e.g. Prust+Chang 2019 exclude it).
Ionization and Recombination
Spatial dependence http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos_ion_277.pdf. To reduce the number of plots I am planning to plot all the tracers in one plot, but to avoid overlapping them by only showing the tracer with the highest density at that location. This should be sufficient to make the points we want to make. Overlapping leads to ambiguity because the order of overlapping affects the shades so one can no longer read off the density from the color bar, so best to avoid overlapping.
Next steps
- Compare the two methods of computing the released recombination energy and check that they agree at all times
- Combine tracer figures and make colors non-overlapping
- Continue to extend Runs 277, 282 and 283
- Make progress on paper write-up
- Explore overlapping ionization species regions to get a sense of how important they might be (< 10% difference?)
- Calculate total angular momentum and check angular momentum conservation
CEE
Computing
- Frontera issues for running CE code resolved by Baowei
- Stampede2 allocation is basically used up — now moving all runs to Frontera
Jet paper
- Ready to submit I think
EOS paper
Status of runs
Note that the frame interval is about 0.2315 days
- Run 277: MESA EOS (completed up to frame 264 or 61 days on Stampede2)
- Run 282: Ideal gas gamma=5/3 EOS (completed up to frame 268 or 62 days on Stampede2)
- Run 283: MESA EOS with recombination energy removed from EOS tables (completed up to frame 218 or 50 days on Frontera)
- Run 276: MESA EOS with maxlevel increased by 1 compared to Run 277 (for convergence study — completed up to frame 47 or 11 days on Frontera)
- Run 28?: MESA EOS with maxlevel reduced by 1 compared to Run 277 (for convergence study — not yet started on Frontera)
- Run 271: MESA EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 235 or 54 days and will not extend)
- Run 143 (fiducial run of past papers): Ideal gas gamma=5/3 EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 173 or 40 days and will not extend)
New analysis
Unbound mass
Unbound mass including envelope gas only (i.e. excluding ambient) for runs 277 (MESA EoS without radiation), 282 (gamma=5/3 ideal gas), 283 (MESA EoS without radiation or recombination energy)
- These are basically the final graphs except that the runs are all still being extended in time
Separation
Updated separation graph now including Run 283
Energy conservation
Updated energy conservation graph now including Run 283
Ionization and Recombination
Spatial dependence http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos_ion_277.pdf.
- Now for Run 277 (instead of old Run 271 which had a 7 times higher ambient density, slightly lower resolution and poorer energy conservation)
- Instead of worrying about transparency or truecolor plotting, I decided to make separate graphs for each ionic tracer
- Note that both the tracers and the graphs showing the ionization state at time t plotting only the gas density of the ionization species which is highest at that location.
- I checked and the regions of overlap are small (as expected given the exponential temperature dependence) but not completely negligible…it is just something that needs to be looked at a bit more carefully and mentioned in the text somewhere, but not a problem really. And I think unavoidable given the nature of tracers.
Analysis involving spatially integrated quantities http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos_ion_vol_integ_277.pdf.
- This analysis, too, considers a given species only in the region where it dominates (but separately for H and He)
- Results are consistent with those obtained for Run 271 but now I've done it for the full time resolution (1 data point per frame).
Next steps
- Continue to extend Runs 277, 283 and 282 and also extend the existing analysis (but need to worry about energy conservation, mass leaving box, and available SUs)
- Energy terms vs time and check whether energy supplied by recombination leads to corresponding increase in thermal energy, as already done in comparison between old EOS run 271 and old ideal gas run 143.
- Explore overlapping ionization species regions to get a sense of how important they might be (< 10% difference?)
- Make progress on paper write-up and organize a meeting for all involved
- Calculate total angular momentum and check angular momentum conservation (a must I would say)
CEE
Computing
- Extension on Frontera — no news, write an email to Chris Hempel?
- Parallel HDF5 (currently only being used for post-processing)
- Bug has been identified and debugging ongoing (Jonathan)
Jet paper
- Waiting for the OK to submit
- Do another run? Or two? If so, what?
- WD (as Run J6) but with flat profile? 10 x higher Mdot? Accretion off for simplicity? — but WD is almost order of magnitude more expensive because of jet speed
- MS star with flat profile? 10 x higher Mdot as with Run J5? Accretion off for simplicity?
EOS paper
New analysis
- Did unbound mass calculation for production runs 277 (MESA EoS without radiation) and 282 (gamma 5/3 ideal gas)
- Results are generally consistent with the previous results from Run 271 (higher ambient density, lower resolution MESA EOS) and Run 143 (old gamma 5/3 ideal gas run from our other papers)
- However, the difference between MESA EOS and gamma 5/3 runs is a bit larger
- Also, unbinding remains flatter and goes up more at the end — this must be due to the 7 times decrease in ambient density
- Note that these are not the final graphs because they include ambient gas, but the overall conclusions are unlikely to change
- Did the energy conservation analysis for both runs — we are under ~2% percent change
- This is what their separation curves look like
Status of runs
The plan is to compare 3 runs (277,282,283) which are identical except for the EOS:
- Run 277: MESA EOS (completed up to frame 247 on Stampede2)
- Run 282: Ideal gas gamma=5/3 EOS (completed up to frame 250 on Stampede2)
- Run 283: MESA EOS with recombination energy removed from EOS tables (completed up to frame 109 on Frontera)
- Run 276: MESA EOS with maxlevel increased by 1 compared to Run 277 (for convergence study — completed up to frame 47 on Frontera)
- Run 28?: MESA EOS with maxlevel reduced by 1 compared to Run 277 (for convergence study — not yet started on Frontera)
Next steps
- Mass unbinding analysis of Runs 277 and 282, as above but now with star material only (i.e. excluding the ambient)
- Extend Runs 277 and 282 — but for how long?
- Energy conservation
- Available SUs
- What more will we learn?
- Outflow through boundaries
- Do we trust it as much after reductions in softening radius?
- Extend Run 283 (but needs Frontera extension)
- Ionization/recombination analysis as done with Run 271, now for Run 277
CE EOS Simulations
Computing
- Allocation on Frontera ends on Dec. 31 — update?
- Parallel HDF5 (currently only being used for post-processing)
- Bug has been identified and debugging ongoing (Jonathan)
Energy conservation
- Tested new poisson.f90 designed to explicitly conserve energy (though not yet including particles), as in Jiang+13.
- Used low resolution CE run with periodic boundary conditions (so that flux of energy through boundaries does not change total energy in domain)
- Found that energy conservation is worse than with the original poisson.f90, not better.
- This means that there is a bug in the new poisson.f90 (could it be something obvious?)
EOS Runs
- Computed volume integrated mass and released energy for Run 271, using Python, plotted, and made pdf file. Includes only 3 frames (frame 0, 100 and 200).
- See these notes.
Runs for the paper
The plan is to compare 3 runs which are identical except for the EOS:
- Run 277: MESA EOS (completed up to frame 170 and will go as far as energy conservation allows, maybe frame 300
- Run 282: Ideal gas gamma=5/3 EOS (completed up to frame 33 and will go up to frame ~300).
- Run 283: MESA EOS with recombination energy removed from EOS tables (not yet started, will go up to frame ~300)
We are also doing a high resolution run for a convergence study:
- Run 276: MESA EOS with maxlevel increased by 1 (completed up to frame 47 and will go up to at least frame 65)
Next steps
- Complete all runs and do basic analysis (separation vs time, energy conservation)
- Redo unbound mass vs time plots to include only envelope gas (exclude ambient) — can wait for runs 277 and 282
CE EOS
Computing
- Allocation on Frontera ends on Dec. 31
- Parallel HDF5 (currently only being used for post-processing)
- Bug has been identified and debugging ongoing (Jonathan)
EOS Runs
- Continued analysis of Run 271:
- New PLOT of energy terms that includes recombination energy
- Volume integrated mass and energy released for the products of the various ionic transitions, for 3 snapshots (t=0, 23 d and 46 d)
- Same, but divided into gas that is unbound and gas that is bound (at time t)
- This analysis so far only on IDL (plot to screen)
Next steps
- Do the above analysis (volume integrated mass and released energy for each species) but now for all simulation frames of Run 271, using Python
- Continue with production runs (Stampede2 and Frontera)
- Compute ambient unbound mass and subtract from total (as Amy has now done for jet runs)
CE (EOS)
Computing
- Allocation on Frontera ends on Dec. 31
- Need to ask for extension ASAP
- Could also request transfer SUs to Stampede2 if necessary
- https://portal.xsede.org/allocations/managing includes info from XSEDE about extension and transfer requests
- Parallel HDF5 (currently only being used for post-processing)
- Bug has been identified and debugging ongoing (Jonathan)
EOS Runs
- Slices comparing density of tracers for original ionization state with density of gas with a given ionization state at time t
- See these notes.
- Trying to improve energy conservation — Goal is to get simulation up to >100 days (c.f.~Ohlmann+16: 125 days; Prust+Chang19: 240 days)
- Do this by testing adding refinement in different ways:
- One extra AMR level
- Larger region for AMR level 4
- Larger region for max AMR level
- Do we work to implement the new algorithm that includes gas potential energy in the explicit energy conservation (though not particle-gas potential energy) or do we carry on with what we have?
- Do this by testing adding refinement in different ways:
- Energy conservation normalized to initial energy of star, not including recombination energy:
Figure
- So continuing to 100-150 days and staying <10% should be possible, particularly if we reduce softening radius 2-3 times…
- Currently running a test where the highest AMR level refinement region is enlarged…results very soon
Next steps
- Production runs on Frontera?
- Compute ambient unbound mass and subtract from total (as Amy has now done for jet runs)
- Compute total recombination energy of each species (e.g. HII, HeIII) as a function of time
- Compute total recombination energy of each species (e.g. HII, HeIII) as a function of time for bound and unbound mass separately
- This will tell us whether recombination energy is being released into bound gas (where it can be "useful") vs. unbound gas (where it cannot), c.f. Fig. 1 of Paper II
- Some version of Figs. 9 and 10 of Paper IV that includes recombination energy
CEE
Computing
- Allocation on Frontera ends on Dec. 31
- Need to ask for extension ASAP
- Could also request transfer SUs to Stampede2 if necessary
- https://portal.xsede.org/allocations/managing includes info from XSEDE about extension and transfer requests
- Storage
- We have already exceded our storage on Ranch but they have moved most of it to tape to free up space for us. So we have almost 200 TB available.
- Parallel HDF5
- Debugging with Jonathan and Baowei
EOS Runs
- Analyzed unbound mass comparing EOS Run 271 to old fiducial Run 143.
- See these notes.
- Ongoing Runs (Trying to optmize parameter values for final production run)
- Run 273: ambient density reduced from 6.7e-9 g/cm^{3} to 1e-9 g/cm^{3}
- Run 274: RGB core particle mass equals m(r_soft) of original profile (skipping iteration over particle mass)
Next steps
- Analyze energy conservation for runs 273 and 274
- Analyze peak density for runs 271, 273 and 274
- Compute ambient unbound mass and subtract from total (as Amy has now done for jet runs)
- Make 2D slices (to compare) of:
- Mass density of Ionization state tracer (tracing gas with a given ionization state at t=0)
- Mass density of Ionization state (actual ionization state at time t)
- Compute total recombination energy of each species (e.g. HII, HeIII) as a function of time
- Compute total recombination energy of each species (e.g. HII, HeIII) as a function of time for bound and unbound mass separately
- This will tell us whether recombination energy is being released into bound gas (where it can be "useful") vs. unbound gas (where it cannot), c.f. Fig. 1 of Paper II
- Some version of Figs. 9 and 10 of Paper IV that includes recombination energy
COMMON ENVELOPE SIMULATIONS
Jet paper
- https://www.overleaf.com/project/601963d151b22065e09417a9
- Meeting?
- Figures still need improvement (see my comments in the figure captions)
- A bit more analysis
- J8 (WD run)
- J2 (half companion mass run)
- normalized binding energy slices (blue-red) to get a sense of where extra unbinding is happening
EOS project
- Run 271 has now reached Frame 83 (almost 20 days)
APN8e Talk
- Given the time constraint (12 minutes + 3 minutes for questions) I have decided to talk only about the jet paper
COMMON ENVELOPE SIMULATIONS
New EOS runs
- Similar to fiducial RGB run from Papers 1-4.
- Same r_soft=2.4 Rsun
- Same ambient density and pressure
- 1 extra level of AMR around particles to improve energy conservation
- A bit more automation to refinement part of code
- Uses more recent version of AstroBEAR
- If energy is well conserved can evolve up until separation = 2 r_soft=4.8 Rsun (do not expect full unbinding by then)
- This is less ambitious compared to first two attempts which used factor of 6.7 lower density ambient, 4x smaller softening length, and either 3 or 2 extra levels of AMR around particles compared to fiducial run from Papers 1-4 (but these runs kept hanging, apparently due to insufficient memory).
Description | Run ID | Paper | Primary | Secondary | Status | Last complete frame | Remaining cost | Hanging? | Resolution | Ambient density | Comments |
---|---|---|---|---|---|---|---|---|---|---|---|
MESA EOS | 271 | EOS | RGB | 1 Msun | In progress | 23 | ~25% of remaining SUs? | Not so far | 4 AMR (envelope), 5 AMR (near particles) | 6.7e-9 g/cc | As fiducial RGB Run 143 but with extra AMR level, tracers for core/envelope/ambient and for initial ionization, and some minor code improvements including a bit more automation |
MESA EOS without recombination energy | ? | EOS | RGB | 1 Msun | Not yet submitted | -1 | ~25% of remaining SUs? | N/A | 4 AMR (envelope), 5 AMR (near particles) | 6.7e-9 g/cc | Same as Run 271 |
MESA EOS without hydrogen recombination energy (but including helium recombination energy) | ? | EOS | RGB | 1 Msun | Not yet submitted | -1 | ~25% of remaining SUs? | N/A | 4 AMR (envelope), 5 AMR (near particles) | 6.7e-9 g/cc | Same as Run 271 |
Ideal gas EOS (gamma=5/3) | ? | EOS | RGB | 1 Msun | Not yet submitted | -1 | ~25% of remaining SUs? | N/A | 4 AMR (envelope), 5 AMR (near particles) | 6.7e-9 g/cc | Same as Run 271 |
CE
Allocation usage
- Already used almost 2/3 of present allocation (expires 6/30/2022)
- Of that which was used, 2/3 was used for jet runs and 1/3 was used for other runs
Projects and Simulations
Paper | Runs | Run IDs | Progress | Last complete frame | Remaining cost | Hanging? | Resolution | Ambient density | Comments |
---|---|---|---|---|---|---|---|---|---|
CE jet | See paper on Overleaf | 10 runs (9 main sequence + 1 white dwarf companion) | Completed | 173 | 0 | No | 4 AMR | 6.7e-9 g/cc | Run by Amy |
EOS | AGB: As C+20 but with (1)MESA EOS; (2)MESA EOS without recombination energy; (3)MESA EOS without hydrogen recombination energy (but including helium recombination energy) | 270/ ? / ? | In progress/ Not yet started/ Not yet started | 72 / -1 / -1 | ~80% of remaining SUs | Sometimes, but after running for ~36 hours | 3 AMR (envelope), 5 AMR (near particles) | 1e-9 g/cc | I'm also retrying the original RGB EOS run which has higher resolution (4 AMR for envelope, but now 7 AMR near particles), smaller softening length (0.6 Rsun instead of 2.4 Rsun), lower ambient (1e-9 g/cc instead of 6.7e-9 g/cc), tracers for core/envelope/ambient and for initial ionization, and some minor code improvements including a bit more automation |
WD planets paper II | RGB or AGB +low mass companion | 151(RGB+0.25 Msun companion)/ 259(AGB+0.01 Msun companion)/ 268(AGB+0.08 Msun companion, ideal gas EOS)/ 269(AGB+0.08 Msun companion, MESA EOS) | Completed / Completed / Paused / In progress | 173 / 1366 / 264 / 271 | ~20% of remaining SUs — will keep running 269 but 268 was hanging so I will keep it on pause for now | Sometimes | 4 AMR for RGB run 151 / 3 AMR (envelope), 5 AMR (near particles) for AGB runs | 6.7e-9 g/cc for RGB run / 1e-9 g/cc for AGB runs | To get a sense of how much expansion is possible during plunge-in for a low-mass companion. See also recent work by Kramer+2020 |
Drag force paper II | AGB: As C+20 but now companion has same mass as primary core particle (0.53 Msun, instead of 1 Msun) | 263 | Completed | 1291 | 0 | Happened 1 time | 3 AMR (envelope), 5 AMR (near particles) | 1e-9 g/cc | With particles of equal mass, we can use/test the phenomenological model of Escala+2004 which was applied to inspiraling super-massive black holes of equal mass, because with equal particle masses there will be extra symmetry at late times, which simplifies the problem and could therefore lend itself better to physical interpretation…remember our goal is to understand and model the drag force at late times, something we left for future work in C+19b |
Neutron star CE Jet | Similar to 10xEddington jet run, but with ~1.6 times higher Mdot and ~35 times higher jet speed | ? | Cannot make it to frame 1 (times out on stampede at frame 0.7 or 0.8) | 0 | ~estimated 35 times as expensive as typical jet run and ~3.5 times as expensive as WD jet run | Not so far | 4 AMR | 6.7e-9 g/cc | Set up and attempted by Amy. Runs but just takes long (lots of resources). Would be high impact research. Would likely not be quenched. Nothing comparable in the literature. |
Questions
- Use of Frontera?
- NS jet run
- Jet speed 0.1c — could it be smaller — or should it be larger (simulation time is roughly proportional to jet speed)?
- Shorten frame time? But even then we lack SUs on Stampede
- Is present fixed Mdot_Jet with Krumholz accretion good enough — or should we cap accretion rate at 10Mdot_jet? — or should we set Mdot_jet to equal 0.1 Mdot_acc?
COMMON ENVELOPE SIMULATIONS
Insights from CEPO2021 conference
- Noteworthy viewpoints?
- Convection is too slow to be important (Fritz Roepke)
- Triples are extremely important (Silvia Toonen)
- The collimation mechanism for PNe does not work (Noam Soker)
- The mechanism we proposed for explaining WD planets does not work (Noam Soker)
- Accretion rates and jet feedback efficiencies are too low to matter (Hagai Perets)
- Opportunities?
- Accretion and jets — super-Eddington, hyper-Eddington, neutron stars
- Triples
- Eccentricity
- Mergers
- "Double CE"
- GW waves, especially during mergers
- Zoom sims to study accretion (long way off but we have good tools)
- MHD (do we get the jets seen by the AREPO group?)
Papers in progress
- Jet paper (will be ready soon, plan to submit by Month's end)
- WD planets paper II (plan to submit by year's end)
- EOS paper
- Recall that I moved from RGB to AGB since could not get RGB to work at "modern" resolution and ambient density (code HANGS)
- AGB run is going on "okay" but also sometimes HANGS — this is the test run
- I must redo the EOS analysis of MESA profile using the AGB star (not that hard)
- Plan to make the improvements to the code that were there in the old EOS RGB run that was hanging
- automatic refinement shape modification (depending on inter-particle separation)
- tracers
- ambient/star/core region
- HI/HII/HeII/HeIII
- Then plan to perform 4 runs
- MESA EoS without radiation — must verify that radiation is unimportant for AGB star
- MESA EoS without recombination energy or radiation
- MESA EoS without hydrogen recombination energy or radiation
- Ideal gas gamma=5/3 (or use old run if we have to)
- Force paper II (future)
- understanding the drag force at late times
- equal particle mass simulation (Run 263, now completed) and Escala+04 model…
Simulation work
Completed
- Run 259: AGB run with 10 M_Jupiter companion (ran up to frame 1366 and completed analysis — may use it for WD planets paper)
- Run 263: AGB run with 0.53 Msun companion, equal to mass of core particle (ran up to frame 1291 and completed analysis — for future force paper)
Paused
- Run 268: AGB ideal gas run with 0.08 Msun companion (reached frame 265 and hangs; I have paused it for now — for use in WD planets paper)
In progress
- Run 269: AGB MESA EOS run with 0.08 Msun companion (reached 245 and I'm still running it, but about half as fast as 268 — for use in WD planets paper)
- Run 270: AGB MESA EOS run (reached frame 36 out of ~1137, hangs but maybe problem is just a one-off)
COMMON ENVELOPE SIMULATIONS
Tentative plan for new CE runs
All runs will use AGB setup from C+2020
Run | EOS | Run ID | Progress | Remaining cost | Potential impact | Comments | Relevant papers |
---|---|---|---|---|---|---|---|
equal mass particles | gamma=5/3 | 263 | ran up to 170 d | low | medium | To explain drag force | Escala+2004 |
~0.08 Msun companion | gamma=5/3 | N/A | N/A | medium-high | medium | How much expansion? | Kramer+2020, Observations by Xu+2021 submitted |
EOS+CE | MESA | N/A | N/A | medium-high | high | Compare with C+2020 gamma=5/3 run | Sand+2020 |
EOS+CE no rec energy | Modified MESA | N/A | N/A | medium-high | high | See Xsede proposal |
COMMON ENVELOPE SIMULATIONS
Evolved binary runs planned/ongoing
Actively running now = bold
Run | Run ID | Progress | Remaining cost | Potential impact | Energy conservation |
---|---|---|---|---|---|
EOS+CE (RGB) | 248,252,253 | runs but hangs | medium | high | |
RLOF+CE (RGB) | 195 | ran up to 47 d | medium | medium | not yet checked |
RLOF+CE (AGB) | 264,265,266 | runs but hangs | high | medium | |
CE equal mass particles (AGB) | 263 | ran up to 170 d | low | medium | not yet checked |
CE low mass companion (AGB) | 259 | ran up to 250 d | none | high | 4% increase |
CE (AGB), 4x higher resolution | 267 | ran up to 0.7 d | high | high | not yet checked |
Wind+accretion with low mass companion | N/A | not started | low? | medium | Z.Chen+2017 setup |
Runs
- Continued running Run 263 (equal particle mass AGB run). Now up to 170 days.
- Next step is to plot separation and energy conservation, before resuming run
- Goal is to explain the drag force at late times. Steps are
- test the Escala+2004 model using this run (263), and then
- try to generalize it to the unequal particle mass case, and compare with published AGB run (183)
- Started Run 267. Like published run (183) but max resolution is 4x higher.
- It ran up to 0.7 days (3.0 frames) in 48 hours on 64 skx nodes; each chombo is 212 GB
- Next step is to plot a(t), density slices, and energy conservation.
- How does energy conservation compare to Run 183? If much better, then perhaps worth continuing.
- Goal would be to run for 3 times as long as Run 183 (also serves as a convergence study).
Analytical model for WD 1856+534 system
- First key new idea is that planet 1 was actually a brown dwarf (maybe 50 M_J, i.e. about 0.05 Msun).
- Not massive enough to eject the envelope during inspiral
- But massive enough to expand the star, which engulfs planet 2 (this could happen at this stage or possibly later on)
- BD tidally disrupts and forms disk, which accretes and also spreads radially.
- Planet 2 inspirals and encounters disk.
- Accretion of disk material gradually releases potential energy, eventually resulting in envelope ejection.
- Second new idea is that planet 2 enters the disk left over from the tidal disruption of planet 1 and migrates, coming to rest near its present position. In this version of the model, there would be no need for planet 2 to eject any of the envelope (its ejection of <~1 % had always seemed like fine-tuning to me)
- Is the disk spreading fast enough to spread out to the current separation of planet 2 (4 au) from disruption separation of planet 1 (~0.4 au)?
- What governs the migration?
- Is it type II migration (gap formation)?
- Is the disk dense enough to pull the planet with it as it spreads viscously?
- Does the planet still experience drag with the envelope while it is embedded within the disk?
- Is the drag from dynamical friction or is it hydrodynamic, or are both important?
- Assuming inward migration owing to drag balances outward migration owing to disc spreading, at what orbital separation does the planet come to rest?
- Does it agree with the observed separation?
- Or can we used the observed separation to constrain its mass?
Planetary winds
- Chatted with Eric about his analytic model
- Had the idea that turbulence in the wake behind planet might produce random motions with velocity ~v_orb~150 km/s
- However, ambient stellar wind material is ionized so turbulence needs to be in neutral planet wind gas
- Turbulence would be driven by K-H instability.
- Using equation 2 of Hillier et al. 2020, I estimate that mixing leads to rms turbulent velocities of ~30 km/s, assuming a density contrast of 100 between planetary wind material and ambient stellar wind material. So unlikely to work.
- One difficulty with the magnetic field model is that the radial field is too small near the orbital plane if one assumes a dipole geometry.
- However, it seems like beyond about 2 solar radii, the sun's field is almost radial (and curves into a Parker spiral further out) - see Fig. 1 of Owens+Forsyth 2013.
- According to that last paper, the transition to radial occurs at the source surface, at a few solar radii. The planet is at 0.047 au ~= 10 Rsun, so a radial field is probably a reasonable (though somewhat optimistic) assumption.
- See also this paper Eric sent which could be used to estimate the field strength in the stellar wind at the planet: Wang+Sheeley 2002.
Upcoming meetings
- CE meeting Tues July 20 to discuss runs
- WD planet meeting Tues July 27
Job interview
- July 28 (requires quite a bit of prep)
Vacation
- July 30- back on Aug 9
COMMON ENVELOPE SIMULATIONS
Work in progress
- CE with low-mass companions
- More work to constrain the origin of the WD 1856+534 system
- We are now using MESA models to constrain our model
- For a given WD mass, what scenario is possible?
- Mass of companion — planet, brown dwarf, or low-mass M-dwarf?
- How common would BDs and low-mass M-dwarfs be? Soszy\'{n}ski+2021
- Simulations that could help to understand this:
- How common would BDs and low-mass M-dwarfs be? Soszy\'{n}ski+2021
- Did WD 1856+534 b play a role in ejecting the envelope or was it passive?
- Did WD 1856+534 b get engulfed during the plunge-in of planet 1 or after the tidal disruption of planet 1?
- Mass of companion — planet, brown dwarf, or low-mass M-dwarf?
- More work to constrain the origin of the WD 1856+534 system
Evolved binary runs planned/ongoing
Run | Run ID | Progress | Remaining cost | Potential impact | Energy conservation |
---|---|---|---|---|---|
EOS+CE (RGB) | 248,252,253 | runs but hangs | medium | high | |
RLOF+CE (RGB) | 195 | ran up to 47 d | medium | medium | ? |
RLOF+CE (AGB) | 264,265,266 | runs but hangs | high | medium | |
CE equal mass particles (AGB) | 263 | ran up to 100 d | low | medium | ? |
CE low mass companion (AGB) | 259 | ran up to 250 d | none | high | 4% increase |
CE high resolution (AGB) | N/A | not started | high | high | N/A |
Wind+accretion with low mass companion | N/A | not started | low? | medium | Z.Chen+2017 setup |
COMMON ENVELOPE SIMULATIONS
- update on EoS CE simulations
- update on WD planet project
Here are some preliminary notes for white dwarf planet project.
COMMON ENVELOPE SIMULATIONS
EoS stuff
Estimate of resource use
- I'm getting roughly 1 frame per 6 hours on 32 nodes for the test run closest to what I'm planning.
- Let's assume that the average frame rate during the course of the whole simulation (as the separation reduces) is double that, so 1 frame every 3 hours or 96 node-hours per frame.
- Since the softening radius is small, we can go up to at least 300 frames. So we are talking 28,800 node-hours per run.
- We want to do at least 4 runs (not counting any single star run). That means 115,200 node-hours.
- That is 51% of our total stampede allocation.
- The code is almost ready and there is ample time to complete these runs before the allocation expires in April.
- We have so far used 27% (15% planets project, 6% jets, 6% eos test runs).
- This would leave only 22% for other things (radiative transfer, convection, Roche lobe overflow, planets)
- Since the proposal was for the CE project, I suggest we put a hard cap on non-CE related projects at 20% of the allocation.
- If we submit the supplement proposal and it is approved for a significant amount of resources, then obviously we re-evaluate.
Work done
- More investigation of core stability
- More investigation of surface stability
- Experimentation with refinement
- Various other small improvements to the code
- Tracers
- New EoS Notes (in progress)
- New EoS tables (Yisheng)
Results
- The core gains 2% during the first frame (0.23 d) but is remarkably stable over the next three frames (Run 221), fluctuating at a level of 0.2%. For comparison, the sound-crossing time of the core is ~0.01 days.
- This 2% gain is not caused by the EoS, because I performed a run (Run 229) which is the same as 221 but for the ideal gas EoS with gamma=5/3 and the same behaviour is seen.
- It is probably caused by a combination of the following:
- discretization effects
- limited resolution in MESA
- error when interpolating MESA profile into astrobear
- inability to fully resolve the very centre of the modified Lane-Emden solution, which causes a slight reduction in the peak pressure while hardly affecting the potential energy since the latter is dominated by the particle contribution (this effect goes in the right direction but can only account for a small part of the 2%)
- interpolation error at the softening radius where I matched the modified Lane-Emden solution with the MESA profile
- slight mismatch in dP/dr at the softening radius because we chose to match rho and drho/dr as the two conditions to fit the two parameters (as in Ohlmann 2017) (and the pressure is also forced to match as an integration constant)
- possibly something to do with producing frame 0 on bluehive and then restarting from this frame on stampede (I will avoid doing this in the next stampede run, but I doubt this explains it).
- discretization effects
- For both the core and the surface, I find that the minimum number of resolution elements per pressure scale height is EIGHT. To be precise it is somewhere between 5.1 and 8.2 but let's use 8 to be conservative.
- If ~4 is used at the core, the peak pressure rapidly loses its shape. I found that to resolve the core at 8.2 cells per scale height, the maxlevel 4 refinement region should start outside 9e10 cm (1.3 Rsun). Currently (e.g. Run 221) I am using 1e11 cm (1.4 Rsun) with 16 buffer zones, so more than adequate. This core region only accounts for about 3e6 cells, or about 1% of the total cells, which suggests there is no real need to skimp here. However, doubling it to 2e11 cm does slow down the code by about 25%. I will leave it at 1e11 cm and 16 buffer zones.
- If 5 is used at the surface instead of 8, this creates an artificial wave pulse traveling outward that leads to large pressure variations and catastrophically slows the code. This catastrophic slow-down is delayed by refining at a high level out to a larger radius in the ambient, but it is not clear whether this could avert the slow-down completely. Moreover, such a wave pulse is unphysical and affects the morphology at the surface. For Pamb=1.0e5 dyn/cm^{2}, (as used in the original RGB fiducial run, Run 143) we have 8 level 4 cells per pressure scale height at the surface. For recent trial runs with Pamb=1.2e4 dyn/cm^{2}, we have 5 level 4 cells per pressure scale height at the surface, which is inadequate. This result is independent of the EoS used, as the same problem happens when the gamma=5/3 ideal EoS is used.
- I managed to implement a new refinement scheme such that a shell covering the surface can be refined at a higher level than the rest of the envelope. In order to use Pamb=1.2e4 dyn/cm^{2} and fully resolve the surface (at least 8 cells per pressure scale height), I found that the shell needs to have a thickness of at least ~4 Rsun. If I use 5 Rsun, I find that the total number of maxlevel 5 cells in this shell is 4e8, which happens to be almost the same as the number of maxlevel 4 cells needed in the rest of the initial condition. I also experimented with gradient based refinement but could not get it to work very predictably or smoothly.
- I implemented tracers for
- core, star and ambient (3 tracers)
- Initial dominance of HI or HII and HeI, HeII or HeIII (5 tracers; testing still to be done). For example HII traces the gas which has an initial ratio HII/HI>1.
- I am working on some EoS notes that Yisheng will be using to create the remaining EoS tables (particularly the one that includes helium but not hydrogen recombination energy).
- Yisheng has completed the tables for the full MESA EoS with and without radiation energy.
Discussion
The numbers below correspond to those above.
- This problem is not all that serious and although it would be nice to improve it in the future, I think the stability is good enough to move forward.
- Better to resolve the surface even if it means settling for a higher ambient pressure. Therefore, I will go back to Pamb=1e5 dyn/cm^{2}, as in the fiducial run 143. However, I will reduce the ambient density from 6.6e-9 g/cc to 1e-9 g/cc. This will cause a slow-down, probably by a factor of ~1.5, but that should be manageable. Also, now that aT^{4} has been removed from the EoS, the higher ambient temperature that this causes will not lead to a high ambient energy density, which could have posed a problem.
- Another option is to refine at level 5 in a thin shell containing the surface which would allow us to run with Pamb~1e4 dyn/cm^{2}. The slow-down caused by the extra refinement would be compensated, to some extent, by the lower ambient temperature.
- However, there are limitations:
- The star becomes aspherical due to tidal forces, but the shell is spherical, so parts of the surface will become unresolved. This would happen during the plunge-in. Refining on pressure gradient would fix this in theory, but I couldn't get it to work very well in the tests I did. It tends to refine almost everything or nothing, and for some reason the tolerance needs to be set to ~0.8 instead of 8 to get the 8 cells per scale height desired, which I don't understand.
- The file sizes would be larger by a factor of ~2 since the number of cells would go up by that factor.
- The shell is never perfectly spherical or of precisely constant thickness, which might mean that it will need to be thicker than the 5 Rsun estimate, which would require even more resources.
- So I think it is best to keep things simple and refine the whole star at level 4 (out to 5e12 cm) as in past runs (with level 7 at the core) and settle for high pressure and temperature in the ambient medium.
- However, there are limitations:
- The tracers will be useful for distinguishing ambient gas from star gas, tracking the core gas to understand how stable the core is, and for understanding how the ionization ratios of specific gas elements change with time.
- The notes will be ready soon.
- The new tables (table 3 with no recombination or radiation energy and table 4 with no hydrogen recombination energy or radiation energy) will be ready soon.
Next steps
- Test tracers
- Implement new tables, having slurm script specify which EoS tables directory to use, and properly recording this info during the run.
- Start runs 0 (gamma=5/3 ideal gas) and 1 (MESA EoS)
- Finish EoS notes
- Once I am happy with how those runs are going, I will work on doing a single star run to explore convection
- Rename module to "CE" and upload to github?
- Start writing the paper
COMMON ENVELOPE SIMULATIONS
EoS stuff
Work done
- Explored effect on recombination energy of including temperature dependence of partition function.
- Made pdf with all the initial profile plots, for easy reference in the future.
- Went back and did a bit more reading on the EoS, particularly the OPAL EoS which is used everywhere in the initial RGB profile Rogers+ 1996, Rogers+Nayfonov 2002.
- Some reading, including this preprint, which is relevant for our EoS CE project: Hirai+ 2020.
- Figured out that we were missing the recombination energy from recombination of two hydrogen atoms to produce a hydrogen molecule, which is included in the MESA EoS and discussed in Hirai+ 2020. So included that contribution in the plots.
Results
- The temperature dependence of the partition function cannot explain the decrement in the internal energy near the surface (see last blog post). Therefore it must be caused by other physics included in the EoS but not captured by the contributions included (thermal+thermal radiation+recombination) or, another possibility is that the Saha equation does not accurately predict the recombination energy near the surface, perhaps because local thermodynamic equilibrium cannot be assumed. In any case, the profile gets modified near the surface (r >~ 45 Rsun up to the outer radius of 48.1 Rsun) because of the matching onto the ambient, so we are not too concerned about this region. However, during the simulation there will also be regions where it doesn't quite work…is this a problem for what we want to do?—update: I now realize that the decrement is caused by the neglect of the latent recombination energy due to recombination of H atoms into molecular H2! See the last item of Results and discussion below…
- Here is the pdf with all the various profile plots for easy reference: eos_figs.pdf.
- The Hirai paper mentioned above also has the same idea as me of including the recombination energy of H or not, of He or not, etc. in the simulation…but they do not use a tabular EoS. Rather, they use an analytic solution to approximate the tabular EoS.
- Although the number density of H2 molecules is completely negligible, this component of the recombination energy H+H —> H2 is not negligible, and in fact dominates at temperatures below 10^{4} K (see Fig 17 in the above pdf). When we include all the contributions, excluding recombination energy of metals, the results for the internal energy density agree to within 0.6% everywhere. If we include recombination energy of metals as well, we do a bit worse, especially at radius below 12 Rsun, where the percent difference becomes as high as 1.4% (over predicts the internal energy by up to 1.4%).
Discussion
- We have confirmed that by adding the thermal energy contributions of gas and of radiation and the recombination energy from hydrogen and helium, one gets back the MESA internal energy profile (the discrepancy is on the order of half a percent at most).
- We can now say that it is reasonable to estimate the recombination energy contribution using the sum of hydrogen and helium recombination energies computed from the Saha equation.
- We need not worry about the temperature dependence of the partition functions, as ignoring it produces results in good agreement with MESA.
- Recombination energy of metals can safely be neglected, it seems, but recombination energy of H+H —> H2 cannot be neglected, though it was not considered in Reichardt+ 2020.
- As mentioned in the last blog post, one can see from the above pdf that the latest version of MESA (12778) gives results that are completely consistent with the version used (8845) (the slight differences apparently come from the small mismatch in the times of the snapshots). One could run the simulation with higher time resolution and better match the snapshot, and then use the snapshot from the latest version of MESA. Or it could be simply mentioned that the results are completely consistent and just use the original MESA 8845 RGB profile for consistency with earlier papers. It does not make a difference so might as well do the latter.
- I also ran into a problem when doing test runs, which is that one cannot add much refinment around the secondary at t=0 because by doing this one asks for more resolution than contained in the initial profile. It is easy to increase the resolution in the ambient, but the extra refinement region (i.e. particle buffer) around the secondary could overlap the envelope if the separation between the secondary and RGB radius is smaller than the particle buffer size. To increase the resolution in the envelope profile, one needs to rerun MESA at higher spatial resolution. Since we know from the AGB paper (see Fig B1) that the orbital evolution is insensitive to the resolution around the secondary before the first periastron passage, it is unnecessary to refine around the secondary at a high level right from t=0. So I did not bother rerunning MESA to get higher spatial resolution in the profile. However, if we, for example, want to add even one level of AMR in the outer envelope from t=0 in the future, we would need to rerun MESA with higher spatial resolution and reproduce the initial condition. Something to keep in mind.
Next steps
- Reproduce EoS tables using mean atomic weight of metals as 17.35 instead of 18 (differences will be minor but might as well).
- Migrate new code to Stampede and test (produce 1 frame for run 207 and make sure it agrees with bluehive result).
- Prepare the new fiducial run with gamma=5/3 EoS (increased resolution, etc.) and perform test runs (This was named Run R1 in the Plan for EoS project presentation).
- Prepare new EoS run where recombination energy is completely thermalized (Run R2) and perform test runs.
- Prepare new EoS run where recombination energy is completely radiated away (Run R3—this will involve a bit of coding in astrobear—how to proceed?) and perform test runs.
COMMON ENVELOPE SIMULATIONS
EoS stuff
Work done
- More plots and analysis of MESA RGB
- Downloaded and installed latest version of MESA (12778 instead of 8845). Ran "same" MESA simulation with this version and compared to old sim.
Results
- Initial conditions
- RGB energy profiles.
- mass fractions (direct MESA output).
- number densities of ions, neutrals and electrons. Oxygen shown as an example but can also plot C, N, Ne, Mg.
- neutral fractions (direct MESA output).
- mean atomic weight.
Discussion
- Gas thermal energy + recombination energy (+Prad which is negligible) almost equals to internal energy but a small decrement that grows with radius, becoming sizable right near surface.
- Went to trouble of including metals but rather negligible!
- Used Saha equation with T—>0 partition functions, which are just the degeneracies of states (so positive integers). In reality the partition functions can be much larger at the temperatures found in the star >~10^{4} K. And their ratios, which is what is important for the Saha equation, can change appreciably. One can estimate these from atomic databases (NIST, ViZieR) but numbers can also depend on electron pressure…complicated. What effect would this have on the recombination energy?
- Found that the average atomic mass of metals is 17.35. This is an input into Yisheng's code that produces the tabuler EoS because it is a parameter for the ideal EoS part of the table. He used 18 and anyway, the ideal EoS part of the table is rarely utilized.
- Found that new MESA version 12778 gives very similar results. Should we go with new MESA RGB model or stick with the old one?
Next steps
Initial conditions
- Estimate recombination energy using partition functions from NIST and/or ViZier databases and see what difference this makes.
- Learn more about the EoS to understand what other physics contributes near the surface (optically thin region).
- Put all the MESA profile figures in a pdf, with figure captions, for reference (to be used throughout the EoS CE project).
- Write a short section on EoS for the paper while it's all fresh, with help from Yisheng and Jonathan.
Simulation
- Reproduce tables using mean atomic weight of metals as 17.35 instead of 18 (differences will be minor but might as well).
- Steps mentioned in last blog post.
Idea for paper
- I had the idea of subtracting out the recombination energy (physically it is escaping by radiating away) and seeing what effect this has. Results will be at least somewhat different from ideal gamma=5/3 EoS. But it would also be interesting to do a run where we subtract ONLY the H recombination energy, say, to see what happens if recombination energy of hydrogen leaks out, but that of helium (and metals) is retained, to constrain the importance of H rec energy vs He rec energy.
COMMON ENVELOPE SIMULATIONS
EoS stuff
Work done
- Plotted pressure and temperature profiles from frame 0 of simulation and compared with previous results.
- Plotted sound speed profile from frame 0 of simulation and compared with that of fiducial RGB Run 143.
- Plotted free electron fraction, gamma1 and mu profiles from frame 0 of simulation and compared with MESA profiles.
- Added gamma3 (MESA) to plot from last blog showing gamma1.
- Planning for Paper 5 on EoS.
Results
- Initial conditions
- The pressure profile from frame 0. Orange=Run 143 (fiducial ideal gas EoS), Green=Run 207 (MESA EoS). Profiles match perfectly, as expected (pressure profile was inputted in a data file).
- The sound speed profile from frame 0. Red=Run 143 (fiducial ideal gas EoS), Black=Run 207 (MESA EoS). Profiles are slightly different. Consistent with P and rho profiles being the same between simulations, but gamma1 differing. Since c_s propto gamma1^{½} and gamma1 reduces by no less than a factor of about 4/5, we get no less than a factor of about 0.9 in c_s. So the difference in c_s profiles is very small.
- RGB Pressure profile from MESA. As shown in the last blog but now with the new curve showing the simulation initial condition.
- RGB Temperature profile from MESA. As shown in the last blog but now with the new curve showing the simulation initial condition.
- RGB Various profiles from MESA. As shown in the last blog but now with new curves for electron fraction, mean molecular mass mu and gamma1=(dlnP/dlnrho)_S showing the simulation initial condition.
- Yisheng's plot of initial profile (temperature) in cgs units.
- Yisheng's plot of initial profile (specific internal energy) in cgs units.
- Derivation of expression for mu in terms of X, Z, average number of nucleons per metal species A, and electron fraction
- Plan for EoS project, presentation given during meeting
Discussion
- mu was computed using an analytic formula which assumes a mean atomic mass for metal species of 16 (the result is not sensitive to this number).
- It is not possible to compute the recombination energy (total or from each species individually)
- Since the hydrogen, helium and metals fractions are CONSTANT in the envelope (and are assumed to be constant for the duration of the simulation), then to compute mu we would need the ionization fraction of each species, e.g. n_HII/n_HI, n_HeII/n_HeI, n_HeIII/n_HeII, and the same for all the metal species included in the EoS.
- These ionization fractions can be estimated using the Saha equation but this would not take fully into account the EoS. This was the method used by Reichardt+2020 to compute the recombination energy—but they neglected ionization and recombination of metals.
- Can the ionization fractions for each species as well as mu be obtained directly as part of the MESA EoS? If not, we need to use the Saha equation.
Next steps
- Use Saha equation to estimate the ionization fractions and recombination energy and make some plots.
- Migrate new code to Stampede and test (produce 1 frame for each run).
- Prepare the new fiducial run (increased resolution, etc.) and new EoS run (Runs R1 and R2 in the Plan for EoS project presentation above), and perform test runs.
COMMON ENVELOPE SIMULATIONS
Putting in the MESA equation of state
Work done
- Examined MESA RGB model (used as initial condition in our simulation) in more detail, including
- Temperature profile
- Free electron fraction profile
- Mean molecular weight profile
- Condition for convective instability as a function of radius
- Convective time scale as a function of radius
Results
- Initial conditions
- RGB Pressure profile from MESA showing total pressure, gas pressure and radiation pressure. We see that gas pressure dominates outside the softening sphere.
- RGB Temperature profile from MESA. We see that outside the softening sphere the temperature is predicted accurately by assuming the gas to be ideal. Also, the temperature is higher than that obtained by assuming pure fully ionized hydrogen (mu=m_H/2), and lower than that obtained assuming pure fully neutral hydrogen (mu=m_H), except within 1 Rsun from the surface, where it is higher than both. The ionization temperatures of H and He are also plotted for reference.
- Graph showing gamma1 (adiabatic index) free electron fraction and mean molecular mass profiles from MESA. We see that gamma1 remains below 5/3 and dips below 4/3 near the surface. This behaviour is roughly predicted by an analytic model contained in these notes by G. Glatzmaier that assumes pure hydrogen, using the free electron fraction profile from the MESA simulation, shown in black in the plot. We also see that gamma1=(dlnP/dlnrho)_S is quite similar to the polytropic Gamma1=dlnP/dlnrho calculated for the stellar profile, which tells us that the envelope is probably convective. The electron fraction is fairly constant but dips after about r=30Rsun, which coincides with where mu increases. Finally we plot Del=dlnT/dlnP and the critical value of Del=dlnT/dlnP for (i) an ideal gas with gamma1=5/3, which gives (gamma1-1)/gamma1=2/5, (ii) the MESA simulation neglecting the compositional gradient (Schwarzchild criterion) and (iii) the MESA simulation including the compositional gradient (Ledoux criterion). The plots below zoom in on this region to show more clearly what is happening as per convective stability/instability.
- Graph showing condition for convective instability. This graph should be compared with Figure 6 (bottom left) from Ohlmann+2017. Our results are consistent with theirs as long as we use the Ledoux condition outputted from MESA directly. If we compute the compositional gradient dln mu/dln P from mu and P we get the red line instead of the blue line. I don't understand why, but anyhow, as we will see in the next graph, both lines are consistent in that they predict convective instability. The black dash-dotted curve would be the relevant curve for the fiducial RGB simulation with adiabatic EoS (gamma1=5/3). We see that for that simulation, the star is predicted to be convectively stable.
- Graph showing condition for convective instability, plotted in a way that more clearly shows whether profile is stable or unstable. We clearly see that for the Ledoux criterion (blue line), which is the relevant criterion in our case, we are convectively unstable everywhere outside the softening radius. Note that the red line should match the blue line, but doesn't for some reason (see above), but in any case the red line also predicts convective instability. So to summarize, we see that the profile is convectively stable if the adiabatic gamma1=5/3 EoS is assumed, but convectively unstable for the more realistic EoS, consistent with Ohlmann+2017.
- Graph showing convective speed from MESA model. We see that the typical convective speed is ~0.7 km/s, rising to ~1 km/s near the softening radius and steadily rising to ~4 km/s near the surface.
- Graph showing convective Mach number from MESA model. This can be compared with Figure 9a from Ohlmann+2017.
- Graph showing convective time scale computed from MESA. The convective time scale is computed either by taking H_P/v_conv where H_P is the pressure scale height, or H_P^{2}/eta_MLT where eta_MLT is the diffusion coefficient from mixing length theory, outputted by MESA, or L_MLT^{2}/eta_MLT where L_MLT is the mixing length outputted by MESA.
- AstroBEAR results
- I ran the simulation up to 2 frames on bluehive. It slowed down by about a factor of 3 compared to the first frame. The reason is probably that the code was struggling to resolve the large gradients near the particles. The density reduced markedly around the RGB core particle between frames 1 and 2, which does not happen in the fiducial run. The velocity with respect to the RGB core particle points outward. Could this be caused by convection? Or is it just that more resolution is needed at the RGB core when the MESA EoS is used? (Note that inside the softening radius, the profile is the reconstructed profile, not the original MESA profile.)
- The gas profile around the secondary is quite different from the fiducial run.
- Zoom-in on secondary, MESA EoS Run 207
- Zoom-in on secondary, fiducial Run 143 Although it would be worth adding more resolution around the secondary, the difference seen is probably physical and likely has to do with the smaller gamma1 near the surface in the MESA EoS model. A smaller gamma1 means that more compression is required to achieve a given pressure, so we might expect greater density in Run 207, which is what is seen.
Summary
- Pressure is dominated by gas pressure.
- Temperature is as expected for an ideal gas.
- Adiabatic gamma = gamma1 = C_P/C_V (with C_P and C_V the specific heats at constant pressure and volume) = (dlnP/dlnrho)_S (at constant entropy), which is 5/3 for a monatomic ideal gas. Here we obtained gamma1 from MESA and find that it is close to the polytropic Gamma1 in the envelope (as expected for a convective envelope) except near the surface.
- We then used gamma1 along with the stellar profile, to compute Del-Del_Ledoux at each point, where Del=dlnT/dlnP and Del_Ledoux=(gamma1-1)/gamma1 +dln mu/dln P. We find the envelope to be convectively unstable outside the softening radius. For the adiabatic EoS with gamma1=5/3 as used in the fiducial model, we find that the envelope is stable to convection.
- Our results for convective instability for the adiabatic gamma1=5/3 model (stable) and also for the MESA tabular EoS model (unstable) agree with those presented in Ohlmann+2017 for their profile, which is very similar to ours.
- The convective time scale varies between a few days near the surface, to ~50-400 days in the bulk of the envelope, to ~10-50 days at the softening radius. Thus, we would expect the surface layers to be somewhat less stable than in the fiducial run during the dynamical plunge-in (about 12.5 days to the first periastron passage in the fiducial run). Futhermore, we would likely see more mixing inside of the particle orbit at late times in the simulation since the simulation time (40 days) is comparable to the convective time near the softening radius.
- More resolution is probably needed at the primary core.
COMMON ENVELOPE SIMULATIONS
Putting in the MESA equation of state
Work done
- Modified my own version of the code on bluehive to incorporate changes made by Yisheng and Jonathan
- Substituted Yisheng's /scratch/afrank_lab/EOS/astrobear/src/objects/tables.f90, src/physics/EOS.f90, src/physics/abundances.f90, src/hyperbolic/riemann_solvers.f90 and src/module_control.f90 (the only change in the latter is to comment out the Jean's length refinement criterion), src/Makefile (only differences is that it changes the order of compilation of EOS.o and tables.o to avoid a compilation error).
- Other files kept my own: important differences include src/particle/particle_control.f90, where I comment out creation of new particles. Certain other files are different between our versions but I decided to keep my own: src/objects/ambients.f90 (not used by me anyway), src/particle/particle_info_ops.f90 (apparently recent changes were made to the Bondi-Hoyle-Lyttleton accretion rate algorithm, but this does not affect simulations where subgrid accretion is turned off), src/data/data_info_ops.f90 (new lines of code, not sure of significance), src/distribution/distribution_control.f90 (Intent OUT had been changed to INOUT for pointer newgrids—-not sure of significance), src/hyperbolic/sweep/sweep_declarations.f90 (small differences, not sure whether significant).
- Compiled and ran the version of the code which was basically the same as Run 143 (fiducial RGB run) but with iEOS=6 in physics.data (tabular EoS) on BlueHive (110 cores, one frame of 2e4 seconds—same as for fiducial Run 143 which lasted 173 frames—takes about 24 hours). This run is called Run 207.
- Analyzed the AstroBear initial condition from Run 207 to see if it agrees with expectations.
Results
- Initial conditions
- The density profile from frame 0 of Run 207 is the same as what was inputted, as expected. Red=Run 143 (fiducial ideal gas EoS), Purple=Run 207 (MESA EoS).
- The internal energy density profile from frame 0 of Run 207 is different from that of Run 143, as expected.
- The internal energy density profile from frame 0 of Run 207 matches very well the internal energy profile directly obtained from MESA. See figure. Thus, the code passes this initial test!
- However, we see that there is an inversion of the internal energy density at large radius. This happens in the region where the pressure is almost constant (~1e5 dyne/cm2) and the density had decreased to quite low values (~7e-9 g/cc). Yisheng plotted the profile of specific internal energy (i.e. E_int per unit mass) in the rho-P plane, and found that the specific internal energy turns up at small density, which is consistent with what we are getting. See figure1 and figure2. We are not sure what causes this in the EoS, but it is not necessarily a problem. One could in principle get rid of it by using a lower ambient pressure (but this would require increasing the resolution near the stellar surface).
- mass fractions. The ratios of number densities of He and H and of metals and H are specified in physics.data. These are used to calculate the mass fractions X and Z and then the MESA EoS table with this X and Z are selected. I went over this calculation to make sure that everything is consistent. But what about ionization??
- free electron number and mean molecular weight per gas particle (ions + free electrons).
- Simulation results
- Density profile for new run at frame 1 (0.23 d): whole star with mesh and zoom-in on secondary and zoom-in on primary core.
- Same thing but for fiducial RGB run 143: whole star with mesh and zoom-in on secondary and zoom-in on primary core.
Next steps
- Modify mu for ideal EoS since current choice of 2.21 seems too high. But we are mostly not in the ideal gas regime, so should not matter much if at all. Need to redo tables to reflect this change. Keep gamma=5/3 for ideal gas.
- Plot radiation pressure and gas pressure to get sense of contribution of radiation pressure (it will be small, but worth plotting).
- Better understand what is causing the difference between initial E_int profiles in MESA EoS and ideal gas EoS (latent recombination energy? radiation?)
- Get thermodynamic variables like pressure and temperature to be outputted in chombos and plot them; also compare with ideal gas case.
- Compute and output gamma
- Re-read Nandez+Ivanova, Ohlmann+2017, Reichardt+2020
- Putting recombination energy into our simulations
Plan
- What is the plan for this paper?
- Convection?
- Compare fiducial RGB run with MESA EoS RGB and recombination run?
- Improve fiducial RGB?
- Compare fiducial AGB run with MESA EoS AGB and recombination run?
- Which analysis to do?
- Unbinding
- Orbital evolution
- Energy transfer
- Do we try to compute opacities, optical depths, and diffusion times to assess whether recombination energy can be thermalized locally, or just assume that it can be?
CE meeting notes
Notes on EAS CE conference held July 2-3, 2020
- Morgan MacLeod's CE bibliography. He says you can email him to suggest more relevant papers.
- Worth checking out Paul Ricker's talk for his implementation of flux-limited radiative transfer: [recording https://portalapp.kuonicongress.eventsair.com/VirtualAttendeePortal/eas-annual-meeting-2020/virtual-eas/] but I'm unable to view it, possibly because I was a speaker during that session? Anyway, my notes say that his radiative transfer algorithm triggers on temperature gradient. He uses OPAL opacities. He says that a challenge of their simulations is that energy is trapped closer to the star than what may be realistic.
- During my talk there was a question by Friedrich Roepke about AM conservation. We should measure it for the next paper.
- Christian Sand's talk on CE with AGB star: gets 7.4 to 9.4 years ejection if recombination energy is included. Does not get enough unbinding with ideal gas EOS but not clear whether extra unbinding is caused by recombination or the difference in the initial profile between ideal gas EoS case and the OPAL EoS case (I think they use OPAL rather than the full MESA EoS). They think it's the recombination rather than the initial profile that makes the difference but have not done a test to confirm this. Both Paul Ricker and I were wondering about this.
- David Jones: mass transfer could happen before, during or after CE phase. Since main sequence companions are almost always observed to be inflated (by up to 3 times), sometimes mass transfer may get reinitiated at the end of the CE phase (speculative). But worth thinking about. Would RLOF occur at the end of the simulation if the companion gets puffed up? Or would the secondary get tidally shredded?
- Wouter Vlemmings: water fountain sources with high Mdot ~ 0.01 to 0.1 Msun/yr outflows, M_torus ~ 0.2-1.3 Msun. Estimate initial mass of system is ~ 1.4-2.4 Msun, so we are talking about low mass stars. I think it might be possible to explore these systems with CE simulations.
- M. Santander-Garcia: Their hypothesis was that post-CE PNe should be more massive compared to non-post-CE PNe. They find confirmation of this at what he feels is a somewhat marginal level (~0.24 Msun for post-CE and ~0.17 Msun for regular sample). What he says is that a more interesting result is obtained when the post-CE sample is separated into single degenerate and double degenerate. DD have larger mass ~0.63 Msun compared to SD ~0.15 Msun. Something to think about.
- In the discussion following Amy's talk Noam was arguing that there is not enough momentum in the regular AGB winds to explain the high momenta outflows observed in PPNe, so basically he was questioning the assumption of the model (echoed by another participant, Alcolea). He says therefore one needs a jet. Also appeals to the precession seen in some sources to argue for jets. Says that jets have been seen in post-AGB objects (refers to Van Winckel). Interestingly, Noam thinks that jets can emerge/break out before or after the CE phase, but are unable to do so during the CE phase.
- In the discussion it was also mentioned by Paul Ricker (echoed by Morgan MacLeod) that in the Heidelburg group sims that utilize recombination energy, they compute that the energy is used in regions where tau>1, but maybe the radiative diffusion time is still small enough that the energy escapes to the surface, so maybe it could not be used so easily. They didn't seem to have an answer for that.
- In the discussion, David Jones commented that post-CE PN CSs seem to be tidally locked, at least there is no evidence for asynchronous rotation. Again, perhaps something to think about.
- In the discussion, David Jones also mentioned that mass is still missing in PNe. It is not all contained in the equatorial disk, so where is the rest? Alocolea says velocity profile does not fit story that equatorial material is left over CE ejecta, and he sees the velocity turning around (I guess this would imply fallback).
- J. Jencson: SPRITES: rapid dust formation and dust obscures optical counterpart. I think this is another reason to have dust in our CE simulations.
- N. Blogorodnova: From her talk I wonder if the secondary peak/plateau in LRNe/ILOTs caused by a second unbinding phase+merger. This does not seem to be the popular idea people have. They found for M31LRN 2015 that temperature increases with time at late times and that the luminosity agrees with gravitational contraction at fixed temperature. Anyway, her talk is mainly about observations of that source, and may be worth watching.
COMMON ENVELOPE SIMULATIONS
Mass unbinding
Notes comparing unbinding using different criteria for "unbound"
Energy conservation and effective core profile in simulation
Notes on algorithm that conserves energy and effective core profile in simulation
Energy paper erratum
Draft of erratum for Paper II to correct unbound definition and initial PE profile figure
COMMON ENVELOPE SIMULATIONS
AGB paper
The current version of the AGB paper (with latest changes in red)
Some notes to illustrate the reason for the changes
RLOF and CE sims in general
Textbook chapter on the two-body problem showing that eccentricity can be computed from total energy and angular momentum
These notes can be found at https://tmg-web.lehman.edu/faculty/anchordoqui/chapter25.pdf
I got the idea from this preprint, which is of interest: Kuruwita, Federrath & Haugbolle 2020
Energy conservation in the code
Some notes (now wrong I realize because Eq. 1 is wrong!) which prompted me to correct the ½ factor — extending energy conservation routine to include particles should be trivial
Relevant paper (just putting it here for easy access)
COMMON ENVELOPE SIMULATIONS
Papers Relevant for dependence of initial separation on CE outcomes and transition from RLOF phase to CE phase)
Iaconi, Reichardt, Staff, De Marco, Passy, Price, Wurster & Herwig 2017
MacLeod, Ostriker & Stone 2018a
MacLeod, Ostriker & Stone 2018b
Reichardt, De Marco, Iaconi, Tout & Price 2019
MacLeod, Vick, Lai & Stone 2019
MacLeod & Loeb 2019
MacLeod & Loeb 2020
Goals
- Achieve a numerically stable simulation with separation equal to Roche Limit separation
- Calculated to be 108 Rsun for our fiducial RGB primary (radius 48.1 Rsun, M_1=2 Msun) and secondary (M_2=1 Msun).
- It would be fine to gradually increase the separation in successive runs, thus working our way out to 108 Rsun, if necessary.
- Low ambient density
- But ambient pressure needs to be high to cut off stellar pressure profile and thus avoid inability to resolve pressure scale height
- Hence usual problem is that by making density low, temperature gets high and timestep gets very small, making the simulation slow.
- Is there a way around this problem?
- One possibility is to just be patient!
- Another is to include a hydrostatic atmosphere (typically with some constant temperature—see MacLeod+18a, but they use a spherical mesh)
- This atmosphere cannot extend all the way to the mesh boundary because produces gradients at corners that crash the code (results from 3 years ago)
- Can try making the atmosphere transition to a uniform ambient medium at some radius (See Run 199, below)
- Rotation of the primary
- The Roche analysis is technically only valid for stars that are in corotation with the orbital angular velocity
- I have not yet tried to give the star an initial rotation (an important step in the near future)
- Part of the reason the primary star distorts in some of the simulations below may be physical and related to the results of MacLeod+19a
- Stable primary core
- We have seen with recent models (AGB run) that this can be achieved by putting higher resolution at the core
- Larger simulation domain
- the strategy I am using is to double the mesh size while reducing the base resolution by a factor of two (so 512^{3} would stay as 512^{3}), and increasing maxlevel by 1. (Alternatively, one could keep the base resolution the same (512^{3} becomes 1024^{3}) and keep maxlevel the same, which would result in ~8 times more base cells but one less AMR level.)
Comments
- Goal 1 is the main goal.
- Goal 2 is desirable but not essential in the short term.
- Goal 3 is also desirable but not essential in the short term, though it may make achieving goal 1 easier (see below).
- Goal 4 we know how to achieve at a high enough fidelity for the time being.
- Goal 5 is also desirable but not essential in the short term.
RLOF+CEE Simulations
- Continuation of old runs (only the last chombo of each had been kept!)
- Run 195: Separation of 1.5 times old separation, restarted from frame 50 of Run 161 with higher density thresholds for refinement and one extra refinement level for very high density—> completed up to frame 201
- Run 201: Roche-limit separation (=2.2 times old separation), restarted from frame 53 of Run 160 with higher density thresholds for refinement and one extra refinement level for very high density—> completed up to frame 251
- Run 202: Roche-limit separation (=2.2 times old separation) with low density ambient (67 times lower than fiducial), restarted from frame 27 of Run 162 with higher density thresholds for refinement and one extra refinement level for very high density—> completed up to frame 57
- New runs
- Run 199: Setup with smoothly matched hydrostatic atmosphere matching on to constant ambient at larger radius and density thresholds for refinement. >>Crashes ~immediately due to high pressure gradients just outside primary. Rerunning now with AstroBEAR default refinement. —> get insufficient memory error
- Run 196: Setup with low constant ambient, refined on density, eventually slows down a lot. Restarted from frame 29 with AstroBEAR default refinement. Runs fast but chombo sizes are HUGE since much more volume is refined. (First I tried qTolerance 0.2, then later changed to 0.4 to reduce file size. DesiredFillRatios set to 0.7.) Ran but then crashed on a restart when reading chombo (not sure why). Restart from frame 33 with qTolerance 0.2, ran up to frame 40. After that slurm and chombo output stopped, presumably because of insufficient memory. Chombo file sizes >130 GB and increasing. Get problem where no slurm output or chombos produced (in the past this problem was found to be caused by insufficient memory).
Run 195
Movies of gas density slices
- Face-on, simulation coordinates, frames 0-40 (old movie of Run 161 from ~two years ago))
- Face-on, simulation coordinates, frames 50-201
- Face-on, simulation coordinates, frames 50-201, zoomed in
Snapshots of Pressure and Temperature
- Pressure frame 50
- Temperature frame 50
- Pressure frame 70
- Temperature frame 70
- Pressure frame 90
- Temperature frame 90
- Pressure frame 140
- Temperature frame 140
- Pressure frame 201
- Temperature frame 201
Snapshots showing mesh
- mesh frame 50 -- for frames 0-50 used more conservative density-based refinement
- mesh frame 51 -- for frames 51-201 used less conservative density-based refinement with additional AMR level for extra resolution near particles
- mesh frame 77
- mesh frame 50, zoomed in
- mesh frame 51, zoomed in
- mesh frame 77, zoomed in
Separation vs time
Run 201
Movies of gas density slices
- Face-on, simulation coordinates, frames 0-251 (frames 0-53 are from ~2 years ago and frames 54-251 are new)
- Face-on, simulation coordinates, frames 53-170, now showing mesh
Snapshots with and without mesh
- Frame 53 with mesh
- Frame 53 without mesh
- Frame 53 pressure
- Frame 53 temperature
- Frame 54 pressure
- Frame 54 temperature
- Frame 116 pressure
- Frame 116 temperature
Run 202
Movies of gas density slices
Snapshots
- Frame 27 Density
- Frame 27 Density extended colorbar
- Frame 27 Pressure
- Frame 27 Temperature
- Frame 27 Temperature with mesh
- Frame 28 Density
- Frame 28 Density extended colorbar
- Frame 28 Pressure
- Frame 28 Temperature
- Frame 28 Temperature with mesh
- Frame 57 Density
- Frame 57 Density extended colorbar
- Frame 57 Pressure
- Frame 57 Temperature
- Frame 57 Temperature with mesh
Run 196
Snapshots
- temperature frame 25
- temperature frame 25, with mesh
- density frame 29
- density frame 29, with mesh
- temperature frame 29
- temperature frame 29, zoomed colorbar
- density frame 40
- density frame 40, with mesh
- pressure frame 40
- temperature frame 40
- temperature frame 40, with mesh
Comparing setup to that of Run 195
- Recall differences in setup from Run 195:
- twice bigger simulation box than Run 195 (and base resolution coarser by factor of two)
- extra AMR level not present in Run 195 for refinement around particles
- start out with higher density threshold for bulk of envelope so not as much of ambient is refined compared to Run 195, but after frame 29 more of ambient is refined than before frame 29 (switched from density threshold to default gradients-based refinement)
- ambient density is 6.7 times lower than for Run 195 (and 6.7 times lower than at the stellar surface)
Results and Interpretation
- Less stable at stellar surface than Run 195.
- Is this partly caused by density jump between surface and ambient medium?
- But surface is also less stable than Run 202, where ambient density was 10 times lower still, so this is probably not the reason.
- Is it related to refining less of the ambient at the beginning of the simulation than for Run 195?
- From the snapshots, it does seem like numerical instabilities form where the mesh transitions between AMR levels and propagate inward, "squeezing" the star along the rectangular mesh
- It seems like more refinement of the ambient medium helps to avert this problem
- This is consistent with what MacLeod was finding (that lower base resolution exarcebates this effect, also seen in his sims, private communication)
- Is this partly caused by density jump between surface and ambient medium?
Conclusions
- Tentatively, it seems necessary to refine very conservatively such that much of the surrounding ambient is refined at the beginning of the simulation before the dynamical plunge-in phase.
- When the dynamical plunge-in phase begins, this can be relaxed and the refinement can be concentrated on the stellar material only.
- Fundamental oscillation modes can be excited when the primary does not rotate synchronously with the orbit at the Roche limit separation (MacLeod+19). This instability is likely being seen in our Runs 201 and 202. Initializing the primary in synchronous rotation might drastically improve stability.
- Seeing as how the numerical instability occurs at the stellar surface, it would probably also be beneficial to increase the resolution there, if possible
Run 199
Snapshots (screenshots for debugging)
- density frame 0, with mesh
- density frame 0, with mesh, extended range
- pressure frame 0, with mesh, extended range
- pressure frame 0, with mesh, extended range, zoomed in
- temperature frame 0
- density frame 1, extended range
- pressure frame 1
- pressure frame 1, small range
- pressure frame 1, small range, zoomed in
- temperature frame 1
COMMON ENVELOPE SIMULATIONS
AGB paper
I have "completed" all the figures for the AGB paper. Will now write it up.
AGB paper (pay attention to the figures and ignore everything else).
RLOF+CEE Simulations
Goal for this month is to (1) set up new high resolution, large box, optimal RLOF run (now undergoing testing) and (2) restart from end of old RLOF runs with improved refinement and evolve as long as possible (to serve ultimately as low resolution comparison runs).
- New runs
- Run 199: Setup with smoothly matched hydrostatic atmosphere matching on to constant ambient at larger radius and density thresholds for refinement. >>Crashes ~immediately due to high pressure gradients just outside primary. Rerunning now with AstroBEAR default refinement. —> queued
- Run 196: Setup with low constant ambient, refined on density, eventually slows down a lot. Restarted from frame 29 with AstroBEAR default refinement. Runs fast but chombo sizes are HUGE since much more volume is refined. (First I tried qTolerance 0.2, then later changed to 0.4 to reduce file size. DesiredFillRatios set to 0.7.) Ran but then crashed on a restart when reading chombo (not sure why). Restart from frame 35 is now in the queue.
- Continuation of old runs (only the last chombo of each had been kept!)
- Run 195: Separation of 1.5 times old separation, restarted from frame 50 of Run 161 with higher density thresholds for refinement and one extra refinement level for very high density—> completed up to frame 201
- Run 201: Roche-limit separation (=2.2 times old separation), restarted from frame 53 of Run 160 with higher density thresholds for refinement and one extra refinement level for very high density—> running, completed up to frame 146
- Run 202: Roche-limit separation (=2.2 times old separation) with low density ambient (67 times lower than fiducial), restarted from frame 27 of Run 162 with higher density thresholds for refinement and one extra refinement level for very high density—> queued
COMMON ENVELOPE SIMULATIONS
More Papers Relevant for Force in CEE (in chronological order, I would start with the ones labeled with asterisks)
Sanchez-Salcedo & Brandenburg 1999
Sanchez-Salcedo & Brandenburg 2001*
Escala et al. 2004*
Kim & Kim 2007*
Kim, Kim & Sanchez-Salcedo 2008*
Kim 2010*
Canto et al. 2011
Sanchez-Salcedo 2012
Bernal & Sanchez-Salcedo 2013
Sanchez-Salcedo & Chametla 2014*
Sanchez-Salcedo & Chametla 2018
AGB paper
COMMON ENVELOPE SIMULATIONS
New Work
- Plan for Paper IV
- Started analysis for Run 183 (AGB)
- Backing up files on TACC Ranch (about half full)
- Force postprocessing for Run 183 completed on bluehive
Results
Plan for Paper IV
- Title: Effects of varying the primary star evolutionary state in 3D global simulations of common envelope evolution
- Abstract:
- First AGB CE simulation with high resolution (“present generation” resolution)
- Result 1: summarize simulation outcome
- Compare with RGB simulation to assess the differences and similarities
- Result 2: orbital evolution comparison
- Result 3: force comparison
- Result 4: envelope mass unbinding evolution comparison
- Result 5: potential for constraining alpha
- Result 6: lessons learnt about the numerics
- Figures
- RGB and AGB initial profiles (density, internal energy, total energy)
- Separation vs time curves comparison, with a(t/Porb0)/a0
- Density, orbital plane, 4 snapshots
- Normalized energy, orbital plane 4 snapshots at same times as for density
- Force on particle 2 (in rest frame of particle 1) vs t/Porb0
- Unbound mass vs t/Porb0
- Percent energy change —convergence study
- Unbinding efficiency epsilon as a function of time (or leave for paper on energy formalism?)
Separation vs time
Detail of flow near particles at late times
Density and normalized gas energy
Run 183 Density and Normalized gas energy
Run 183 Normalized gas energy definition comparison (a-b)/max(a,b), as in Paper II, on the left, and (a-b)/(a+b) on the right
Next steps
- Carry out analysis, one figure at a time
- Keep adding to draft of paper
- Prepare Xsede proposal (renewal) for Jan 15
- Compute mean separation abar(t) from orbit data (non-trivial!)
- Submit by Apr 1
COMMON ENVELOPE SIMULATIONS
New Work
- Advanced Run 183
- Estimated remaining cost of simulation assuming evolve to t=700 days (same as low res run 164) and assuming no changes to refinement (Answer: 30% of the total allocation or about half of the remaining node-hours, and about 40 TB of additional storage in addition to 30 TB currently)
- Modified slurm script to exit loop if error occurs (to avoid wasting node-hours)
Results
- Energy gain in 183 is again too fast! Now crossed 5% threshold and energy gain is accelerating.
Figures
Interpretation
- The most likely reason for the energy gain is (again) lack of resolution around the point particles
- In particular, I suspect that as particle 2 accretes more and more mass, the pressure gradients become too high to resolve
- Other, less likely (non-mutually exclusive) possibilities are:
- insufficient resolution around particle 1 (but we know it was adequate at earlier times, so less likely)
- insufficient resolution in the ambient gas, where Rayleigh Taylor instabilities are occurring (but this material has much lower density, and development of instabilities does not seem to correlate very well with increase in energy, so less likely)
Strategy
- I plan to add two AMR levels of resolution around particle 2 and see if this helps.
- If yes, then I need to perform tests to determine a more optimal refinement strategy.
- If we find that the refinement needs make the simulation too expensive to perform, then it will be time to write up the results for a paper.
Next steps
- More analysis to better understand what is causing the energy gain (extend 1D movies of pressure profiles around particles, and make movies to understand better the development of instabilities in the ambient and to what extent this correlates with energy gain)
- Test with higher resolution around particle 2 (restarting from an earlier time in the simulation)
- If the test shows improvement, then need to perform additional tests to optimize refinement strategy
COMMON ENVELOPE SIMULATIONS
New Work
- Advanced Run 183 and produced figures and movies
- Progress on deriving expressions for total energy conservation prescription
- Plotted convergence test 185 to confirm that changing refinement region center from particle 1 to particle CM has negligible effect on energy conservation (confirmed)
- Encountered (and solved) particle creation issue that was crashing code (code is now running on stampede2)
Results
- Rate of energy gain for Run 183 is now quite small and apparently on track for staying below 10% of the old AGB run (Run 164).
- Run 183 crashed because of particle creation….I created a switch that turns off particle creation.
Figures
Movies
Run 183 Density
Run 183 Density with mesh
Run 183 Pressure profiles (sliced along x-axis in simulation frame of reference)
Next steps
- Continue Run 183 (and increase speed by using more nodes)
- Further modify new energy conserving routines to take into account particle-gas and particle-particle energy terms
- Further automate and improve simulation:
- predefine refinement radius as a function of time (should vary smoothly rather than in sudden steps)
- center of refinement shape should transition smoothly in time from particle 1 to particle CM (instead of suddenly)
- experiment with using true AMR, e.g. refine on density or pressure gradients within refinement shape
COMMON ENVELOPE SIMULATIONS
New Work
- Advanced Run 183 (restarted at frame 194 = 44.9 days of Run 177 now with extra refinement around particle 2)
- With JC coded in new routines that conserve total gas energy including PE due to self-gravity but not including particles. These new routines have not yet been tested.
Results
- Rate of energy gain after first periastron passage is much smaller in Run 183 compared to 177, as expected.
Notes
Notes on AGB high resolution run 183.
Next steps
- Continue Run 183
- Plot results from Run 185 (convergence test)
- Further modify new energy conserving routines to take into account particle-gas and particle-particle energy terms
- Further automate and improve simulation:
- predefine refinement radius as a function of time (should vary smoothly rather than in sudden steps)
- center of refinement region should transition smoothly in time from particle 1 to particle CM (instead of suddenly)
- experiment with using true AMR, e.g. refine on density or pressure gradients within refinement shape
COMMON ENVELOPE SIMULATIONS
New Work
- Advanced Run 177 (AGB run with increased resolution at AMR level 5 around particle 1 compared to the old AGB run, Run 164) and found that after the first periastron passage, the rate of energy increase becomes dramatically higher (going from 10% to 60% of that of Run 164)
- The cause of this is likely that the resolution around particle 2 is not high enough to resolve the accreted mass around particle 2. Therefore, I have submitted two new runs which put the same extra resolution around particle 2 as well (each run has a different restart time, both restart times are before first periastron passage). I've also submitted a third run which does NOT change the center of the AMR level 3 spherical refinement zone from particle 1 to the particle CM just after periastron passage, to make sure that this was not the cause of the sudden increase in the rate of energy gain in Run 177. Waiting for Stampede queue.
- I read this paper and discussed with Jonathan. It gives a way to conserve energy explicitly including potential energy from self-gravity. We think that we could take it a step further and include the PE due to particle-gas interaction as well. This should not be too hard to implement.
Updated Notes
Notes on AGB high resolution run 177, comparison with low resolution run 164.
COMMON ENVELOPE SIMULATIONS
New Work
- Continuing high res AGB run
AGB Paper
New notes
Notes on AGB high resolution run 177, comparison with low resolution run 164.
COMMON ENVELOPE SIMULATIONS
New Work
- Ran test runs + analysis + comparison with fiducial run, for AGB CE simulation
AGB Paper
New notes
Movies
Pressure profile evolution, inner 0.6 Rsun (Note Rsoft = 2.4 Rsun)
Run 164
Run 164 frames 0-1
Run 170
Run 170 frames 0-1
Run 173
Run 173 frames 0-1
Run 174
Next steps
- 2-3 more test runs to try to improve energy conservation further
- Tracer? Ambient, AGB core (e.g. to track energy)
COMMON ENVELOPE SIMULATIONS
New Work
- 2D movies for force paper for fiducial run 143 (q=0.5), using de-resolved data.
- 1D plots for force paper for runs 143 (q=0.5), 149 (q=0.25) and run 151 (q=0.125), using original data (not de-resolved data).
- Redoing force post-processing using reservation on bluehive (pp seems to be more stable with a reservation, but results should hardly change, if at all).
- Deleted most of AGB run from bluehive, keeping only 1/5 of frames, to save space (the other frames are still available for now on stampede scratch, but I may move them to backup drive).
- Analysis: begun comparison with Macleod+17b
Force Paper
New notes with 1D plots
Movies
all movies are in the corotating (with the particle orbit) reference frame of particle 2, and particle 2 is at center of the frame, while particle 1 is situated on the
Particularly interesting movies are highlighted in bold font
Force per unit volume between particle 2 and gas along phi-direction (magnitude), with contours also showing the same quantity plotted in color with contour values equal to values labeled on the color bar, and with vectors on particle 2 showing velocity of particle 2 relative to particle 1, and on particles 1 and 2 showing net force on each particle exerted by the gas , slice through orbital plane (view size ):
Force per unit volume along phi direction
Force per unit volume between particle 2 and gas along direction of particle 2 velocity relative to particle 1 (magnitude), with contours also showing the same quantity plotted in color with contour values equal to values labeled on the color bar, and with vectors on particle 2 showing velocity of particle 2 relative to particle 1, and on particles 1 and 2 showing net force on each particle exerted by the gas, slice through orbital plane (view size
Force per unit volume along velocity wrt particle 1
Force per unit volume between particle 2 and gas along phi-direction (magnitude), with contours also showing the same quantity plotted in color with contour values equal to values labeled on the color bar, and with vectors on particle 2 showing velocity of particle 2 relative to particle 1, and on particles 1 and 2 showing net force on each particle exerted by the gas , slice through orbital plane (view size
Force per unit volume along phi direction
Force per unit volume between particle 2 and gas along direction of particle 2 velocity relative to particle 1 (magnitude), with vectors on particle 2 showing velocity of particle 2 relative to particle 1, and on particles 1 and 2 showing net force on each particle exerted by the gas, slice through orbital plane (view size
Force per unit volume along velocity wrt particle 1
Density, slice through orbital plane, with velocity vectors (view size
Density
Density normalized to
Normalized density, slice through orbital plane
Density normalized to
Normalized density, perpendicular to orbital plane
Mach number, in frame of particle 2 corotating with particle orbit, slice through orbital plane (view size
Mach number, slice through orbital plane.
Mach number, in frame of particle 2 corotating with particle orbit, perpendicular to orbital plane (view from particle 1) (view size
Mach number, perpendicular to orbital plane.
Phi-component of velocity about particle 1, slice through orbital plane, in the frame corotating with the particle 1-particle 2 orbit, with vectors showing the same quantity. Units are km/s. In this movie, particle 1 is to the LEFT of center (view size Phi-component of velocity about particle 1, in frame corotating with particle 2
).Phi-component of velocity about particle 1, slice perpendicular to orbital plane (view from particle 1), in the frame corotating with the particle 1-particle 2 orbit, with vectors showing the same quantity. Units are km/s (view size Phi-component of velocity about particle 1, in frame corotating with particle 2
).Phi-component of velocity about particle 1, slice through orbital plane, in the frame corotating with the particle 1-particle 2 orbit, with vectors showing the same quantity, now NORMALIZED to the velocity Normalized phi-component of velocity about particle 1, in frame corotating with particle 2
computed using the initial RGB profile. Note the changing colorbar and zoom level.Next steps
- Understanding 1D plots in terms of 2D movies (in progress, for discussion at meeting)
- Comparison with MacLeod+17b (in progress, for discussion at meeting)
- Comparison with Rheichardt+19 (in progress, for discussion at meeting)
- Comparison with Ricker+Taam12 (in progress, for discussion at meeting)
- Understand better the BHL theory/Dodd+McCrea theory and adjust analytic formulae if necessary, also estimate factor.
- Redo movies using full resolution data (after deciding which ones are most important)
- Movies for runs 149 and 151
- Post-processing of simulations to extract forces: I'm re-doing it with a reservation on bluehive to ensure that the results are correct as there had been some issues when I had done this the first time without a reservation (in progress)
- Movies and analysis for run 132 (subgrid accretion run) (partly complete)
- Calculate force from loss of angular momentum
COMMON ENVELOPE SIMULATIONS
AGB Run
See http://www.pas.rochester.edu/~lchamandy/CE_papers/AGB/agb.pdf.
Poster for Baltimore conference
COMMON ENVELOPE SIMULATIONS
New Work
- Did force plots for runs 149 (half m2), 151 (fourth m2), 132 (subgrid accretion).
- Found paper with analytic formula for drag force in presence of density gradient.
- Continued AGB run on stampede 2: problem with code.
- CM relative motion and energy plots for runs 149 & 151 (with Yisheng, ongoing).
- Hubble proposal.
Force
Here are the updated notes on drag force which now include the same figures for the other runs: see notes, especially Fig. 9-12.
Here are the relevant papers with the analytic formula:
- Taam & Bodenheimer 1989, which quotes the formula from Dodd & McCrea 1952
AGB Run
See en_fig_run164.pdf.
Hubble proposal
See ce.pdf.
Next steps
- Finish Hubble Theory proposal and submit by Friday.
- Analysis for drag force work.
- Plot new analytic formula that takes into account density gradient.
- New 2D slices/movie.
- Color as force/volume and contours as density (before I plotted the reverse).
- Subtract out axisymmetric contribution to force/volume at each radius (radius measured from particle 2? particle 1?).
- Put force and velocity vectors on particle 2 in VisIt.
- Do all the same graphs for runs 149, 151 and 132.
- AGB simulation.
- Fix bug that is slowing down code and eventually making it crash.
- Continue to plot a(t) and 2D slices showing bound/unbound gas.
- Runs 149, 151 figures as in Paper II with Yisheng.
- Posters for Baltimore conference.
COMMON ENVELOPE SIMULATIONS
New Work
- More analysis on force in fiducial run 143.
- Continued AGB run on stampede 2.
- Finished postprocessing for forces for runs 149, 151 and postprocessing still underway for energy terms.
Force
Here are the new notes on drag force for run 143: notes.
Next steps
- Write Hubble Theory proposal.
- Analysis for drag force work.
- Put force and velocity vectors on particle 2 in 2D plots from previous post.
- Calculate contribution of drag force out to different distances from particle 2.
- Do all the same graphs for runs 149, 151 and 132.
- Continue to run AGB sim and plot results.
- Continue postprocessing work, also postprocessing to get forces in run 132 (sub-grid accretion run).
COMMON ENVELOPE SIMULATIONS
New Work
- Referee report
- Ready to re-submit?
- CEJet module
- Reran tests on bluehive with much low ambient and larger initial separation by factor of two.
- Jet does not turn on! We don't know why.
- Could have something to do with density protections but lowering threshold doesn't solve it.
- AGB run
- Continuing to run the simulation, now up to 185 days. Material is leaving the box so analysis will have to consider fluxes through the boundary.
- See new separation vs time plot below
- Forces
- Wrote post-processing script, tested it against VisIt results (including a frame with the full-resolution data that I managed to obtain before VisIt crashed)
- Now running post-processing script (with reservation on bluehive) on data from fiducial run (143) as well as runs with ½ and ¼ the secondary mass (149 and 151, respectively)
- Before writing the script I tried using parallel visit on stampede as Gabe has done, but still there was insufficient memory, so gave up!
- Alternative energy formalism
- Will write a draft when paper is accepted
- Hubble Theory proposal
- How could it be relevant to Hubble data?
- Explaining post-CE binary separations in single and double degenerate systems?
- Explaining transient objects believed to be CE events?
- How could it be relevant to Hubble data?
- XSEDE allocation
- Need a plan for using the roughly 185,000 node-hours that remain!
- AGB simulation in a very large box leading to PN initial condition?
- Need a plan for using the roughly 185,000 node-hours that remain!
AGB run
Next steps
- Continue to run AGB CE simulation on stampede (3-4 day queue time) and plot results, including movies.
- Analysis of force in runs 143, 149 and 151 using new force data from post-processing.
- Continue to test CEJet module and get rid of the bugs! (with Amy).
- Do post-processing for energy terms for runs 143, 149 and 151, and also unbound mass
- Need to redo fiducial run 143 with new script, which shows slight differences at 1% level to that used in Paper II—this is a small concern, hopefully will help to account for the 5% apparent violation in energy conservation.
COMMON ENVELOPE SIMULATIONS
New Work
- CE Jet (with Amy)
- Continued AGB run on stampede 2
CE Jet Movies
Movies are in the frame of reference of secondary, with secondary at the center.
Here are the old notes on CE Jets.
Here is the Xsede proposal.
Below we compare two test runs, identical except that the jet is turned on in Run 014, whereas the jet is turned off in Run 015.
The jet model is adapted from Federrath et al. 2014.
For both Run 014 and Run 015, parameters are as in the fiducial run 143 (Model A of Paper 1) except:
Base resolution = 64^{3};
Max AMR level = 4;
Region of maxlevel refinement = sphere of radius 57 Rsun around particle 1 (primary radius is 48 Rsun);
Size of smallest resolution element = 1.1 Rsun.
For Run 014, the jet parameters are:
Jet mass loss rate = 0.02 Msun/yr;
Jet velocity along jet axis = 10^{3} km/s;
Jet temperature = 3000 K;
Jet collimation half opening angle = pi/12;
Jet radius = 64 grid cells.
Other jet runs are similar to Run 014 except with certain differences, mentioned below.
Comparison of Run 015 with Run 014
Density, face-on (left = no jet, right = jet)
Density, edge-on through particles (left = no jet, right = jet)
Density, edge-on view from particle 1 (left = no jet, right = jet)
Comparison of Run 015 with Run 016 (like Run 014 but 100 times the jet mass loss rate)
Density, face-on (left = no jet, right = superstrong jet)
Density, edge-on through particles (left = no jet, right = superstrong jet)
Density, edge-on view from particle 1 (left = no jet, right = superstrong jet)
Comparison of Run 015 with Run 017 (like Run 016 but with ½ the jet radius)
Density, face-on (left = no jet, right = superstrong jet with small radius)
Density, edge-on through particles (left = no jet, right = superstong jet with small radius)
Density, edge-on view from particle 1 (left = no jet, right = superstong jet with small radius)
Comparison of Run 014 with Run 016
Density, face-on (left = jet, right = superstrong jet)
Density, edge-on through particles (left = jet, right = superstrong jet)
Density, edge-on view from particle 1 (left = jet, right = superstrong jet)
Comparison of Run 016 with Run 017
Density, face-on (left = superstrong jet, right = superstrong jet with small radius)
Density, edge-on through particles (left = superstrong jet, right = supersrong jet with small radius)
Density, edge-on view from particle 1 (left = superstrong jet, right = superstrong jet with small radius)
Comparison of Run 014 with Run 018 (like Run 014 but with 1/100 of jet radial velocity
Density, face-on (left = superstrong jet, right = superstrong jet with low velocity)
Density, edge-on through particles (left = superstrong jet, right = supersrong jet with low velocity)
Density, edge-on view from particle 1 (left = superstrong jet, right = superstrong jet with low velocity)
Comparison of Run 018 with Run 019 (like Run 018 but with ½ the jet radius, like Run 017 but with 1/100 of jet radial velocity)
Density, face-on (left = superstrong jet with low velocity, right = superstrong jet with small radius and low velocity)
Density, edge-on through particles (left = superstrong jet with low velocity, right = superstrong jet with small radius and low velocity)
Density, edge-on view from particle 1 (left = superstrong jet with low velocity, right = superstrong jet with small radius and low velocity)
Comparison of Run 017 with Run 019
Density, face-on (left = superstrong jet with small radius, right = superstrong jet with small radius and low velocity)
Density, edge-on through particles (left = superstrong jet with small radius, right = superstrong jet with small radius and low velocity)
Density, edge-on view from particle 1 (left = superstrong jet with small radius, right = superstrong jet with small radius and low velocity)
Comparison of Run 015 with Run 019
Density, face-on (left = no jet, right = superstrong jet with small radius and low velocity)
Density, edge-on through particles (left = no jet, right = superstrong jet with small radius and low velocity)
Density, edge-on view from particle 1 (left = no jet, right = superstrong jet with small radius and low velocity)
Notes on CEJet runs
- Notes on the results
- The late emergence of the jets with lower radius is hard to comprehend. It seems like one quadrant emerges first and then spreads to cover all 4 quadrants.
- It appears that the mass loss rate needs to be quite large or the radial velocity quite small to get an obvious effect on the morphology, but that's also because the radius is too large. We need to understand the dependence on jet radius and whether the effects we're seeing are physical or numerical.
- Notes on the simulations
- Number of resolution elements per softening radius is only 2.2, leading to numerical instability of primary core region.
- Particle orbits are not reliable as their separation increases even in the no jet case, due to insufficient resolution.
- Partly for these reasons, stopped movie around t=7 days.
- The simulations take a few hours to run up to this time with 115 cores on bluehive. Increasing the max AMR level by 1 or 2 should be possible.
- Also, we should start to move away from uniform resolution inside a sphere and toward full AMR.
- It would be good to introduce a tracer into astrobear for the jet material
- The ambient density and pressure could be lowered considerably. (I realized that the whole reason for the high ambient, namely to stabilize the outer layers, is not really relevant because that numerical instability that we saw when the scale height at the surface was not highly resolved was likely mostly due to grid effects when the star was fixed on the grid (e.g. during the damping run). Now we no longer do damping runs anyway. Amy and I have seen that the surface of the primary appears stable, even when the initial separation is increased and for much lower resolution than the fidicial run 143. The lesson seems to be that these pesky grid effects mostly go away when the star moves over the grid since errors accumulate randomly rather than uni-directionally. Bottom line is we should be able to get away with much lower ambient pressure and density, alleviating various headaches…)
- Currently, it is not possible to do restarts from the fiducial run since they used a different version of astrobear and the chombos are not quite compatible (the jet feedback module contains new outputs to the chombo that were not present in the previous version of astrobear used to run the fiducial CE run 143).
- The above item is not really a problem. Anyway, we should do a new fiducial run without jets, with low ambient, more efficient refinement strategy and bigger box.
- We should also try starting the secondary from farther out, as this case is likely to be interesting.
- Notes on the analysis
- It would be good to plot planes parallel to the orbital plane (say 10 Rsun above it) to see the jet cross-section.
- Velocity vectors would be useful.
- Plots of normalized energy density (blue/red for bound/unbound) would be helpful.
- Put circular contour with radius=jet_radius around point particle 2 for reference.
Next steps
- Test CEJet module, e.g. is it adding mass to the grid at the correct rate (Amy).
- Continue to experiment with CEJet module on bluehive.
- Continue to run AGB CE simulation on stampede and plot results.
- Begin writing post-processing to obtain forces from full resolution data sets of Run 143 (fiducial), 149 (half secondary mass of fiducial) and 151 (fourth secondary mass of fiducial), as serial VisIt cannot handle the data sets (parallel VisIt is another option but we weren't successful when we tried to get it to work—anyway postprocessing means that in later simulations these quantities could be calculated on the fly, which would be useful).
COMMON ENVELOPE SIMULATIONS
New Work
- Drag force/secondary mass paper:
- Movies showing contours of component of force per unit volume exerted on secondary…
- along direction
- along direction of (=drag if net force is negative and =thrust if net force is positive)
- Movies showing contours of component of force per unit volume exerted on secondary…
Movies
Movies are in the frame of reference co-orbiting with the particles, with the secondary at the center.
Face-on density with contours showing magnitude of force/volume exerted by gas on particle 2 along direction of velocity of particle 2 relative to particle 1
Density with drag force/volume contours (Run 143: No subgrid accretion, M2 = 1 Msun)
Face-on density with contours showing magnitude of force/volume exerted by gas on particle 2 along direction:
Density with drag force/volume contours (Run 143: No subgrid accretion, M2 = 1 Msun)
Future work to improve the above movies
- Add vector to show direction of force exerted on particle 2 by the gas .
- Add vector to show -component of force exerted on particle 2 by the gas .
- Add vector to show direction of velocity of particle 2 with respect to particle 1 .
- Add vector to show ( )-component of force exerted on particle 2 by the gas .
(adding these is somewhat non-trivial in VisIt so haven't quite gotten to it yet.)
COMMON ENVELOPE SIMULATIONS
New Work
- Jets paper: wrote problem module for phase 1 (no subgrid accretion), compiled on bluehive, but run error. At this point it would be wise to merge my version of astrobear with the version that implements jet feedback.
- Drag force/secondary mass paper:
- Made movies for runs 149 and 151 (M2 = 0.5 Msun and M2 = 0.25 Msun)
- Wrote script to compute drag force
- Ran script to compute drag force on reduced resolution run 143 and produced various plots (see below)
- Started draft of paper
Drag force plots for Run 143 (de-resolved version to enable faster analysis using VisIt)
1) Force exerted by gas on particles, calculated numerically
Description: Force and components of for both particles, with inter-particle separation curve plotted in grey for reference.
Velocity components for each particle are also plotted for reference (with an arbitrary linear scale). Note that positive -component means away from the other particle, while positive -component means in the sense of the orbit.
Comments: Force on secondary in frame of primary is shown by black line. Phi-component is shown by orange line.
Note that at early times, is dominated by since is so large.
At later times the orange and black lines coincide, so is dominated by .
We see that the -component of the force (orange) is positive during plunge-in (so of opposite sign to the predicted drag force). The secondary is being accelerated around in its orbit by the posterior side of the envelope, which lags the primary particle in its orbit (paper 2). Subsequently, the force is mostly a drag force (-ve component) but the component actually oscillates from positive to negative .
2) Force exerted by gas on particles, calculated semi-analytically
Description: Force is now calculated using formula, but with velocity inputted from simulation. Black line is drag force on secondary in the frame of the primary. Density and sound speed are equal to the values in the initial RGB profile, at radius equal to the current inter-particle separation . Density, relative speed and inter-particle separation are plotted for reference (with arbitrary linear scales; density and speed increase with time while separation decreases).
Comments: The drag force on the secondary in the frame of the primary is predicted to be higher in magnitude when is smaller and density and speed are larger. The low density is predicted to cause the drag force to be negligible at early times.
3) Force exerted by gas on particles, numerical normalized by semi-analytical
Description: Numerical solution normalized by semi-analytical solution for a few choices of formulae.
Comments: At late times, the magnitude of the drag force is of order a few per cent of the predicted value.
4) Bondi radius
Description: Various definitions of Bondi radius plotted for both particles. Also plotted for reference are the inter-particle separation (grey) and pressure scale height of the original RGB profile at .
Comments: The most relevant Bondi radius is probably the one represented by the thick solid red curve, corresponding to the Bondi radius around the secondary in the frame of the primary, including the sound speed in the denominator. However, for all definitions, a uniform medium is assumed. That is, the density and pressure gradients are neglected. Also, the initial sound speed of the original profile is assumed. Even more problematic, the envelope is assumed to be stationary in the frame in which the Bondi radius is computed (lab frame or frame of primary point particle). In any case, looking at the thick red line, we see that is comparable to and comparable to the pressure scale height . Thus, applying the Bondi-Hoyle-Lyttleton formalism to this case is highly questionable. However, it remains to beseen whether applying this formalism would be more justified as is reduced (in the limit , since , so independent of , in that limit. This can be tested with Runs 149 and 151 which have equal to ½ and ¼ of the value in the fiducial run (Run 143) plotted here.
Updated Movie Library for Runs 132, 143, 149, 151
Density (zoomed in) in lab frame
Face-on density (Run 143: No subgrid accretion, M2 = 1 Msun)
Face-on density (Run 149: No subgrid accretion, M2 = 0.5 Msun)
Face-on density (Run 151: No subgrid accretion, M2 = 0.25 Msun)
Movies corresponding to figures in Paper 1
Movies are in the reference frame corotating about the secondary with the instantaneous orbital angular speed of the particles, and with the secondary at the center.
Figure 1/Figure 2—-face-on density:
Face-on density (Run 143: No subgrid accretion, M2 = 1 Msun)
Face-on density (Run 132: Subgrid accretion, M2 = 1 Msun)
Face-on density (Run 149: No subgrid accretion, M2 = 0.5 Msun)
Face-on density (Run 151: No subgrid accretion, M2 = 0.25 Msun)
Figure 4 top panel—-edge-on density:
Edge-on density (Run 143: No subgrid accretion, M2 = 1 Msun)
Edge-on density (Run 132: Subgrid accretion, M2 = 1 Msun)
Edge-on density (Run 149: No subgrid accretion, M2 = 0.5 Msun)
Edge-on density (Run 151: No subgrid accretion, M2 = 0.25 Msun)
Figure 4 bottom panel—-edge-on density, zoomed in:
Edge-on density (zoomed in) (Run 143: No subgrid accretion, M2 = 1 Msun)
Edge-on density (zoomed in) (Run 132: Subgrid accretion, M2 = 1 Msun)
Edge-on density (zoomed in) (Run 149: No subgrid accretion, M2 = 0.5 Msun)
Edge-on density (zoomed in) (Run 151: No subgrid accretion, M2 = 0.25 Msun)
Figure 6—-flow around companion:
Tangential velocity with velocity vectors (Run 143: No subgrid accretion, M2 = 1 Msun)
Tangential velocity with velocity vectors (Run 132: Subgrid accretion, M2 = 1 Msun)
Tangential velocity with velocity vectors (Run 149: No subgrid accretion, M2 = 0.5 Msun)
Tangential velocity with velocity vectors (Run 151: No subgrid accretion, M2 = 0.25 Msun)
Movies corresponding to figures in paper 2
Movies are in the lab (~system CM) reference frame with the CM of the particles located at the center of the frame.
Figure 3 top row—-face-on normalized gas binding energy (red means unbound, blue means bound, yellow is density contours, vectors are velocity):
Face-on normalized energy (Run 143: No subgrid accretion, M2 = 1 Msun)
Face-on normalized energy (Run 149: No subgrid accretion, M2 = 0.5 Msun)
Face-on normalized energy (Run 151: No subgrid accretion, M2 = 0.25 Msun)
Figure 3 second from top row—-face-on normalized gas kinetic energy (magenta means thermal energy dominates, green means bulk KE dominates, yellow is density contours, vectors are velocity):
Face-on normalized kinetic energy (Run 143: No subgrid accretion, M2 = 1 Msun)
Face-on normalized kinetic energy (Run 149: No subgrid accretion, M2 = 0.5 Msun)
Face-on normalized kinetic energy (Run 151: No subgrid accretion, M2 = 0.25 Msun)
Extra Movies
Temperature (Run 143: No subgrid accretion, M2 = 1 Msun)
Temperature (Run 132: Subgrid accretion, M2 = 1 Msun)
Temperature (Run 149: No subgrid accretion, M2 = 0.5 Msun)
Temperature (Run 151: No subgrid accretion, M2 = 0.25 Msun)
Sound speed (Run 143: No subgrid accretion, M2 = 1 Msun)
Sound speed (Run 132: Subgrid accretion, M2 = 1 Msun)
Mach, lab frame (Run 143: No subgrid accretion, M2 = 1 Msun)
Mach, lab frame (Run 132: Subgrid accretion, M2 = 1 Msun)
Mach, frame corotating about secondary (Run 143: No subgrid accretion, M2 = 1 Msun)
Mach, frame corotating about secondary (Run 132: Subgrid accretion, M2 = 1 Msun)
Side-by-side comparison of Model A/143 (left) and Model B/132 (right) from Paper 1
Face-on density
Edge-on density
Edge-on density, zoomed
Tangential velocity
Temperature
Sound speed
Mach in lab frame
Mach in frame corotating about secondary
Questions for further analysis
- What is the relative velocity between the particle and gas in its vicinity?
- Could make movies of relative gas velocity (had this a while back)
- What is the relative contribution to the gas-particle force as a function of distance from the particle?
- Could plot net gas-particle force including only gas in spheres of different radii around the particle
- What does the 2D map of gas-particle force look like for each particle?
- Could make movies with vectors for the particle-gas force at each point
Next steps
- Energy analysis for runs 149 and 151, including 5 figures:
- Energy components vs time plots (Fig 1a and 1b of Paper 2) for runs 149 and 151 (Yisheng)
- Mass unbinding vs time plots (Fig 2 of Paper 2) for runs 149 and 151 (Yisheng)
- Particle CM — Envelope CM relative motion (Fig 6a and 6b of Paper 2) for runs 149 and 151 (Yisheng)
- Stability analysis comparing runs 143 (without damping run) and 132 (with damping run) initial conditions, to go into appendix of Paper 3 (Yisheng)
- Drag force computation for Run 143 (full resolution), Run 149 and Run 151 (may need post-processing)
- Jet test runs (need to merge versions of astrobear)
COMMON ENVELOPE SIMULATIONS
Summary of recent work
- Continued to write/edit energy paper (see overleaf)
- Plots for energy paper (see en_fig.pdf, last post)
- New longer movie of AGB run (see last post)
- Energy plots for AGB run (this post)
- Plan for other papers
Energy paper
Overleaf: https://www.overleaf.com/project/5bd20d99379a851a13bfd103
2D plots for AGB run 164: http://www.pas.rochester.edu/~lchamandy/CE_papers/Energy/en_fig_run164.pdf
Planned papers
- Parameter space—dependence on secondary mass (~15 pages):
- Compare energy/mass unbinding for different runs.
- Analysis of orbital dynamics including damping force. Compare with theory and compare the three different runs.
- Convergence tests.
- Suggest to extend the runs in time somewhat (but stop before material exits box).
- ALTERNATIVELY: could study orbital dynamics for the fiducial run in a shorter separate paper.
- Jet (Letter): See previous posts
- AGB (Letter)
- Present the run since not really done by anyone before
- Compare with RGB run
- Orbit
- Energy
- Orbital dynamics
- QUESTION: Do we perform a new run or use the present run? Material has just started to exit the box!
COMMON ENVELOPE SIMULATIONS
Summary of recent work
- Continued to write/edit energy paper
- Plots for energy paper
- New longer movie of AGB run
Conferences
- Grand Challenges in Stellar Physics: Pulsating Stars in the Universe
- Apr 1-5, 2019
- Nice, France
- website doesn’t seem to be up yet
- The Deaths and Afterlives of Stars
- Apr 22-24, 2019
- Space Telescope Science Institute, Baltimore
- http://www.stsci.edu/institute/conference/spring2019
- Registration fee: $200
- Deadline for abstract submission: Dec 15 if want to be considered for financial assistance
- New Perspectives on Galactic Magnetism
- June 10-14, 2019
- Newcastle upon Tyne, UK
- The Beginnings and Ends of Double White Dwarfs
- Jul 1-5, 2019
- Dark Cosmology Centre, Niels Bohr Institute, Copenhagen, DK
- https://dark.nbi.ku.dk/the-beginnings-and-ends-of-double-white-dwarfs/
- The Role of Outflows in Compact Binaries
- Jul 1-3, 2019
- Amsterdam, NL
- https://outflows2019.com/
Tentative plan:
- First trip: Attend #2 (within USA)
- Second trip: Attend #3 and #4 (or #5) (Europe)
Energy paper
Overleaf: https://www.overleaf.com/project/5bd20d99379a851a13bfd103
New 2D plots I am using to write the section on the spatial analysis: http://www.pas.rochester.edu/~lchamandy/CE_papers/Energy/en_fig.pdf
Medium resolution AGB run (one less level of AMR than fiducial RGB run)
Face-on density (zoomed in) (Run 164, m2=1 Msun)
Papers on CE simulations involving AGB primaries
COMMON ENVELOPE SIMULATIONS
Summary of last two weeks' work
- Finished XSEDE proposal with Baowei & Eric
- Continued to write/edit energy paper
- Continued running simulations
- Preliminary analysis of simulations
Energy paper
- Will be on Overleaf before Oct 31
- Meeting on Nov 6?
- en.pdf.
Roche lobe overflow in high resolution
Face-on density (zoomed in) (Run 160 a=109Rsun), equal to theoretical Roche limit separation for this system.
Face-on density (zoomed in) (Run 161 a=73.5Rsun)
Face-on density (zoomed in) (Run 162 a=109Rsun with ambient density 10^-10^ g/cm^3^)
The sound-crossing time for the RG is about 8 days or ~35 frames. This is the approximate time the star would take to deform to fill the Roche lobe.
While this deformation is happening, the secondary accretes from the ambient medium.
Runs like fiducial run 143 (Model A of Paper I) but with different secondary mass
Face-on density (zoomed in) (Run 149, m2=0.5 Msun)
Face-on density (zoomed in) (Run 151, m2=0.25 Msun)
Convergence study for softening length and resolution
Convergence study for size of maxlevel refinement region
Medium resolution AGB run (one less level of AMR than fiducial RGB run)
COMMON ENVELOPE SIMULATIONS
Summary of last two weeks' work
- Running simulations:
- As Model A of Paper 1 but with
- ½ secondary mass (mostly complete) [Run 149]
- ¼ secondary mass (half completed) [Run 151]
- RLOF tests (partial runs, complete, need to analyze output)
- Separation of 109 Rsun, equal to Roche limit separation [Run 160]
- Separation of 73.5 Rsun, equal to 1.5 times the separation of Model A of Paper 1 [Run 161]
- Separation of 109 Rsun, with ambient density 10^{-10} g/cc instead of 6.7x10^{-9} g/cc [Run 162]
- Convergence tests for resolution and softening length (3 partial runs, each about half completed) [Runs 152, 153, 154]
- Convergence test for max refinement volume (full run, half completed) [Run 163]
- AGB test run (Pending) [Run 164]
- Box is the same as Model A of Paper 1
- AGB has radius 122 Rsun (instead of 48 Rsun for RGB)
- Primary mass 1.8 Msun (instead of 2.0 Msun)
- Primary core mass 0.53 Msun (instead of 0.37 Msun)
- Secondary mass 1.0 Msun identical to Model A of Paper 1
- Initial separation 124 Rsun
- Refined out to radius 1e13 cm= 144 Rsun (instead of 5e13 cm= 72 Rsun)
- Reduced the resolution to maxlevel=3 (from maxlevel=4)
- Chose ambient pressure P_amb=10^{4} dyne/cm^{2}—-expect to resolve scale height at surface
- Chose ambient density rho_amb=10^{-9} g/cm^{3}—-compare to surface density of 4x10^{-9} g/cm^{3}
- As Model A of Paper 1 but with
- Working on Xsede proposal:
- Decided that the main objective should be to run a simulation with an AGB star
- 8 times bigger box but degrade ambient resolution by the same factor
- Might have to refine only core of AGB and surface shell of AGB at maxlevel
- Hydrostatic atmosphere that matches to a uniform pressure-uniform density atmosphere at a certain radius, to avoid larger ambient density/pressure
- Could explore dependence on secondary mass again
- And/or could try 3-body problem
- Use about ¼ of time to do convergence tests
- Decided that the main objective should be to run a simulation with an AGB star
- Plan for papers (not including work on recombination and dust led by Amy):
- Energy/envelope unbinding paper (November)
- Jets (~6 months)
- Dependence on secondary mass (~9 months)
- Energy and envelope unbinding
- Drag force
- Convergence tests
- Simulation with AGB star (~12-15 months)
- Energy and envelope unbinding
- Drag force
- Comparison with RGB simulations
- Possibly dependence on secondary mass (if resources permit)
- Three-body problem (if resources permit)
- RLOF or RLOF+CEE with RGB/AGB (let's see)
Ivanova+2013 equation 3:
New equation suggested by us:
Run 143 (Model A of Paper I) has initial separation
. The Roche limit radius for as in our case is .Run 164 (AGB) has initial separation
. The Roche limit radius for the same secondary mass as in the RGB run is .Then at what value of
should the envelope be completely unbound, for a given value of ?RGB (lambda=1.3) | ||||
Ivanova+2013 with | ||||
Ivanova+2013 with | ||||
New equation with | ||||
New equation with |
AGB (lambda=0.9) | ||||
Ivanova+2013 with | ||||
Ivanova+2013 with | ||||
New equation with | ||||
New equation with |
So the final separation needed for envelope removal is almost 4 times larger for the AGB!
Note also that the final separation is roughly given by the following asymptotic formula (
):,
where
. This formula also says that should go up even more if we make larger.But it might take a lot longer to get there than for the RGB case. We need to estimate how long it would take in simulation days from the preliminary test run 164 and also from analytic estimates (I will try to do this today). We will use this estimate to set what computing resources we ask for.
COMMON ENVELOPE SIMULATIONS
Summary of last week's work
- Worked on alpha prescription stuff for energy paper and discussed with Eric.
- Continued running simulation with secondary mass halved (run 149) separation vs time plot
- Started running new simulations to explore effects of softening length and resolution.
- This consisted of 3 new simulations restarted from frame 72 (t=16.7 days) of run 143 (Model A of Paper I), where the softening length and smallest resolution element had been halved.
- do not halve softening length nor double resolution (Run 152)
- halve softening length but but do not double resolution (Run 153)
- do not halve softening length but double resolution (Run 154)
- This consisted of 3 new simulations restarted from frame 72 (t=16.7 days) of run 143 (Model A of Paper I), where the softening length and smallest resolution element had been halved.
- Discussed jets with Jonathan.
- Ran low resolution simulations to explore the possibility of simulating Roche lobe overflow (leading up to common envelope evolution).
Energy paper
Ivanova+2013 equation 3:
New equation suggested by us:
Run 143 (Model A of Paper I) has initial separation
. The Roche limit radius for as in our case is .
With
LHS | RHS | |
Ivanova+2013 with | 1.9 | 0.23 |
Ivanova+2013 with | 1.9 | 0.64 |
New equation with | 3.1 | 1.23 |
New equation with | 2.4 | 1.09 |
So one would never expect the envelope to be completely unbound at this point in the simulation because this would require
. Therefore, that the envelope is not completely unbound at the end of the simulation is consistent with the alpha prescription.Then at what value of
should the envelope be completely unbound, for a given value of ?Ivanova+2013 with | ||||
Ivanova+2013 with | ||||
New equation with | ||||
New equation with |
So if we say that there are no extra energy sources or sinks and take the most optimistic (but not very realistic) case
, then the final separation is predicted to be about . Compare this to the softening radius at the end of the simulation of .In the probably more realistic case of
, we would have a final separation of about . This would imply a merger if the secondary is a main sequence star, but not necessarily if the secondary is a white dwarf.An AGB star is less tightly bound so would be more promising for ejecting the envelope.
Roche lobe overflow tests
Face-on density (zoomed in) (Run 156 a=109Rsun), equal to theoretical Roche limit separation for this system.
Face-on density (zoomed in) (Run 157 a=98Rsun)
Face-on density (zoomed in) (Run 159 a=73.5Rsun)
Face-on density (zoomed in) (Run 158 a=49Rsun)
The sound-crossing time for the RG is about 8 days or ~35 frames. This is the approximate time the star would take to deform to fill the Roche lobe.
While this deformation is happening, the secondary accretes from the ambient medium. The freefall time onto the point mass
is . So in 5 days, or about 20 frames, this corresponds to gas being accumulated out to a sphere of radius from the secondary, corresponding to about of gas falling onto the secondary from the ambient medium ( grams/cc).There are numerical problems in the low resolution runs that cause the RG to bulge out opposite to the direction of motion along the orbit.
It is probably worth starting a full resolution run to see what happens. But at which separation?
COMMON ENVELOPE SIMULATIONS
Plan for XSEDE proposal 2018
Summary of current allocation
- A bit less than 130,000 node hours remain.
- It is estimated (still very rough though) that we can complete about 15 runs like the non-accretion run from paper I (run 143).
- We have thus far used about 23% of the allocation so about 77% remains.
- To get this down to <50% by Oct 15, we need to use up about 27% of the full allocation or a little over 1/3 of what remains.
- This translates to about 5-6 runs by Oct 15.
Plan for now until Oct 15
The following runs do not involve major changes to the code so can hopefully be done in this time frame:
- Test dependence on secondary mass (parameter regime 1).
- Run 149: As 143 but with secondary mass smaller by a factor of 2, i.e. m2=0.5 Msun instead of 1.0 Msun (running).
- Test dependence on secondary mass (parameter regime 2).
- Run 151: As 143 but with secondary mass smaller by a factor of 4, i.e. m2=0.25 Msun instead of 1.0 Msun (submitted).
- Test convergence with respect to softening length and resolution.
- Run 152: As 143 restarted from frame 72, which is the frame where the softening radius and smallest resolution element were halved in 143, but now do not halve the softening length nor the resolution element (submitted).
- As 152 but halve softening length only.
- As 152 but halve smallest resolution element only.
- Roche lobe overflow.
- Put secondary at Roche limit separation.
- Must think about refinement.
- Increase q to 1 both to reduce Roche limit separation and also increase .
- Test dependence on initial spin of the RG.
- Repeat run 143 but now initialize RG in solid body rotation at the initial orbital angular velocity.
- Test convergence with respect to size of refinement region (parameter regime 1).
- Repeat run 143 using a more liberal choice for the refinement radius for each interval (c.f. Fig 3 in Paper I)
- Test convergence with respect to size of refinement region (parameter regime 1).
- Based on the results of the above, repeat run once more using either an even more liberal refinement radius or else a refinement radius that is more conservative than run 143.
- Another possibility is to restart run 143 from the end of the simulation at t = 40 days. This is easy to do but the drawback is that material will flow out of the box soon after.
Plan for Oct 15 to Dec 31
We can expect about 10 more runs equivalent to run 143 but I provide 15 possibilities below:
Questions to answer for jet project:
- How does the jet affect the morphology of the envelope?
- How does the jet affect the ejection of the envelope?
- How does the jet evolve, does it get quenched?
- What is the dependence of these questions on when the jet gets turned on?
- What is the dependence on accretion rate?
- Opening angle?
- Simulate CEE with a jet from the secondary (parameter regime 1) (Restart from run 143)
- Simulate CEE with a jet from the secondary (parameter regime 2) (Restart from run 143)
- Simulate CEE with a jet from the secondary (parameter regime 3) (Restart from run 143)
- Simulate CEE with a jet from the secondary (parameter regime 4) (Restart from run 143)
- Simulate CEE with a jet from the secondary (parameter regime 5) (Restart from run 143)
- Simulate RGB/AGB star in improved simulation including (part I of a long run)
- larger box (but smaller ambient resolution): the larger the box the longer we can run it before material starts leaving the box,
- ambient consisting of hydrostatic atmosphere surrounded by very low density and low pressure gas,
- start from Roche limit separation (optional)
- Simulate RGB/AGB star in improved simulation including (part II of a long run)
- Simulate RGB/AGB star in improved simulation including (part III of a long run)
- Simulate RGB/AGB star in improved simulation including (part IV of a long run)
- Simulate RGB/AGB star in improved simulation including (part V of a long run)
- Triple system involving a planet or tertiary star orbiting the secondary… (parameter regime 1)
- Triple system involving a planet or tertiary star orbiting the secondary… (parameter regime 2)
- Triple system involving a planet or tertiary star orbiting the secondary… (parameter regime 3)
- Triple system involving a planet or tertiary star orbiting the secondary… (parameter regime 4)
- Triple system involving a planet or tertiary star orbiting the secondary… (parameter regime 5)
Storage
- The size of run 143 data is about 10 TB.
- To do 15 more runs like 143 would require 150 TB.
- This would cost an additional $15,000 per year on bluehive which is unaffordable.
- We need to look for other options like free space somewhare on blue hive.
- We probably need to keep only ½ of the data, i.e. every second chombo file.
COMMON ENVELOPE SIMULATIONS
Summary of last week's work
- Reran first part of simulation with secondary mass halved, after deriving orbital parameters and carefully testing the initial orbit p_mult_143_149.png
- Worked on energy paper (on the section dealing with the energy prescription with en.pdf. formulation)
- Worked with Thomas (Orsola's student) to set up an AGB star for CE simulations.
- Worked with Amy to debug the CE-wind with self-gravity simulation.
All of these are ongoing—-I expect to report more progress next Monday.
COMMON ENVELOPE SIMULATIONS
Working on first draft of energy paper
http://www.pas.rochester.edu/~lchamandy/CE_papers/Energy/en.pdf
COMMON ENVELOPE SIMULATIONS
Working on first draft of energy paper
http://www.pas.rochester.edu/~lchamandy/en.pdf
Future plans and how to use our remaining computer time
COMMON ENVELOPE SIMULATIONS: Movie Library for Paper 1
New Work
- Revision of paper
- Progress on energy project with Yisheng, Eric
- Progress on recombination/dust project with Amy
- Movies of simulations from paper 1
Some new notes on energy in CE simulations
notes on energy and envelope ejection in common envelope simulations
Movies corresponding to figures in paper
All movies are in the reference frame corotating about the secondary with the instantaneous orbital angular speed of the particles, and with the secondary at the center.
Figure 1:
Face-on density (Model A no subgrid accretion)
Figure 2:
Face-on density (Model B Krumholz accretion)
Figure 4:
Edge-on density (Model A no subgrid accretion)
Edge-on density (Model B Krumholz accretion)
Edge-on density (zoomed in) (Model A no subgrid accretion)
Edge-on density (zoomed in) (Model B Krumholz accretion)
Figure 6:
Tangential velocity with velocity vectors (Model A no subgrid accretion)
Tangential velocity with velocity vectors (Model B Krumholz accretion)
Extra Movies
Temperature (Model A no subgrid accretion)
Temperature (Model B Krumholz accretion)
Sound speed (Model A no subgrid accretion)
Sound speed (Model B Krumholz accretion)
Mach, lab frame (Model A no subgrid accretion)
Mach, lab frame (Model B Krumholz accretion)
Mach, frame corotating about secondary (Model A no subgrid accretion)
Mach, frame corotating about secondary (Model B Krumholz accretion)
Side-by-side comparison of Models A (left) and B (right) from Paper 1
Face-on density
Edge-on density
Edge-on density, zoomed
Tangential velocity
Temperature
Sound speed
Mach in lab frame
Mach in frame corotating about secondary
Next steps
- Submit revision?
- Testing Jonathan's new conservative jet prescription
- Explore jet parameter space with Bondi accretion flow
- Set up jet for CE simulation
- Restart CE simulation with imposed jet
COMMON ENVELOPE SIMULATIONS
Here are some notes on putting a jet into the simulation.
Movies of outflow added to a Bondi accretion setup with
Computational units are: density scale = cm^{-3}, time scale = yr, length scale = AU
1) Fixed grid outflow with particle at center.
- Solution without outflow (not shown) adjusts and then is stable, approximating Bondi accretion.
- Subgrid accretion routine is set to Krumholz.
- Fixed grid, resolution 64^{3}
- Box dimension L = 10 AU
- Ambient density 10^{5} cm^{-3}
- Ambient temperature 370 K
- Outflow parameters are:
Particle%Feedback%efficiency=1d0 —> all accreted mass goes into outflow
Particle%feedback%radius=16 —> outflow set every time step in bipolar regions of radius 16 cells
Particle%feedback%rsurface=0.01d0 —> jet assumed to be launched from 0.01 solar radii from the secondary (white dwarf surface)
Particle%feedback%jefficiency=1d0 —> all of accreted angular momentum goes into outflow (so none into spin of secondary)
Particle%feedback%collimation=pi/12 —> collimation angle
Particle%feedback%T=0d0 —> made jet have zero temperature
Particle%feedback%p=1 —> parameter that determines smoothness of jet edges
particle%feedback%spin_axes=(/0d0,0d0,1d0/) —> forces outflow axis to be z axis
particle%feedback%vfact=2d0 —> jet assumed to be launched with 2 times the Keplerian speed at launch radius
xz slice of density with velocity vectors
2) Next increased box size by factor of 4 to L = 40. Base resolution 64^{3} and 2 levels AMR. Tested solution first without outflow. Not completely stable. Not surprising because accretion radius of 4 cells is now smaller with finer resolution around particle, so Krumholz underestimates Bondi accretion rate more.
xz slice of density
xz slice of density with velocity vectors
3) Same but now added outflow and initialized particle and gas with constant velocity.
xz slice of density
xz slice of density with velocity vectors relative to moving frame
4) Similar but now initialize particle with constant velocity but not gas.
xz slice of density
xz slice of density with velocity vectors
Discussion
- The outflow prescription seems to work okay.
- As a next step, I could go to a CE setup but in low resolution.
- Control case would have no outflow but Krumholz accretion turned on (Krumholz just used for testing purposes, but we will change subgrid accretion model).
- Then same thing but with outflow also turned on.
COMMON ENVELOPE SIMULATIONS
New Work
- Updates to the paper
- New movies corresponding to figures in paper
Update on Paper
Here is the pdf so far.
- Address comments
- Decide the way forward.
- Next paper?
Movies corresponding to figures in paper
Figure 1:
Face-on density (Model A no sub-grid accretion)
Figure 2:
Face-on density (Model B Krumholz accretion)
Figure 4:
Edge-on density (Model A no sub-grid accretion)
Edge-on density (Model B Krumholz accretion)
Edge-on density (zoomed in) (Model A no sub-grid accretion)
Edge-on density (zoomed in) (Model B Krumholz accretion)
Figure 6:
Tangential velocity with velocity vectors (Model A no sub-grid accretion)
Tangential velocity with velocity vectors (Model B Krumholz accretion)
COMMON ENVELOPE SIMULATIONS
New Work
- Update on Yisheng's work
- Update on Paper
Update on Yisheng's work
- Detailed study of initial conditions. Here are the notes.
- Improving graphs
- Sampling rate for inter-particle separation
- Mark locations of periastrons and apastrons on accretion vs time graphs
Update on Paper
Here is the pdf so far.
- Explanation for inter-particle separation graph.
- Other comments I inserted in the text (about issues to address).
- Decide the way forward.
- Next paper?
COMMON ENVELOPE SIMULATIONS
New Work
- Corrected the main figures from last post
Plots relating to the force
- The quantity being plotted is
where (repeated from last post):
- and are the potentials due to the primary (RG core) and secondary (companion), respectively. Actually, inside the softening radius, we have also corrected for the spline potential by including extra terms, not written out here;
- is the potential of the gas;
- is the centrifugal potential in the frame corotating with the particles' orbit. Here is the angular velocity of this frame with respect to the lab frame and is the distance from the secondary in the x-y plane;
- is the potential due to the shift of the rotation axis of the rotating frame from the CM to the secondary;
- Last post, there was an error in which had the incorrect sign.
- is the Coriolis term;
- is the angular velocity of gas about the secondary in the frame corotating about the secondary with the instantaneous orbital angular velocity of the particles, and is the centrifugal force due to the motion of the gas IN THE COROTATING FRAME (i.e. we have already accounted for the rotation of the reference frame, but here we account for the rotation of the gas within the rotating reference frame);
- We normalize with respect to , that is, the magnitude of g due to the secondary alone at the location of the primary.
- Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right.
- Comments (itmes repeated from last post):
- Vectors have been ommited from inside the softening circle of the secondary for clarity as the magnitudes were large in some cases.
- In both cases, some of the gas around the secondary is accelerating inward while some is accelerating outward.
- So it is probably incorrect to conclude that gas is bound to the secondary.
Plots relating to the energy
- The quantity being plotted in pseudocolor is the Bernouilli parameter , where the first term is the specific kinetic energy, the second term is the specific enthalpy ( ), and the last term is the external potential.
- Since and , we have . Here is just the total energy density minus the bulk KE density of the gas.
- For plots in the frame rotating around the secondary, we set (so exclude the gas).
- For plots in the frame rotating around the particle center of mass, we set ,
where
.- Contours show . Contour levels are the same in each panel.
- Both pseudocolor and contours are normalized by .
In the frame rotating around the particle CM:
In the frame rotating around the secondary:
COMMON ENVELOPE SIMULATIONS
New Work
- Figure of radial force/unit mass (=instantaneous acceleration) pseudocolor with force/unit mass vectors overplotted.
- Figure of Bernouilli parameter pseudocolor with contours of potential overplotted.
Plots relating to the force
- The quantity being plotted is
where
- and are the potentials due to the primary (RG core) and secondary (companion), respectively. Actually, inside the softening radius, we have also corrected for the spline potential by including extra terms, not written out here;
- is the potential of the gas;
- is the centrifugal potential in the frame corotating with the particles' orbit. Here is the angular velocity of this frame with respect to the lab frame and is the distance from the secondary in the x-y plane;
- is the potential due to the shift of the rotation axis of the rotating frame from the CM to the secondary;
- is the Coriolis term;
- is the angular velocity of gas about the secondary in the frame corotating about the secondary with the instantaneous orbital angular velocity of the particles, and is the centrifugal force due to the motion of the gas IN THE COROTATING FRAME (i.e. we have already accounted for the rotation of the reference frame, but here we account for the rotation of the gas within the rotating reference frame);
- We normalize with respect to , that is, the magnitude of g due to the secondary alone at the location of the primary.
- Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right.
- Comments:
- Vectors have been ommited from inside the softening circle of the secondary for clarity as the magnitudes were large in some cases.
- It would be much easier to simply plot the instantaneous acceleration instead of computing it, but we do not have this quantity available in the chombo.
- In both cases, some of the gas around the secondary is accelerating inward while some is accelerating outward.
- So it is probably incorrect to conclude that gas is bound to the secondary.
- What we need are streamlines (or actually, pathlines) https://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlines to really get a sense for what kinds of orbits the fluid is making in the vicinity of the secondary.
- Below are the plots of the various contributions to the force per unit mass, first for run 143 (no sub-grid accretion). In order from left to right, we have
- Pressure term ;
- Gravity terms ;
- Gravity terms (excluding gas);
- Gravity terms (lab frame);
- Centrifugal term .
- Coriolis term ;
- Now for Run 132:
Plots relating to the energy
- The quantity being plotted in pseudocolor is the Bernouilli parameter , where the first term is the specific kinetic energy, the second term is the specific enthalpy ( ), and the last term is the external potential.
- Since and , we have . Here is just the total energy density minus the bulk KE density of the gas.
- We set (so exclude the gas).
- Contours show .
- Both pseudocolor and contours are normalized by .
- Comments:
- Contours show the values -2.5, -2.25, -2, -1.75, -1.5, -1.25. The contour -1 is plotted but does not appear, which means that the values are < -1 everywhere on the plot.
- The divide gives a sense for which gas is bound to the particles (red) or unbound (blue).
- The gas in the vicinity of the particles is mostly bound.
- To get a sense of whether the gas is bound to the secondary, in particular, we can refer to the Roche potential contours.
- Note that alternatively we could have omitted from the calculation, to try to get a sense of whether material is bound to the secondary (rather than to both the secondary and primary together). However, this would not really be correct because it would imply that any "red" material near the primary was bound to the secondary when in reality it would be more tightly bound to the primary than to the secondary.
Discussion
- I think it might be worth including three plots in the paper (for each of the two runs). All are in the frame corotating with the particles' orbit and rotating around the secondary:
- Tangential velocity (blue/red pseudocolor), normalized with Keplerian speed for a point potential, with velocity vectors overplotted (see Feb 15 post).
- Force/unit mass (ie. instantaneous acceleration) along radial direction (blue/red pseudocolor, normalized) with acceleration vectors overplotted (this post).
- Bernouilli parameter (blue/red pseudocolor, normalized) with external potential overplotted (this post).
- We should also have the pathlines, ideally, but if this is not possible, then streamlines, to get a better sense of the trajectory of the gas near the secondary.
Next steps
- Finalize the remaining plots and insert into paper.
- ADAF papers; read and discuss.
- Text of paper.
- Explore energy conservation in the simulations.
- Is there enough power to drive a jet through the envelope? Estimates.
COMMON ENVELOPE SIMULATIONS
New Work
- Generated skeleton of paper including most of the "polished" figures and put on sharelatex.
- "Settled" the "enthalpy vs. thermal energy" issue and also the "gas bound to itself" issue with Eric's help.
- Wrote up method to calculate velocities in the corotating frame.
- Made polished plots of edge-on (to the orbital plane) views of gas density at two different zoom levels and inserted into paper.
- Made zoomed in plots of face-on gas density similar to the edge-on ones.
- Plots of the potential in the frame corotating with the particle orbit, centered on the companion, with and without the gas potential.
- Plots of , which relates to the force per unit mass along the radial direction with respect to the companion.
- Plot of square of tangential velocity with respect to the companion, in the corotating frame, but normalized with respect to .
Skeleton of paper
Here is the pdf so far.
"Enthalpy vs. thermal energy" and "gas bound to itself" issues
- Enthalpy vs thermal energy
- When assessing whether the gas is bound we evaluate whether a given quantity relating to the gas energy density is >0 (unbound) or <0 (bound).
- The question arose whether it should be the internal energy density that enters the equation (more specifically, the internal translational kinetic energy density of the gas particles related to the gas kinetic temperature), or the enthalpy per unit volume (the work per unit volume required to place a fluid element at that position within its environment, equal to the thermal energy density + the pressure).
- Since the pressure can also contribute to the outward motion of the gas (work against gravity), it makes sense to include the enthalpy per unit volume in the calculation, not just the thermal energy per unit volume.
- Gas bound to itself
- Similarly, the question arose whether to include the negative contribution of potential energy arising from gas self-gravity.
- On one hand, one would think yes because this gravity contributes to the binding of the gas-particle system.
- However, some of the gas may be unbound and escape, and the binding energy associated with this unbound gas should not contribute. For example, for a gas parcel that is bound to itself but not bound to the rest of the system, the potential energy associated with its self-gravity should not be included.
- To resolve this conundrum it helps to be precise about what we really want to call "bound". What we are probably most interested in is whether gas is bound to the particles (the RG core and companion). We are not as interested in whether the gas is bound to itself. Therefore, it is best NOT to include the potential energy due to the gas self-gravity.
The conclusion then is that 1) we should consider the enthalpy per unit volume rather than just internal translational kinetic energy per unit volume, and 2) we should consider the potential energy associated with the gas-particle interaction only, not including the gas-gas interaction. Both of these choices work in the direction of making the gas less "bound".
Method to calculate velocities in corotating frame
Here are some notes.
Edge-on plots of density
- Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right. Units are grams/cm^{3}. Color bar is the same for both plots.
- Zoomed-in with different color scheme. Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right. Units are grams/cm^{3}. Color bar is the same for both plots.
New face-on plots of density
- As above but now face-on. Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right. Units are grams/cm^{3}. Color bar is the same for both plots.
New face-on plots of potential
- Total potential in frame rotating with orbital angular velocity and centered on the companion in cgs units. Includes gas potential. Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right.
- Same as above but NOT including gas potential in cgs units. Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right.
- Ratio of gas potential to total potential not including gas potential in cgs units. Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right.
- Comments: the gas potential contributes at about the 20% level at most.
Plots relating to the force
- The quantity in cgs units. Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right.
- Comments: Here includes the particle and gas gravitational potentials in the frame corotating with the orbit and centered on the companion. The force therefore includes the centrifugal force due to the rotating frame. HOWEVER, it does not include the Coriolis force/unit mass .
- Positive values indicate that the radial force with respect to the companion is directed outward (in the corotating frame), while negative values indicate that it is directed inward (in the corotating frame).
Plot of tangential velocity squared (with respect to the companion) normalized against the quantity plotted above (with a minus sign inserted)
- The quantity in cgs units. Run 143 (no sub-grid accretion) on the left and Run 132 (Krumholz sub-grid accretion) on the right.
- Comments: Values are plotted from 0 to 1. Below 0, the radial force is outward (white). The colored region is for inward radial force. (But note that the colored region does have parts that are almost white, which is a drawback of the color scheme used).
- For circular motion we would expect this quantity to be equal to unity because the centrifugal force in the frame of a moving gas parcel would balance the inward radial force. Therefore < 1 suggests accretion while > 1 suggests outflow.
- However, we have not considered the radial or vertical gas motions, so it is not clear from the above quantity alone whether gas will end up moving toward or away from the companion.
- Moreover, we have neglected the Coriolis force , which should be included in the analysis. Positive (counter-clockwise) values of would produce an outward radial acceleration.
Next steps
- Finalize the remaining plots and insert into paper.
- ADAF papers; read and discuss.
- Text of paper.
- Explore energy conservation in the simulations.
- Is there enough power to drive a jet through the envelope? Estimates.
COMMON ENVELOPE SIMULATIONS
New Work
- Plotted v_phi/v_Kepler and v_phi/c_s in frame that is corotating with instantaneous particle orbit, centered on particle 2 (the companion).
- Plotted potential in the corotating frame with coordinate origin at particle 2.
- Added a section to "en.pdf" energy notes to include the potential in a rotating frame.
Plots of velocity relative to particle 2 in corotating frame
- Plots below show a slice through the companion, parallel to the orbital plane, with companion at the center and RG core at the left.
- Each particle is surrounded by a green circle with radius equal to the instantaneous softening length.
- Plots are in the frame corotating with the orbit (instantaneous value of ).
- Pseudocolor represents where both numerator and denominator are relative to the companion (first plots), or , with relative to the companion.
Run 143 (no accretion):
- v_phi relative to particle 2 in corotating frame normalized by Keplerian circular speed (Keplerian speed is uncorrected for spline potential):
- same plot but different color scheme:
- normalized by sound speed:
Run 132 (Krumholz accretion):
- normalized by Keplerian circular speed (Keplerian speed is uncorrected for spline potential):
- same plot but different color scheme:
- normalized by sound speed:
Plots of potential in corotating frame with origin at particle 2
- Potential does not include that of the gas (Roche potential).
- Potential is normalized to , where and is the interpartical distance.
- Note that is almost equal to from Kepler's 3rd law, but not quite since that would ignore the effect of gas on the particle orbit.
- Contours are at -3 to -1.25, in spacings of 0.25.
- Run 143 (no accretion):
- Run 132 (Krumholz accretion):
Updated notes on energy, with the last section just added
en.pdf
Next steps
- Edge-on plots of density and velocity.
- ADAF papers; read and discuss.
- Begin draft of paper.
COMMON ENVELOPE SIMULATIONS
New Work
- Plotted separation vs time for runs 132 (Krumholz accretion) and 143 (no accretion) on the same plot, with orbits as insets.
- Plotted accreted mass and accretion rates for runs 132 and 143 up to t=40 days.
- Accretion radius in Krumholz model: discussion.
Orbital separation with time and orbit
- Below is the orbital separation as a function of time for run 143 (no accretion) in solid blue, and run 132 (Krumholz) in dashed light blue.
- The solid red (dashed gold) line shows the radius of the maximally refined region for run 143 (132). Note that for run 132, the maxlevel refinement was within a sphere centered on the primary, while for run 143, it was initially within a sphere centered on the primary, but from frame 72 (t=16.7 days), the center shifts to the secondary. As well, for run 132, maxlevel refinement is also done inside a cylinder of height 20 Rsun and radius 20 Rsun centered on the secondary, until the time just before frame 215 (32.4 days). (Note that run 132 starts from frame 75 of a damping run, while run 143 starts from frame 0 without any damping having been applied.)
- The solid green (dashed light green) line shows the softening radius for the spline potential for run 143 (132).
- Inset: The trajectories of the RG core (red/gold) and companion (blue/light blue) are shown for runs 143 (left) and 132 (right). Green/light green circles show the softening radius at t=0, and for run 143, also at time t=16.7 days, when the softening radius was halved.
Accretion
- Below is the total mass contained inside a sphere centered on the companion as a function of time for run 143 (no accretion subgrid model), for spheres of four different radii (blue) and the corresponding accretion rates, obtained by differentiating the interior mass (red).
- Below is the accreted mass as a function of time for run 132 (Krumholz accretion model) in blue, and the corresponding rate in red.
Discussion about accretion radius in Krumholz accretion subgrid model (with Bo)
- In the discussion following equation (17) in Krumholz+04, we read:
- The most important sentence is: "In general, the softening length should be smaller than the size of the accretion region, to ensure that softening does not alter the rate at which gas crosses its boundary." Is this true for our run 132?
- In our case, I (unwittingly) left the accretion radius set to the default value, which is 4 grid cells.
- The softening radius is about 16-17 cells, kept constant for each simulation. This was intentionally set to a large number >10 to ensure that the flow near the particle is adequately resolved (Ohlmann+16a).
- However, we used a spline potential, while Krumholz+04 is referring to a Plummer potential.
- As mentioned in a footnote on page 64 of Ohlmann16_thesis, a Plummer softening length of unity is effectively equivalent to a spline softening length of 14/5=2.8 if we choose the softening length such that the spline and Plummer potentials have the same value at r=0. (I have checked this to be true.) This implies that the effective Plummer softening length used is actually ~6 grid cells.
- Therefore, our effective Plummer softening length is still greater (by 50%) compared to the accretion radius.
- This means that the accretion rate would be artifically reduced relative to the Krumholz accretion model.
- The Krumholz accretion is (i) based on the Bondi-Hoyle-Lyttleton theory, which is not really applicable in our case (Macleod+17b) and (ii) ignores pressure feedback onto the flow. For both of these reasons it probably overestimates the accretion rate.
- Thus, our model which (accidentally) reduces artificially the Krumholz rate by having an accretion radius < Plummer equivalent softening radius, is conservative/cautious in the sense that whatever features we find (e.g. accretion) disk would be expected to be more pronounced (stronger) if the full Krumholz model was used. Because in that case the accretion radius would be larger than the softening radius and the accretion rate would be higher.
Next steps
- Plot v_phi/v_Kepler and v_phi/c_s in the frame corotating with the orbit, and adjust vectors and binding energy contours accordingly.
- Edge-on plots of density and velocity.
- Read ADAF papers.
- Start writing paper?
COMMON ENVELOPE SIMULATIONS
New Work
- As last post but now for run 132 (Krumholz accretion).
New Plots of run 132
The binding energy contours are for the binding energy relative to the companion.
The contours are -0.5 (grey), -0.25 (light grey), 0 (white), 0.25 (thin line, light grey).
That is, (i) the kinetic energy density is calculated using the velocity in the frame of the companion instead of the box frame,
and (ii) the RG core is not included in the calculation of the gravitational potential energy density.
- The normalized binding energy, with extrema at -1 and 1, is given by:
- Below are the same plots but with an unsaturated color scheme:
- Below are the same plots but zoomed out, with slightly different scaling for vectors:
- Below are color plots of the binding energy relative to the companion, since color is easier to understand than contours, at different zoom levels:
- Below: Very zoomed out version, with left plot showing binding energy relative to the companion and right plot showing binding energy relative to lab frame (copied from the last post):
- Below: Same view as above but showing density (left) and temperature (right), for comparison
- Below: Density at t = 0, 10, 20, 30 and 40 days
Next steps
- Separation vs time plot for both runs on the same graph.
- Plot(s?) showing orbits of both runs.
- Polish accretion rate plots for both runs and redo plot for run 132 with higher time resolution.
COMMON ENVELOPE SIMULATIONS
New Work
- Explored the case of binding energy relative to the companion, and plotted several figures.
- Snapshots of density at various times.
New Plots of run 143
The plots below are similar to those from the last post but with one main difference:
the binding energy contours are for the binding energy relative to the companion.
The contours are -0.5 (grey), -0.25 (light grey), 0 (white), 0.25 (thin line, light grey).
That is, (i) the kinetic energy density is calculated using the velocity in the frame of the companion,
and (ii) the RG core is not included in the calculation of the gravitational potential energy density.
- The normalized binding energy, with extrema at -1 and 1, is given by:
- Below are the same plots but with an unsaturated color scheme:
- Below are the same plots but zoomed out, with slightly different scaling for vectors:
- Below are color plots of the binding energy relative to the companion, since color is easier to understand than contours, at different zoom levels:
- Below: Very zoomed out version, with left plot showing binding energy relative to the companion and right plot showing binding energy relative to lab frame (copied from the last post):
- Below: Same view as above but showing density (left) and temperature (right), for comparison
- Below: Density at t = 0, 10, 20, 30 and 40 days
Next steps
- Produce the same figures but for run 132 which had Krumholz accretion.
- Separation vs time plot for both runs on the same graph.
- Plot(s?) showing orbits of both runs.
- Polish accretion rate plots for both runs and redo plot for run 132 with higher time resolution.
COMMON ENVELOPE SIMULATIONS
New Work
- Plotted circles for softening length around particles and new script to get softening length from chombo into VisIt.
- Calculated binding energy and plotted contours.
- Wrote general script that plots any pseudocolor, contours, and vector arrows along with softening circles.
- Polished plots and included the option of plotting in units of solar radii instead of cm.
Run 143:
- Similar to run 132 but with subgrid accretion turned off, twice larger box, resolution and softening length that evolve with time, less aggressive refinement, i.e. larger max refinement zones, and no relaxation (damping) run initially
Relaxation run: no relaxation run
First frame: 0
Last frame: 173
Total simulation time: 40 sim-days
Machine and partition: Stampde 2 normal
Number of nodes: 128 or 64, each with 68 (standard nodes) or 96 (skx nodes) cores
Total wall time: TBD
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=8e13 cm (1150 Rsun)
Max refinement level: 4 (frames 0 to 72), then 5 (frames 72 to 117)
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 4 levels AMR, frames 0 to 72), and 0.07 Rsun (8192^{3} cells, 5 levels AMR, frames 72 to 173)
AMR implementation: set by hand to have max level around RG core (frames 0 to 72) or companion (frames 72 to 173)
Max resolution zone: sphere around RG core, radius 5d12 cm (frames 0 to 46), radius 4d12 cm (frames 46 to 72), radius 3d12 (frames 72 to 103), radius 2.5d12 (frames 103 to 161), radius 1.75d12 (frames 161-173)
Buffer zones: 16 cells
Softening length: 2.4 Rsun (frames 0 to 72), 1.2 Rsun (frames 72 to 173)
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
DefaultAccretionRoutine=0 (no accretion)
New Plots of run 143
- All plots below show a slice through the companion, parallel to the orbital plane, with companion at the center and RG core at the left.
- Each particle is surrounded by a green circle with radius equal to the instantaneous softening length.
- Pseudocolor represents where both numerator and denominator are in the frame of the companion (first plot), or ,
with
in the frame of the companion (second plot).- Velocity vectors shown in the frame of the companion, with length scaled to vector magnitude.
- Contours show the values -0.5 (dark grey) and -0.25 (light grey) of the quantity
is the potential energy density, including self-gravity of the gas (which comes with a factor of ½ multiplying the gas potential to avoid double-counting), potential energy of gas-RG core system, potential energy of gas-companion system, but NOT potential energy of RG core-companion system. In other words, includes all potential energy EXCEPT for particle-particle term. Note that the potential being used for the particles is the actual spline potential, which had to be entered by hand. Also is the bulk kinetic energy density in the lab frame, while is the internal energy density in the lab frame. Note that the script also plots the contours -0.75, 0, 0.25, 0.5, 0.75, but they do not appear on the graph so the smallest value is >-0.75 while the largest is <0 for this part of the simulation box.
- Below is a similar plot to the first plot, showing , now zoomed out (with vectors and colors scaled differently).
- The contours for binding energy are -0.75 (dark grey), -0.5 (grey), -0.25 (light grey), 0 (white), 0.25 (dashed light grey).
- Below are color plots of the binding energy, since color is easier to understand than contours.
- Below is a zoomed out version.
- Below is a more zoomed out version, different color scheme.
- Below is a very zoomed out version, with two plots showing two different color schemes. Note that box was rotated so that the RG core was situated to the left of center.
Next steps
- Further polish the above plots (more contour levels? improve resolution of vector arrows?).
- Same plots for run 132 which had Krumholz accretion submodel.
- Separation vs time plot for both runs on the same graph.
- Plot(s?) showing orbits of both runs (possibly as inset on separation vs time graph)
- Plots showing face-on slice and edge-on (slice/projection?) of snapshots of density at various times.
- Polish accretion rate plots for both runs and redo plot for run 132 with higher time resolution.
- Line Integral Convolution using Jonathan's MatLab code.
COMMON ENVELOPE SIMULATIONS
New Work
- We solved the problem of mixing variables from different meshes (fluid and particle), which enables plotting e.g. fluid velocities relative to the companion.
- Extended simulation 143 to 40 days.
- Figured out how to make face-on movies in rotating frame (e.g. rotating along with orbit), and made movie of density.
- Made movie of density in frame of orbit with velocity vectors relative to the companion.
- Plotted circular velocity around the companion, as well as its ratios with the Keplerian circular velocity and with the sound speed.
Results (of new work, point by point from above)
- Apparently there exists a more robust way to do this involving Cross Mesh Field Evaluation or CMFE functions, but Baowei's "quick fix" works!
- Will not go beyond 40 days for now as it is a bit too expensive. Plan is to try to get away with less refinement in ambient region, and also to make central refinement zone smaller in volume. If results are the same, can then get away with this to do more runs.
- This allows us to avoid getting quite as dizzy when looking at the movies!
- We can now see the velocity field in the frame of the companion, rather than just in the lab frame.
- These are key quantities that we are trying to investigate. The ratios are less than unity near the companion but as high as ~0.5.
Run 143:
- Similar to run 132 but with subgrid accretion turned off, twice larger box, resolution and softening length that evolve with time, less aggressive refinement, i.e. larger max refinement zones, and no relaxation (damping) run initially
Relaxation run: no relaxation run
First frame: 0
Last frame: 173
Total simulation time: 40 sim-days
Machine and partition: Stampde 2 normal
Number of nodes: 128 or 64, each with 68 (standard nodes) or 96 (skx nodes) cores
Total wall time: TBD
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=8e13 cm (1150 Rsun)
Max refinement level: 4 (frames 0 to 72), then 5 (frames 72 to 117)
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 4 levels AMR, frames 0 to 72), and 0.07 Rsun (8192^{3} cells, 5 levels AMR, frames 72 to 173)
AMR implementation: set by hand to have max level around RG core (frames 0 to 72) or companion (frames 72 to 173)
Max resolution zone: sphere around RG core, radius 5d12 cm (frames 0 to 46), radius 4d12 cm (frames 46 to 72), radius 3d12 (frames 72 to 103), radius 2.5d12 (frames 103 to 161), radius 1.75d12 (frames 161-173)
Buffer zones: 16 cells
Softening length: 2.4 Rsun (frames 0 to 72), 1.2 Rsun (frames 72 to 173)
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
DefaultAccretionRoutine=0 (no accretion)
New Movies of run 143
- High zoom-in face-on slice, centered on companion, in reference frame of companion that is corotating with the instantaneous orbital angular velocity, with RG core always on the left.
face-on slice, movie rotating with orbit
- As above, density in the frame rotating with orbit, but now including velocity vectors drawn in the reference frame of the companion, but in the non-rotating frame:
New Snapshots of run 143
Left: v_phi relative to the companion. Face-on, slice through companion, view centered on companion with side of 4e12 cm. RG core is visible at the left. Right: same but zoomed out by factor of 4.
As above but now the ratio of v_phi to the Keplerian circular velocity.
Same as the zoomed-in plot above but different color scheme and range.
As above but now the ratio of v_phi to the local sound speed.
Inter-particle separation (up to 40 days)
Red horizontal lines show radius of maxLevel refinement region. Green horizontal line shows softening length (solid) or five times softening length (dashed) for each particle. Finest resolution is proportional to softening length, i.e. resolution improves by factor of 2 when softening length is reduced by factor of 2. Vertical lines show transition from one refinement radius to the next (dotted red, 5e12 to 4e12 to 3e12 to 2.5e12 cm), and transition from one softening radius to the next (green dashed, ~2.4 Rsun to ~1.2 Rsun)
Examples of streamline (left) and integral curve (right) plots for smaller run 125
Next steps
COMMON ENVELOPE SIMULATIONS
New Work
- New run (~half completed) with evolving softening length and resolution, larger box, and subgrid accretion turned off
- Enabled parallel HDF5 output and optimized code to get a bit of speed-up
- Started to analyze accretion onto the particles.
Results
- With accretion turned off, the accretion disk (torus) morphology is no longer present.
- It currently takes about 7000 node-hours on stampede2 skx nodes to complete 43 frames (10 days). But the speed actually varies because the radius of the refinement region as well as highest resolution are made to vary during the run. For comparison, our allocation for 2018 is for 166,000 node-hours. So if each run lasts for ~130 days, we are talking about no more than ~2 runs.
- The accretion rate increases montonically with radius of the control region, as might be expected. It approaches a state where Mdot oscillates around 0 for both the RG core and companion (the mass aroudn each particle stabilizes) BUT when the softening length is reduced, this seems to (artificially) cause more accretion to happen.
Run 143:
- Similar to run 132 but with subgrid accretion turned off, twice larger box, resolution and softening length that evolve with time, less aggressive refinement, i.e. larger max refinement zones, and no relaxation (damping) run initially
Relaxation run: no relaxation run
First frame: 0
Last frame: 117 (so far)
Total simulation time: 27 sim-days
Machine and partition: Stampde 2 normal (completed up to frame 117, or 27 sim-days)
Number of nodes: 128 or 64, each with 68 (standard nodes) or 96 (skx nodes) cores
Total wall time: TBD
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=8e13 cm (1150 Rsun)
Max refinement level: 4 (frames 0 to 72), then 5 (frames 72 to 117)
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 4 levels AMR, frames 0 to 72), and 0.07 Rsun (8192^{3} cells, 5 levels AMR, frames 72 to 117)
AMR implementation: set by hand to have max level around RG core (frames 0 to 72) or companion (frames 72 to 117)
Max resolution zone: sphere around RG core, radius 5d12 cm (frames 0 to 46), radius 4d12 cm (frames 46 to 72), radius 3d12 (frames 72 to 103), radius 2d12 (frames 103 to 117)
Buffer zones: 16 cells
Softening length: 2.4 Rsun (frames 0 to 72), 1.2 Rsun (frames 72 to 117)
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
DefaultAccretionRoutine=0 (no accretion)
Movies of run 143
1) Edge-on slice, centered at companion. Left: slice through both particles. Right: slice through P2 as viewed from direction of P1.
edge-on
2) Face-on slice, centered at companion.
face-on slice
3) Zoom-in face-on slice, inertial frame.
face-on slice
4) Full box face-on slice, inertial frame.
face-on slice, full box
Snapshots of run 143
Left: edge-on, slice through both particles (view centered on companion with side of 4e12 cm). Right: same but zoomed in by 4x.
Inter-particle separation
Red horizontal lines show radius of maxLevel refinement region. Green horizontal line shows softening length (solid) or five times softening length (dashed) for each particle. Finest resolution is proportional to softening length, i.e. resolution improves by factor of 2 when softening length is reduced by factor of 2. Vertical lines show transition from one refinement radius to the next (dotted red, 5e12 to 4e12 to 3e12 to 2.5e12 cm), and transition from one softening radius to the next (green dashed, ~2.4 Rsun to ~1.2 Rsun)
Mass accretion
Accreted mass with time (blue) and accretion rate with time (red) inside spheres around RG core (top) and companion (bottom) of different control radii. Plot of orbital separation is also shown for comparison. The bottom two plots are the same as the upper two plots except that data from an additional control radius is added, and individual points are not overplotted on the curve.
AA
Comments
- Accretion onto companion takes place within ~10 days and then the mass becomes fairly steady.
- Which control radius is most appropriate? The total mass accreted seems to be of order 0.01 Msun or 1% of the companion mass.
- There is an anticorrelation between the mass inside the sphere and the particle separation, which makes sense.
- There is a sudden increase in the accreted mass when the softening length is reduced by a factor of 2, especially for the RG core. This makes sense because the particle's gravity becomes stronger inside of the original softening radius. It's not clear how much of a role this is playing, and it will be interesting to see what happens when we halve the softening length again later in the run.
- Accretion rates onto the companion are of order 0.1 to 1 Msun/yr, which is super Edington, though not as high as what we were getting with Krumholz accretion turned on.
Next steps
- Complete the simulation up to at least 300 frames (about 70 days), using stampede2 skx nodes
- Analysis of:
- mass accretion with time
- angular momentum accretion with time
- Clean up presentation of movies/snapshots
- reference frames/views
- velocity vectors in particle frame
- units
- labels
To think about
- Had we been able to use an arbitrarily small softening radius from t=0, would the steady-state accreted mass be higher? If yes, then would the amount of gas left over in the envelope have been significantly affected? Would the orbit of the particles have been significantly affected?
- As a reminder, the strategy is to keep the number of resolution cells per softening length constant (~17), and to keep the number of softening lengths spanning the separation between the two particles at >5 (as done by Ohlmann 2016).
COMMON ENVELOPE SIMULATIONS
New Work
- Plotted mass accretion rate using mass inside spheres of different radii around point particles.
- Plotted mass budget with time.
- Plotted center of mass of various components with time.
Results
Next steps
- Compute drag force.
COMMON ENVELOPE SIMULATIONS
New Work
- Addressing a difficult issue with making VisIt plots.
- More analysis if high res run 132
- Movies centered on P2 that include velocity vectors (in inertial frame).
- Graph of accretion rate vs time.
Summary of New Results
- Extracting information from one of the particles to use in the variable expressions in VisIt is proving to be extremely non-trivial. Baowei is working on this, but it probably merits a workaround from within astrobear (defining each particle to be a separate subset of the mesh 'particles' might do the trick). Otherwise, as it stands now, one cannot plot within VisIt, for example, the gravitational potential due to a particle, or the gas velocity vectors in the reference frame of the particle.
- Results:
- Edge-on movies show a transient global vertical flow through the center of the torus that changes direction with time.
- The accretion rate from the Krumholz prescription is of order 1 Msun/yr, which seems too large.
Run 132 that uses twice as high resolution and 10x lower ambient pressure as previous runs:
Binary run 132 with double max resolution, lower resolution in ambient medium, 10x smaller ambient pressure than run 116
Relaxation run: 129
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time:
Machine and partition: Stampde 1 normal/Bluehive 2.5 standard/Bluestreak standard (completed up to frame 375, or 70 sim-days)
Number of cores: 1024
Total wall time: around 14 days (starting from frame 75 of relaxation run)
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 4 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 5e12 cm (71.87 Rsun) of primary center and within a cylinder of radius 20 Rsun and height 20 Rsun around secondary center. After t~11d (~frame 123) refinement radius around primary was halved to 2.5e12cm (36Rsun). After t~31d (frame 210) halved again to 1.25e12cm (18Rsun).
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
DefaultAccretionRoutine=2 (Krumholz)
New Movies of run 132
1) Edge-on , centered at P2, with velocity vectors (relative to inertial frame). Left: slice through both particles. Right: slice through P2 as viewed from direction of P1.
edge-on with velocity vectors (relative to inertial frame)
2) Face-on , centered at P2, with velocity vectors (relative to inertial frame).
face-on with velocity vectors (relative to inertial frame)
Comments:
- Movie (1) shows that there is a significant vertical flow of gas of order up to a few times 10^{7} km/s.
- The velocity vectors are in the inertial frame whereas the movie is in the frame of P2. However, the orbital velocity of P2 is at all times less than 10^{7} km/s so the largest vectors shown would be almost unchanged if they were plotted with respect to the velocity of P2. Moreover P2 has close to zero vertical velocity.
- The vertical flow is present only when the torus is present.
- Even when the torus is present, the vertical flow is intermittent.
- When the vertical flow is present it is located in the 'hole' of the torus where the density is low.
- When the vertical flow is present the flow is either upward below and above the orbital plane, or downward below and above the orbital plane, unlike a jet, which would be upward above the midplane and downward below.
- Roughly speaking, it switches from downward (frames 36-40) to non-existent to upward (frames 75-99) to non-existant to downward (frames 119-152) to non-existent to downward (frames 164-168).
- Movie (2) shows rotation around the secondary.
Next steps
- Compute accretion rate using alternative prescription using mass within a sphere centered at the secondary.
- Compute drag force.
- New simulation with a jet.
- Use outflow object in astrobear.
- Can take mdot from RT08/12.
- Velocity of order 100 km/s (or escape veloc at ~1 solar radius say).
- Half opening angle ~10 degrees.
- Plot CM position of system as a function of time.
COMMON ENVELOPE SIMULATIONS
New Work
- Notes about extracting diagnostics on energy from the simulation.
- Analysis of runs:
- 133 (as low res fiducial run 116 and more aggressive refinement run 125 but with even more aggressive refinement algorithm that de-resolves more of the `ambient' envelope).
- 135 (as 133 but with accretion turned off).
- 136 (as 133 but without any relaxation run, so no initial damping of velocities).
- 132 (similar to 125/133 but with maxlevel increased by 1 so twice higher resolution).
- 120 (similar to 116 but ambient density reduced by a factor of about 67).
Summary of New Results
- Procedure to extract energy diagnositics seems quite clear.
- Key results from runs are as follows:
- 133: Results are generally consistent with run 116 but the radius of the maxlevel refinement region around the primary point particle should be kept at a minimum of 2 times the particle separation.
- 135: Results are very similar to 133 with `accretion torus' morphology preserved in spite of accretion being turned off.
- 136: Results are very similar to 133. This means damping is probably unnecessary and can be omitted in future runs!
- 132: Results of this first higher resolution run are closer to the result of O+16a. Qualitatively similar to run 133.
- 120: Results are similar to those of run 116, but expansion and outer shock morphology of expanding envelope are slightly affected.
Notes on energy
I compiled the following notes. Thanks to Bo for a discussion on this:
Please see en.pdf
Notes on accretion and drag force (from last blog post)
Please see df.pdf
Analysis of runs 133, 135, 136, 132, 120
Old run 116 (for comparison)
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 168
Total simulation time: 3.36e6 s or ~4.2 RG sound-crossing times or 21.5 days (93 frames)
Machine and partition: Stampede 1 normal
Number of cores: 1024
Total wall time: 96 hours
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set automatically by AstroBear
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
DefaultAccretionRoutine=2 (Krumholz)
Old run 125 (for comparison)
Binary run 125 with longer simulation time and lower resolution in ambient medium
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 335
Total simulation time: 5.2e6 s or 60 days ~6.5 RG sound-crossing times or 60.2 days (260 frames)
Machine and partition: Bluehive standard
Number of cores: 120
Total wall time: about 8.5 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 50 Rsun of primary and within a cylinder of radius 50 Rsun and height 50 Rsun around secondary
Buffer zones: 0 cells (no buffer zones)
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
DefaultAccretionRoutine=2 (Krumholz)
Run 133 to test making maxlevel refinement zone decrease with time:
Binary run 133 similar to run 125 but now the refinement zone changes with time
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time: 84 days (up to frame 439)
Machine and partition: Bluestreak standard
Number of cores: 8192 (2 cores per task to increase memory)
Total wall time: 6 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 1.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
DefaultAccretionRoutine=2 (Krumholz)
Comparison between runs 125(top left), 133(top right), O+16a(bottom) (FROM LAST BLOG POST)
Comparison between run 125(left) and 133(right)
face-on zoom-in
face-on slice through secondary, extra zoom-in
viewed from P1 with P2 at center
slice through P1 (left side) and P2 (center)
Comments:
FROM LAST BLOG POST (BASED ON ORBITS ONLY):
- The runs are very similar but there is a slightly smaller final separation for run 125(less aggressive refinement)
- This suggests that our refinement criteria for run 133 was probably slightly too aggressive.
- However, the otherwise close agreement tells us that decreasing the refinement zone with time to be a sphere centred on p1 with radius ~2 times particle separation is reasonable.
NEW COMMENTS (BASED ON MOVIES):
- The runs are very similar but having max refinement in a sphere centered around the primary with radius 1.5 times the separation is a bit too aggressive. Could probably get away with about 2 times the separation.
Run 135 to test case where no accretion onto secondary is permitted:
Binary run 135 similar to run 133 but now DefaultAccretionRoutine=0 instead of 2. Also suppress generation of new sink particles.
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 900
Total simulation time: 191 days
Machine and partition: bluehive2.5 standard
Number of cores: 120
Total wall time: 2.8 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 1.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Default Accretion Routine=0 (No accretion)
Comparison between runs 133(top left), 135(top right), O+16a(bottom)
Comparison between run 133(left) and 135(right)
face-on zoom-in
face-on slice through secondary, extra zoom-in
viewed from P1 with P2 at center
slice through P1 (left side) and P2 (center)
Comments:
FROM LAST BLOG POST (BASED ON ORBITS ONLY):
- The results of 135 and 133 are similar, except:
- Run 135 (no accretion) has slightly smaller separation at a given time.
- Run 135 (no accretion) has slightly larger frequency of oscillations.
- Thus accretion cannot fully explain the discrepancy with the O+16a results, but removing accretion does make results slighly closer to those of O+16a, who did not have accretion.
- We must think more about accretion, but it is not making a huge difference at present.
NEW COMMENTS:
- Results are very similar. Most noticeable difference is that density is higher around the point particles for run 135, which does not have accretion. This is most clearly seen in the first, most zoomed out movie. This would be expected since gas is not removed by the particle.
- Particle creation was turned off for run 135 and this may explain some differences.
- Bottom line is that the gas flow around the secondary is very similar regardless of whether accretion is turned on. Even without accretion turned on, there is a torus structure with bipolar outflows.
- Note that for both runs the flow around the secondary undergoes a transition after about 75 days (frame 375) and the torus morphology is no longer present at this time. This corresponds to a particle separation of about 9 Rsun.
Run 136 to test how much relaxation makes a difference:
Binary run 136 similar to run 135 but now start from frame 0 of relaxation run 096 instead of frame 75 (so no damping).
Relaxation run: 096 (but no relaxation! Just start with initial profile
First frame: 0
Last frame: 18, running
Total simulation time: 4 days
Machine and partition: bluehive2.5 standard
Number of cores: 120
Total wall time: 21 hours, running
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 1.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Default Accretion Routine=0 (No accretion)
Comparison between runs 133(left) and 136(right)
Comparison between run 133(left) and 136(right)
face-on zoom-in
face-on slice through secondary, extra zoom-in
viewed from P1 with P2 at center
slice through P1 (left side) and P2 (center)
Comments:
- The results are very similar. This suggests that relaxation (velocity damping before the run) is NOT necessary. (It also confirms that most of the differences between runs 133 and 135 or 125 and 133 above are not due to the particle creation on run 133.)
Run 132 that uses twice as high resolution and 10x lower ambient pressure as previous runs:
Binary run 132 with double max resolution, lower resolution in ambient medium, 10x smaller ambient pressure than run 116
Relaxation run: 129
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time:
Machine and partition: Stampde 1 normal/Bluehive 2.5 standard/Bluestreak standard (completed up to frame 375, or 70 sim-days)
Number of cores: 1024
Total wall time: around 14 days (starting from frame 75 of relaxation run)
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 4 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 5e12 cm (71.87 Rsun) of primary center and within a cylinder of radius 20 Rsun and height 20 Rsun around secondary center. After t~11d (~frame 123) refinement radius around primary was halved to 2.5e12cm (36Rsun). After t~31d (frame 210) halved again to 1.25e12cm (18Rsun).
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
DefaultAccretionRoutine=2 (Krumholz)
Movies of run 132
face-on full box
face-on zoom-in
edge-on full box
edge-on zoom-in
face-on slice through secondary, extra zoom-in
viewed from P1 with P2 at center
slice through P1 (left side) and P2 (center)
Comparison of run 132 with Ohlmann+16a run:
Table
Comparison between run 133(left) and 132(right)
face-on zoom-in
face-on slice through secondary, extra zoom-in
viewed from P1 with P2 at center
slice through P1 (left side) and P2 (center)
Comparison between runs 133(top left), 132(top right), O+16a(bottom)
Comments:
FROM LAST BLOG POST (BASED ON ORBITS ONLY):
- The 1st minimum, 2nd maximum, and 2nd minimum are located roughly at separations, with softening length denoted as h:
- Run 088 (res=0.29Rsun, h=4.8Rsun, cells/h=17): 14 , 21 , 12 Rsun
- Run 125 (res=0.29Rsun, h=2.4Rsun, cells/h= 8): 13.5, 18 , 14.5 Rsun
- Run 132 (res=0.14Rsun, h=2.4Rsun, cells/h=17): 14 , 18.5, 11 Rsun
- O+16a (see above table) : 10 , 23.5, 11 Rsun
- These are found roughly at times:
- Run 088 (res=0.29Rsun, h=4.8Rsun, cells/h=17): 12.5, 15.5, 18 days
- Run 125 (res=0.29Rsun, h=2.4Rsun, cells/h= 8): 12.5, 14.5, 17 days
- Run 132 (res=0.14Rsun, h=2.4Rsun, cells/h=17): 12.5, 14.5, 17 days
- O+16a (see above table) : 13 , 16 , 19 days
- From the difference between 125 and 132, we conclude that h is not adequately resolved in run 125 (8.5 cells/h vs 17 cells/h)
- O+16a advocates >10 cells/h, so this is consistent with their result.
- In our case, we still cannot tell if 17 cells/h is sufficient.
- We could run 088 with double the resolution to see if it converges.
- The softening length of the point particles decreases with time in the O+16a simulation.
- It is not clear whether this procedure is justified.
- The main reason to improve the resolution with time may be to resolve the decreasing softening length.
- Therefore, if we keep the softening length constant, improving the resolution with time may not be necessary or productive.
- O+16a initially resolves the softening length by 20 cells, whereas we resolve it by 17 cells. They advocate >10 cells.
- At 120 days, O+16a resolves the softening radius by 35 cells.
NEW COMMENTS:
- Runs 133 and 132 are very similar for the first 15 days, or when the separation does not dip below 14 Rsun. This suggests that run 133 has inadequate resolution (or resolution per softening length) when the separation is <14 Rsun. Recall that both runs have softening length 2.4 Rsun but that run 133 has best resolution of 0.29 Rsun while run 132 has best resolution of 0.14 Rsun.
- The amplitude of the oscillations in the separation is about the same for run 132 and 133, both lower than that of O+16a.
- The final asymptotic separation is about 6 Rsun for run 132, compared to about 9 Rsun for run 133 and 4 Rsun for O+16a.
- The transition of the flow around the secondary happens earlier in run 132, at about 55 days (frame 320) compared to about 75 days (frame 375) in run 133. For run 132, this corresponds to a mean particle separation of about 7 Rsun, and for run 133, to a mean particle separation of about 9 Rsun. This supports the idea that the transition to a flow without the torus morphology is probably related to the separation. Further, it also supports the idea that such a transition is an artifact of having a too-low resolution per softening length, because the separation at onset is lower when the resolution is higher.
- There is a tendency for the particles to migrate in the direction of larger x and y. This is visible to a lesser extent in O+16a. This should be explained.
Run 120 to test importance of density of ambient medium
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 119
Total simulation time: 3.36e6 s or ~4.2 RG sound-crossing times or 10.2 days (48 frames)
Machine and partition: Stampede 1 normal
Number of cores: 1024
Total wall time: 6 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set automatically by AstroBear
Softening length: 2.4 Rsun
Ambient density: 1e-10 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
DefaultAccretionRoutine=2 (Krumholz)
Comparison between runs 116(left) and 120(right)
Comparison between run 116(left) and 120(right)
face-on
face-on different color bar limits
face-on slice through secondary, extra zoom-in
Comments:
- Results of the two runs are very similar.
- Differences are apparent at the interface of the ambient medium and envelope. Specifically, whisps of low density (Kelvin-Helmholtz unstable?) is visible outside the shock in low ambient density run 120. Also, by the end of the run, the envelope has expanded to a slightly larger size in the low ambient density case (the larger upper lobe is about 10% wider). The outer shock structure also shows minor differences.
- In the region around the point particles, differences are very minor. If our focus is on this region, we should not have a problem with the higher ambient density.
Discussion & conclusions
- The energy contributions can be readily analyzed from the chombo files, now that we have written down the important equations.
- Damping is not necessary (and introduces artifacts through grid effects). Can avoid it in future.
- Turning accretion off does not have a big effect on the flow. Since we do not understand how to model the accretion very well, perhaps we should keep it turned off for now. This would avoid the unphysical removal of pressure during the accretion process, as pointed out by Eric. In addition, the analysis of the drag force and energy budget would be simplified, and we could use the chombo files without having to output additional information. But we need to get an accretion rate to use for the jets, so ultimately we need to decide on an accretion model.
- We are able to be reasonably aggressive with refinement, but max level refinement in a sphere around the RG core with radius of 2 times the particle separation seems to be the limit, and trying to make this region even smaller introduces too much error.
- Ambient density does not seem to matter very much, but not sure yet with regard to binding and ultimate escape of envelope.
- High resolution run is consistent, qualitatively, with lower resolution run, but shows quantitative results closer to those of O+16a. Namely smaller final separation and orbital period than our lower resolution runs, but still not as small as O+16a, and amplitude of oscillations still lower than O+16a.
- There is a transition from a torus/thick disk structure to flow which does not show this structure. This transition seems to happen when the inter-particle separation reduces past a certain threshold. Futhermore, the threshold seems to be smaller for a better resolution, suggesting that this transition may be a numerical artifact due to a lack of resolution (or resolution per softening length).
- We should keep track of the center of mass of the system (gas+particles) which should not change. (Some gas leaves the box during the simulation and it might be worth increasing the box size or at least testing the effect of increasing it.)
Next steps
- We should now start to perform the analysis of the drag force and energy budget using results of run 132. We don't have accreted momentum outputted from that run, but we can still make do with the chombo files for most of the analysis.
- Simultaneously, we should be doing runs on stampede 2 and comet with our remaining resources, as well as on bluestreak and bluehive:
- Rerun from middle of 132 but with softening length now able to decrease with time. Need to increase AMR max level with time accordingly.
- New run like 132 but with initial RG spin equal to 95% of corotation to see what effect this has.
- New run like run 088 (low res, twice the softening length of more recent runs) but with twice as high resolution (i.e. same resolution as run 132) to test the convergence of results as the number of resolution cells per softening length increases (currently we know that 8 is insufficient and 17 may or may not be sufficient…here we would bump it up to 34).
Appendix
Movies of run 133
face-on zoom-in
face-on slice through secondary, extra zoom-in
viewed from P1 with P2 at center
slice through P1 (left side) and P2 (center)
Movies of run 135
face-on zoom-in
face-on slice through secondary, extra zoom-in
viewed from P1 with P2 at center
slice through P1 (left side) and P2 (center)
Movies of run 136
face-on zoom-in
face-on slice through secondary, extra zoom-in
viewed from P1 with P2 at center
slice through P1 (left side) and P2 (center)
Movies of run 120
face-on
face-on different color bar limits
COMMON ENVELOPE SIMULATIONS
New Work
- Notes about extracting diagnostics on accretion and drag force from the sim.
- Work on Xsede proposal.
- Improvement of high res run 132 to suppress unwanted extra refinement.
Summary of New Results
- Procedure to extract accretion and drag force diagnostics is now quite clear.
- Xsede proposal is coming along okay.
- Mysterious refinement to the max level was happening outside the volume for which the error flags are set to 1, slowing down the code. I couldn't prevent it by making changes to global.data so I decided to manually suppress it in problem.f90 (fortunately buffer zones turn out to be preserved).
Notes on accretion and drag force
Please see df.pdf
Discussion
- There are a few issues that need to be discussed going forward:
- Type of accretion (Federrath+10 seems more appropriate to me than Krumholz+04)
- I've turned off particle creation—is this fine?
- Should we reduce the softening length and enhance the resolution with time as the particles get closer, as done by Ohlmann+16a? This seems reasonable except
- do the gains justify the increase in resources?
- is it really meaningful/beneficial/physical to change a "fuzzy" point particle into a less fuzzy point particle while the sim is in progress?
- is it at least worth doing some tests to see what effect this would have?
- How important is it to use a larger box?
- Maybe it would be enough to test this by doing one large-box run for comparison?
Next steps
- Do for energy and angular momentum what has been done for accretion rate and drag force (see above notes).
- Analysis of runs 136 (no relaxation), 120 (low density ambient medium) and 132 (high-res run, in progress)
- New run with initial spin of RG at 95% Keplerian to test what difference this makes.
- New run like run 088 (low res, twice the softening length of more recent runs) but with twice as high resolution (i.e. same resolution as current run 132) to test the convergence of results as the number of resolution cells per softening length increases (currently we know that 8 is insufficient and 17 may or may not be sufficient…here we would bump it up to 34).
COMMON ENVELOPE SIMULATIONS
New Work
- Analysis of runs 132 (high res), 133 (like 125 of last post but max refinement volume that decreases with time), 135 (like 133 but no accretion).
- New run 136 to test importance of RG damping (in progress).
Summary of New Results
- Each of the runs analyzed gives useful information:
- Run 132 shows that doubling the resolution matters, e.g. increases frequency of oscillations, decreases final separation.
- Run 133 shows that it is quite reasonable to use max refinement within a radius min(5e12cm, 1.5*particle_separation) about the primary.
- Run 135 shows that accretion has a small effect on particle separation (decreases) and orbital frequency (increases).
- New run 136: first 4 days so far consistent with runs that start from "relaxed" RG.
Analysis of runs 133, 135, 132
Old run 088 (for comparison)
Binary run 088 with longer simulation time and lower resolution in ambient medium
Relaxation run: 062
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 161
Total simulation time: 20 days
Machine and partition: Comet normal
Number of cores: 1728 (2 cores per task to increase memory)
Total wall time: 4 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set internally by astrobear
Max resolution zone: n/a
Buffer zones: n/a
Softening length: 4.8 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Old run 125 (for comparison)
Binary run 125 with longer simulation time and lower resolution in ambient medium
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 335
Total simulation time: 5.2e6 s or 60 days ~6.5 RG sound-crossing times (260 frames)
Machine and partition: Bluehive standard
Number of cores: 120
Total wall time: about 8.5 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 50 Rsun of primary and within a cylinder of radius 50 Rsun and height 50 Rsun around secondary
Buffer zones: 0 cells (no buffer zones)
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Run 133 to test making refinement zone decrease with time:
Binary run 133 similar to run 125 but now the refinement zone changes with time
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time: 84 days (up to frame 439)
Machine and partition: Bluestreak standard
Number of cores: 8192 (2 cores per task to increase memory)
Total wall time: 6 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 1.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
DefaultAccretionRoutine=2 (Krumholz)
Comparison between runs 125(top left), 133(top right), O+16a(bottom)
Comments:
- The runs are very similar but there is a slightly smaller final separation for run 125(less aggressive refinement)
- This suggests that our refinement criteria for run 133 was probably slightly too aggressive.
- However, the otherwise close agreement tells us that decreasing the refinement zone with time to be a sphere centred on p1 with radius ~2 times particle separation is reasonable.
Run 135 to test case where no accretion onto secondary is permitted:
Binary run 135 similar to run 133 but now DefaultAccretionRoutine=0 instead of 2. Also suppress generation of new sink particles.
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 900
Total simulation time: 191 days
Machine and partition: bluehive2.5 standard
Number of cores: 120
Total wall time: 2.8 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 1.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Default Accretion Routine=0 (No accretion)
Comparison between runs 133(top left), 135(top right), O+16a(bottom)
Comments:
- The results of 135 and 133 are similar, except:
- Run 135 (no accretion) has slightly smaller separation at a given time.
- Run 135 (no accretion) has slightly larger frequency of oscillations.
- Thus accretion cannot fully explain the discrepancy with the O+16a results, but removing accretion does make results slighly closer to those of O+16a, who did not have accretion.
- We must think more about accretion, but it is not making a huge difference at present.
Run 132 that uses twice as high resolution and 10x lower ambient pressure as previous runs:
Binary run 132 with double max resolution, lower resolution in ambient medium, 10x smaller ambient pressure than run 116
Relaxation run: 129
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time:
Machine and partition: Stampde 1 normal (running, completed up to frame 215, or 32 sim-days)
Number of cores: 1024
Total wall time: 8 days (starting from frame 75 of relaxation run)
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 4 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 5e12 cm (71.87 Rsun) of primary center and within a cylinder of radius 20 Rsun and height 20 Rsun around secondary center. After t~11d (~frame 123) refinement radius around primary was halved to 2.5e12cm (36Rsun). After t~31d (frame 210) halved again to 1.25e12cm (18Rsun).
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
DefaultAccretionRoutine=2 (Krumholz)
NOTE: For the last 4 days of wall time the code ran very slow, probably because it was creating many many low mass particles due to the Jeans criterion. I have now commented out this part of the code, so it does not create particles. It is pending on stampede from chombo file 208, before extra particles were created.
Comparison of run 132 with Ohlmann+16a run:
Table
Comments:
- The softening length of the point particles decreases with time in the O+16a simulation.
- It is not clear whether this procedure is justified.
- The main reason to improve the resolution with time may be to resolve the decreasing softening length.
- Therefore, if we keep the softening length constant, improving the resolution with time may not be necessary or productive.
- O+16a initially resolves the softening length by 20 cells, whereas we resolve it by 17 cells. They advocate >10 cells.
- At 120 days, O+16a resolves the softening radius by 35 cells.
- It may be worth doing a run with slightly larger or smaller resolution to ensure that we are adequately resolving the softening length.
Comparison between runs 088(top left), 125(top right), 132(bottom left), O+16a(bottom right)
Comments:
- The 1st minimum, 2nd maximum, and 2nd minimum are located roughly at separations, with softening length denoted as h:
- Run 088 (res=0.29Rsun, h=4.8Rsun, cells/h=17): 14 , 21 , 12 Rsun
- Run 125 (res=0.29Rsun, h=2.4Rsun, cells/h= 8): 13.5, 18 , 14.5 Rsun
- Run 132 (res=0.14Rsun, h=2.4Rsun, cells/h=17): 14 , 18.5, 11 Rsun
- O+16a (see above table) : 10 , 23.5, 11 Rsun
- These are found roughly at times:
- Run 088 (res=0.29Rsun, h=4.8Rsun, cells/h=17): 12.5, 15.5, 18 days
- Run 125 (res=0.29Rsun, h=2.4Rsun, cells/h= 8): 12.5, 14.5, 17 days
- Run 132 (res=0.14Rsun, h=2.4Rsun, cells/h=17): 12.5, 14.5, 17 days
- O+16a (see above table) : 13 , 16 , 19 days
- From the difference between 125 and 132, we conclude that h is not adequately resolved in run 125 (8.5 cells/h vs 17 cells/h)
- O+16a advocates >10 cells/h, so this is consistent with their result.
- In our case, we still cannot tell if 17 cells/h is sufficient.
- We could run 088 with double the resolution to see if it converges.
- I will also continue to run 132 but it will be slow as the queue time in stampede 1 has increased as nodes are being transferred to stampede 2.
Run 136 to test how much relaxation makes a difference (IN PRORESS):
Binary run 136 similar to run 135 but now start from frame 0 of relaxation run 096 instead of frame 75 (so no damping).
Relaxation run: 096 (but no relaxation! Just start with initial profile
First frame: 0
Last frame: 18, running
Total simulation time: 4 days
Machine and partition: bluehive2.5 standard
Number of cores: 120
Total wall time: 21 hours, running
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm (575 Rsun)
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 1.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Default Accretion Routine=0 (No accretion)
Discussion
- Possible reasons for discrepancy with O+16a in (my guessed) order of importance
- resolution (especially number of cells per softening length h) (a new run will test this).
- softening length.
- different RG relaxation runs with different type codes.
- initial spin of RG (a new run will test this).
- very different ambient densities (I have an old run that we can use to check this).
- different accretion algorithms.
- small differences in particle masses.
- some reflection off of boundaries at late times in our smaller box.
- Probably run 132 is at the highest resolution we're going to get for the paper (especially if we need to do multiple runs).
- But we need to make sure that the softening length h is adequately resolved by checking that results are converged.
Next steps
- Continue to run high res run 132 (with particle creation turned off!).
- Continue to run 136 (no relaxation run).
- Make separation plot for old run 120 to see if ambient density matters.
- New run with initial spin of RG at 95% Keplerian to test what difference this makes.
- New run like run 088 but with twice as high resolution to test the convergence with cells/h.
- Continue to improve and extend the outputting of relevant data to various files.
- Clean up code and divide into different modules for relaxation runs and binary runs.
- Think more about the accretion routine, Krumholz vs. Federrath vs. no accretion….
Update on CE project
New Work
- Now able to run code on bluehive 2.5.
- Three runs in progress.
- How to optimize refinement?
- Edited code to be able to write some output to files.
- What other data to output?
- Reading and discussions conerning accretion onto secondary in CEE (presentation?).
Summary of New Results
- Code is running on bh2.5 and seems to be faster than regular bh (which is nice).
- New runs will be analyzed next week. Stampede queue time has increased (will eventually go to infinity as it is phased out)! Bluestreak queue is variable. No queue for Bluehive 2.5 as of now!
- There are a few possibilities:
- Refine to maxlevel up to refinement radius of min(5e12cm,1.5*separation) about primary point particle (trying now)?
- Choose refinement radius by hand at each restart (trying now)?
- Set some refinement criteria within the refinement radius and force to lowest level outside refinement radius?
- Refine to maxlevel within refinement radius but make refinement radius very small and use large buffer zones?
- Can now write accreted mass & momentum as well as time and acceleration on particles from gas gravity each time step.
- Aside from those, other output is also desired, so need to decide what exactly, then spend time implementing that.
- angular momentum
- particle separation
- integrals of damping force out to a given radius around secondary
- gas potential and kinetic energies
- Should I give a presentation at a CE meeting of what has been done so far on this topic of accretion in CEE, and also about what output needs to be generated?
Ongoing runs
Run to test making refinement zone decrease with time:
Binary run 133 similar to run 125 but now the refinement zone changes with time
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time:
Machine and partition: Bluestreak standard (running, completed up to frame 181 in 4 days walltime)
Number of cores: 8192
Total wall time:
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 1.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
DeafaultAccretionRoutine=2 (Krumholz)
Run to test case where no accretion onto secondary is permitted:
Binary run 135 similar to run 133 but now DefaultAccretionRoutine=0 instead of 2. Also suppress generation of new sink particles.
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time:
Machine and partition: bluehive2.5 standard (running, completed up to frame 196 in 2 days wall time)
Number of cores: 120
Total wall time: about
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 1.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
DeafaultAccretionRoutine=0 (No accretion)
Run that uses twice as high resolution and 10x lower ambient pressure as previous runs:
Binary run 132 with double max resolution, lower resolution in ambient medium, 10x smaller ambient pressure than run 116
Relaxation run: 129
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time:
Machine and partition: Stampde 1 normal (running, completed up to frame 153, or 18 sim-days)
Number of cores: 1024
Total wall time: 4 days so far (starting from frame 75 of relaxation run)
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 4 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 5e12 cm (71.87 Rsun) of primary center and within a cylinder of radius 20 Rsun and height 20 Rsun around secondary center. After t~9.6e5s (~frame 123) refinement radius around primary was halved to 2.5e12cm.
Buffer zones: 0 cells (no buffer zones)
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
Next steps
- Analysis of runs 133, 135, 132 and comparison with previous runs.
- Decide what data is needed to output and implement this in the code.
- Improve style of code in preparation for more serious runs.
- Run combining the merits of 132 and 133 that also outputs the relevant data.
Common envelopes: update
New Work
- Performed and analyzed new run 125 that evolves binary for 3 times longer than old run 116 (60 days as opposed to 20 days), made possible by forcing ambient medium to have lower resolution.
- Compared run 125 with run 116 to check to what degree forcing the ambient medium to be low res affects the region of interest in the center.
- Compared run 125 with results of Ohlman+16a.
- Peformed new relaxation run 129 with resolution doubled for RG, made possible by making resolution of ambient medium much lower.
- Set up new high res binary run 132 that uses 129 and also the trick of run 125 which forces low resolution in the ambient medium [pending on stampede].
- Set up new run 133 that uses standard resolution (like 125) but now makes max resoln refinement zone a function of inter-particle separation (so evolves with time) [pending on bluehive].
Summary of New Results
- Run 125, which removes resolution in the surrounding medium, is reasonably consistent with run 116 in the highly resolved region of interest for the first 20 days (first few orbits). This suggests that it is okay to greatly reduce the resolution outside of the region of interest.
- Run 125 is qualitatively similar to the results of Ohlmann+16a for the first 60 days, but the amplitude and frequency of variation with time of the separation are smaller than in O+16a. This suggests that the gravitational force is still not being fully resolved in our sims (but a higher res version is pending).
Detailed Results
Binary run 116 (see also previous blog post) with half the softening length of old run binary run 088 (and relaxation run 062)
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 168
Total simulation time: 3.36e6 s or ~4.2 RG sound-crossing times (93 frames)
Machine and partition: Stampede 1 normal
Number of cores: 1024
Total wall time: 96 hours
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set automatically by AstroBear
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Comments
- See last blog post for movies and discussion.
- Evidence of a disk around secondary.
- Problem: too computationally demanding.
- Solution: reduce resolution in outer regions that are not directly interesting. But will this affect region of interest?
Binary run 125 with longer simulation time and lower resolution in ambient medium
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame: 335
Total simulation time: 5.2e6 s or 60 days ~6.5 RG sound-crossing times (260 frames)
Machine and partition: Bluehive standard
Number of cores: 120
Total wall time: about 8.5 days
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 50 Rsun of primary and within a cylinder of radius 50 Rsun and height 50 Rsun around secondary
Buffer zones: 0 cells (no buffer zones)
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Movies
Density sliced at half-way point of box:
face-on full box
face-on zoom-in
edge-on zoom-in
face-on slice through secondary, extra zoom-in
face-on slice through secondary, extra zoom-in with velocity vectors
Edge-on slice through secondary as viewed from primary point particle:
viewed from P1 with P2 at center
Edge-on slice through secondary AND primary:
slice through P1 (left side) and P2 (center)
Mach number:
face-on full box
Particle mass:
face-on zoom-in
Comparison of runs 116 and 125:
Comparison of density (116 on left, 125 on right):
face-on slice through secondary, extra zoom-in
Comparison of particle mass (116 on left, 125 on right):
face-on zoom-in
Comparison of separation-time graph and orbits (116 on left, 125 on right):
Comparison of density at 10 and 20 days (116 on left, 125 on right):
Density at 40 days (left) and 60 days (right) for run 125:
Ohlmann+16a Fig 3:
Comments
- The results compare well qualitatively to those of run 116. However, there are small differences:
- The "disk" that forms arond the secondary is still slightly less circular and less extended than in run 116.
- The separation variation AMPLITUDE is reduced by about 20% by t=20 days compared to run 116.
- The mass accreted onto the secondary is increased by about 1% at t=21 days compared to run 116.
- The results compare well qualitatively with those of Ohlmann+16a. However, the differences are significant:
- The separation-time plot has a smaller amplitude of oscillations.
- The separation-time plot has a smaller frequency of oscillations.
- The mean separation is larger by about 25% by t=60 days.
Relaxation run 129 with double max resolution, lower resolution in ambient medium, 10x smaller ambient pressure than run 096
First frame: 0
Last frame: 138 (2.76e6 s or 9.2 RG freefall times of primary star, with damping implemented up to frame 75)
Total simulation time: 2.76e6 s or 3.45 RG sound-crossing times
Machine and partition: Stampde 1 normal
Number of cores: 1024
Total wall time: 92.5 hours (about 49 hours to reach frame 75)
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 3 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 5e12 cm (71.87 Rsun) of primary point particle
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
Movies
Density sliced at half-way point of box:
zoom-in
Mach number sliced at half-way point of box:
zoom-in
Comments
- We have run the relaxation run up to frame 138 but present the results up to frame 75 here.
- Frame 75 or 1.5e6s is the point at which damping has been reduced to zero (5 free-fall times).
- We see that the density is reasonably stable, though it is still evolving at t=1.5e6s.
- This suggets that the new refinement criteria used here are reasonable.
- The plot of Mach number shows that grid effects are present.
- In the future we may want to:
- Increase the resolution, enabling higher resolution in the binary runs.
- Increase the relaxation time from 5 freefall times to 5 sound-crossing times with damping + 5 sound-crossing times without damping, as in O+16a.
- Increase the box size.
- Note that the relaxation run is quite costly (but several binary runs can be executed from a single relaxation run). This run up to frame 75 took 49 hours on stampede with 1024 cores.
- One way to speed it up would be to resolve the core and a shell that includes the surface, rather than the whole star. But then the resolution in between would still have to be reasonably high, so would need to use large buffer zones.
- Note that with the higher resolution, we were able to decrease the ambient pressure by 1 order of magnitude. This also helps to reduce the ambient temperature and sound speed, as the density is kept the same as for run 125. This may help to relax the CFL constraint.
- Maybe it would be worth trying a binary run that DOES NOT USE ANY RELAXATION RUN (i.e. no damping) and see how much difference there is.
Binary run 132 with double max resolution, lower resolution in ambient medium, 10x smaller ambient pressure than run 116
Relaxation run: 129
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time:
Machine and partition: Stampde 1 normal (running)
Number of cores: 1024
Total wall time:
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 2.25 Rsun (256^{3} cells)
Highest resolution: 0.14 Rsun (4096^{3} cells, 4 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within 5e12 cm (71.87 Rsun) of primary center and within a cylinder of radius 20 Rsun and height 20 Rsun around secondary center
Buffer zones: 0 cells (no buffer zones)
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{5} dyne/cm^{2}
Binary run 133 similar to run 125 but now the refinement zone changes with time
Relaxation run: 096
First frame: 75 (5 RG freefall times, when velocity damping ended)
Last frame:
Total simulation time:
Machine and partition: Bluehive standard (pending)/Bluestreak standard (running)
Number of cores: 120(bh)/8192(bs)
Total wall time: about
Hydro BCs: extrapolated
Poisson BCs: multipole expansion
Box size: L=4e13 cm
Base resolution: 9.0 Rsun (64^{3} cells)
Highest resolution: 0.29 Rsun (2048^{3} cells, 5 levels AMR)
AMR implementation: set by hand to have max level around point particles
Max resolution zone: within min(5e12cm, 2.5*particle_separation)
Buffer zones: 2 cells
Softening length: 2.4 Rsun
Ambient density: 6.7e-9 g/cc
Ambient pressure: 10^{6} dyne/cm^{2}
Discussion
- Refinement of the central region only works reasonably well and is the way forward.
- Should work toward making the refinement a function of the particle separation as attmpted in ongoing run 133.
- Comparison of separation vs time and orbit plots with those of O+16a suggests we still lack enough resolution.
Next Steps
- Analyze ongoing runs.
- Do run that combines merits of 132 and 133.
- Output diagnostics including accretion rate onto secondary, drag force on secondary
- Experiment with variations to "fiducial parameter values": initial separation, primary spin, accretion onto primary.
First close-ups of accretion onto secondary
New Work
- I created movies of the previous run that follow the secondary point particle, keeping it at the centre of the frame.
Summary of New Results
- The new movies reveal structure around the accreting secondary.
Detailed Results
Binary run 96/116 with half softening length of old run 062/088
Damp116) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm , ambient density g/cc.
(Stampede 1 normal 1024 cores, ~4 days wall time)
( cm, , 5 levels AMR)
Reference frame of secondary:
2d density slice (zoomed)
2d density slice (zoomed), edge-on
Note: I tried to make a similar movie of face-on temperature, but visit could not handle it (don't understand reason)
Now sliced through secondary:
2d density slice (zoomed)
2d density slice now with velocity vectors (zoomed)
2d density slice edge-on (zoomed)
Now sliced through secondary, zoomed in 4x again:
2d density slice (extra zoomed)
2d density slice (extra zoomed)
Box frame (as shown in previous post):
2d density slice zoomed
2d density slice with mesh
Discussion
- Something resembling an accretion disk forms.
Next Steps
- Long run with maxlevel restricted to vicinity of primary and secondary (running on bluehive)
- Run with maxlevel restricted to vicinity of primary and secondary AND max resolution doubled (relaxation run almost completed on stampede)
- Output diagnostics including accretion rate onto secondary, drag force on secondary
- Make AMR maxlevel region a function of time
- Experiment with variations to "fiducial parameter values": initial separation, primary spin, accretion onto primary
Update on CE simulations
New Work
- I performed a new binary run with half the softening length but other parameters the same (run 116 with relaxation run 096) except that I also changed the initial positions and velocities of the particles so that the frame of reference is effectively rotated by 180 degrees.
Summary of New Results
- For the binary runs, the code slows down after about t = 10-15 days and the chombo files get much bigger, probably due to increasing refinement.
- The separation vs time graph is similar to the old run, and about equally similar to O+16a.
Detailed Results
Binary run 96/116 with half softening length of old run 062/088
Damp116) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm , ambient density g/cc.
(Stampede 1 normal 1024 cores)
( cm, , 5 levels AMR)
2d density slice zoomed
2d density slice with mesh
- How does halving the softening length change the results? Let us compare the old run (062/088) with the new run (096/116) with softening length 2.4Rsun instead of 4.8Rsun (for both primary and secondary).
2d density comparison of 062/088 (left) and new run 096/116 (right)
Below are snapshots of density in the orbital plane from t = 10 days (left) and t = 20 days (right). Top row: old simulation 062/088. Next row: new simulation 096/116 with half the softening length. Bottom fig 1 from O+16a. In the O+16a figure, the '+' denotes the primary core particle, while the 'x' denotes the secondary point particle. The core and secondary are denoted as '0' and '1' respectively in my plots.
We see that the two runs are qualitatively very similar, as expected. How do they compare in detail?
On the bottom below I've plotted Fig 1 of Ohlmann+16a and the equivalent figure with these simulations for comparison. Note that the new run went up to 21 days while the old run went up to 20 days. In my plot of separation, I've shown the softening radius as a dotted horizontal line. Circles represent the softening radius, while the green dot shows the initial center of mass of the two stars. The very small green square in the upper right shows the smallest resolution element, which is the same for both runs (about 0.29 Rsun).
Discussion
- Up to a few days after the first minimum, the results look almost identical. Softening length begins to play a role thereafter.
- However it is not clear which run is more accurate because the softening length is not as well-resolved in the new run.
- The new run (096/116) takes about 6 days of wall time (including 2 days for the relaxation run).
- The code becomes even slower after t = 10 days of the binary run, probably because the AMR is refining to the max level over a larger and larger volume.
- Regardless, we need to get higher resolution, larger box size, longer relaxation runs, and longer binary simulation time.
- This will require that we force the resolution to be much lower away from the point particles.
Conclusions
- Halving the softening length produces obvious quantitative differences, but only starting toward the end of the first orbit.
- However, it is unclear whether the differences between the two runs with different softening lengths are due to differences in the softening length per se or to differences in the ratio of softening length to resolution.
Next Steps
- I managed to perform a low-ambient density run (rho = 1E-10 g/cm3 rather than 6.7E-9 g/cm3) on stampede 1 while on vacation…it will take a few more days to complete. This will tell us what difference the ambient density makes.
- We need to modify the code to make it able to refine to a high level only around the (moving) point particles.
- Then it will be feasible to increase the max resolution and isolate the effects of resolution and softening length.
Useful Papers on Common Envelope Evolution
Note: linked pdf files may contain my text highlighting.
Ricker+Taam
Ricker & Taam 2008, ApJ 672:L41, The interaction of stellar objects within a common envelope
Ricker & Taam 2012, ApJ 746:74, An AMR study of the common-envelope phase of binary evolution
De Marco++
Passy et al. 2012, ApJ 744:52, Simulating the common envelope phase of a red giant using smoothed-particle hydrodynamics and uniform-grid codes
Staff et al. 2016a, MNRAS 455, 3511, Hydrodynamic simulations of the interaction between an AGB star and a main-sequence companion in eccentric orbits
Staff et al. 2016b, MNRAS 458, 832, Hydrodynamic simulations of the interaction between giant stars and planets
Kuruwita et al. 2016, MNRAS 461, 486, Considerations on the role of fall-back discs in the final stages of the common envelope binary interaction
Iaconi et al. 2017a, MNRAS 464, 4028, The effect of a wider initial separation on common envelope binary interaction simulations
Galaviz et al. 2017, ApJS 229:36, Common envelope light curves. I. Grid-code module calibration
Iaconi et al. 2017b, arXiv:1706.09786v1, The effect of binding energy and resolution in numerical simulations of the common envelope binary interaction
Ohlmann++
Ohlmann et al. 2016a, ApJ 816:L9, Hydrodynamic moving-mesh simulations of the common envelope phase in binary stellar systems
Ohlmann et al. 2016b, MNRAS 462:L121, Magnetic field amplification during the common envelope phase
Ohlmann et al. 2017, A&A 599, A5, Constructing stable 3D hydrodynamical models of giant stars
MacLeod++
MacLeod & Ramirez-Ruiz 2015a, ApJ 798:L19, On the accretion-fed growth of neutron stars during common envelope
MacLeod & Ramirez-Ruiz 2015b, ApJ 803:41, Asymmetric accretion flows within a common envelope
MacLeod et al. 2017a, ApJ 835:282, Lessons from the Onset of a Common Envelope Episode: the Remarkable M31 2015 Luminous Red Nova Outburst
MacLeod et al. 2017b, ApJ 838:56, Common envelope wind tunnel: coefficients of drag and accretion in a simplified context for studying flows around objects embedded within stellar envelopes
Murguia-Berthier et al. 2017, arXiv:1705:04698v1, Accretion disk assembly during common envelope evolution: implications for feedback and LIGO binary black hole formation
Ivanova++
Ivanova et al. 2013a, A&ARv 21, 59 Common envelope evolution: where we stand and how we can move forward
Ivanova et al. 2013b, Science 339, 433 Identification of the long-sought common-envelope events
Nandez et al. 2014, ApJ 786, 39, V1309 Sco—Understanding a merger
Ivanova et al. 2015, MNRAS 447, 2181 On the role of recombination in common envelope ejections
Nandez et al. 2015, MNRAS 450, L39, Recombination energy in double white dwarf formation
Nandez & Ivanova 2016, MNRAS 460, 3992 Common envelope events with low-mass giants: understanding the energy budget
Ivanova & Nandez 2016, MNRAS 462, 362 Common envelope events with low-mass giants: understanding the transition to the slow spiral-in
Update on common envelope simulations
Recap of Last Post
- I had performed a run up to a simulation time of 20 days which had the same parameters as the Ohlmann+16a simulation, except that:
- the softening length is larger by a factor of 2
- the smallest resolution element is larger by a factor
- the RG primary is not rotating initially
- the ambient density is equal to that at the surface of the RG, which is orders of magnitude larger than in Ohlmann+16a
- the binary run starts just after velocity damping has completely turned off (rather than waiting 5 more dynamical times) and the dynamical time used is the free-fall time, which is about 3/8 of the sound-crossing time used by them
- In the binary run that we had done, the closest separation was already down to about 2.5 smoothing radii. In Ohlmann+16a they set a floor that the softening radius should not exceed 1/5 of the separation. Their softening radius thus changed dynamically.
New Work
- I attended the "Evolved Stars: Role of Binarity" conference in Nice and presented this work.
- I did a relaxation run for the RG star with the softening length reduced by a factor of two but the resolution the same.
- I tried several runs with the same parameters as for the original relaxation run but with lower ambient density.
Summary of New Results
- The talk went well. The slides are available here.
- With limited computing resources, it doesn't make much sense to try one change at a time, so I worked on the density issue (using bluehive).
- The lower ambient density runs are very slow. I present the results of tests below.
- In parallel, Baowei, is trying to optimize the code on Comet.
Detailed Results
- Run with half of previous softening length (2.4Rsun instead of 4.8Rsun) but same resolution 0.29 Rsun: central density decreases by 35% from to s when damping is turned off. This can be compared with 11% for the original run with 4.8Rsun softening length. Should resolution be doubled? For comparison Ohlmann+16a used softening radius of 2.8Rsun and resolution 0.14Rsun for relaxation run.
Relaxation run with single RG star
Damp104) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm , ambient density g/cc.
(bluehive standard 120 cores)
( cm, , 5 levels AMR)
lTrackDensityProtections=T, lTrackPressureProtections=T, MinDensity=1d-14
2d density + velocity
2d pressure
2d temperature
Damp105) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient
(bluehive standard 120 cores)
( cm, , 5 levels AMR)
2d density + velocity
2d pressure
2d temperature
Discussion
- The run with lower density (Damp104) is very slow (estimated wall time 6 months at frame 6.7 of 1500) and eventually crashed (timeout error)
- The more pronounced artefacts in Damp104 compared to Damp105 could be the reason, but it is not clear
- The larger temperature in Damp104 could mean that the computational unit TempScale~ K is too small. However, I've now played around a lot with the computational units and this does not make a significant difference.
- It is possible that AMR is causing the problem, so I'm now doing smaller box runs with and without AMR to see if it makes any difference.
Next Steps
- First try to fix this problem with low ambient densities
- We should use half the smoothing length (now done) but should we double the resolution? Should we increase the time for the relaxation run?
Comparison with O+16a, attempt 2
Recap of Last Post
- In the last post, I performed a run with the same parameters as the Ohlmann+16a run.
- However the simulation went from 2-body to 3-body when the secondary was mistakenly reintroduced after about 7 days.
- This was not a bug in the code, just me forgetting to flip a 'switch'.
New Work
- I flipped the switch and reran the code up to 20 days.
Summary of New Results
- The results match qualitatively those of O+16a. Differences are likely caused by remaining differences in the numerical setups, including softening radius, ambient density, resolution, and degree of corotation.
Detailed Results
I) Circular orbit as in Ohlmann16a
Damp088) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm
(comet compute 1728 cores, 2 cores per task to increase memory per task)
( cm, , 5 levels AMR)
Restarted from run Damp062, at s, just after Damping stopped, to s
2d density
2d density (zoomed)
2d density and velocity (zoomed)
2d density edge-on slice (zoomed)
2d particle velocity (zoomed)
2d particle position (zoomed)
2d Particle mass (zoomed)
Here are PROJECTIONS, instead of slices, zoomed in with a better color scheme, and extended to go up to 20 days:
2d density projection
2d density projection edge-on
Here is a version of the SLICE in the orbital plane, going up to 20 days, rotated 180 degrees to match the orbit of O+16a, color range shifted to match O+16a, and with a better color scheme:
2d density
…or with blue labels for better visibility:
2d density
2d density (zoomed)
Here is temperature:
2d temperature
…and Mach number:
Mach number
Below I've plotted Fig 1 of Ohlmann+16a and the equivalent figure with this simulation for comparison. In my plot of separation, I've shown the softening radius as a dotted horizontal line. In the inset showing particle trajectories, I've inverted the axes and shifted the origin to allow direct comparison (our simulation is rotated by 180 degrees with respect to theirs). Circles represent the softening radius, while the green dot shows the initial center of mass of the two stars. The very small green square in the upper right shows the smallest resolution element.
Below are snapshots of density in the orbital plane from t = 10 days and t = 20 days. Note that to compare directly, I have rotated each figure by 180 deg. In the O+16a figure, the '+' denotes the primary core particle, while the 'x' denotes the secondary point particle. The core and secondary are denoted as '0' and '1' respectively in my plot.
Discussion
- The results match qualitatively those of Ohlmann+16a, but differ in detail.
- The orbit of the secondary is larger, while that of the primary is slightly smaller, compared to O+16a. The separation does not become as small at the first minimum or as large at the first maximum, compared to O+16a. This may be due to the ~5 times larger gravitational softening length used.
- At t = 10 days, the density in the orbital plane appears similar to that of O+16a, but the spiral arm is less pronounced and features are less detailed. This could be due to the resolution being lower by a factor of somewhere between 2 and 12. It may be partly caused by the weaker gravitational interaction due to larger softening radius mentioned above.
- Also, the common envelope has not expanded as much into the ambient medium. This could be due to the >10^{7} times larger ambient density used compared to that of O+16a.
- Recall the differences between our setup and O+16a, outlined in the Table 2 of the following pdf file. The main differences between the two setups are:
- 5x larger softening radius
- 10^{7} times larger ambient density
- up to 12 times smaller resolution
- 9x smaller box size
- no initial rotation vs 95% solid-body corotation with orbit
- some differences in the relaxation run to prepare the red giant star (detailed in the table and in previous posts)
- extrapolated instead of periodic BCs
Next Steps
- The easiest and most obvious thing to do is to reduce the softening radius (= cutoff radius defening RG core. Recall that for r smaller than this radius, we replace the core with a modified Lane-Emden solution). However, reducing this softening radius to 1 Rsun and keeping the same max resolution would mean that we resolve the softening radius by only 3.5 resolution elements, whereas O+16a claim that 10 resolution elements is needed.
- That suggests that we should increase the max resolution by a factor of 2 or 4, but this would slow down the code considerably. It would be best to first lower the softening length without changing the resolution.
- It would also be worth testing lower ambient densities. In past tests the code has crashed, but it should be possible to lower the ambient density by at least a factor of 10 or 30.
- So this suggests the following 3 runs (starting from the beginning of the relaxation run):
- As 088 but reduce the ambient density by 10 or 30
- As 088 but reduce the softening radius by 4.8 to equal that of O+16a
- As 088 but with both of the above changes
Reproducing Ohlmann+16a results: 1st attempt
Recap of Last Post
- In the last post, I performed several runs with varying separation and secondary mass.
- However it was determined that point particles were not feeling the gravity of the gas, so the results were wrong.
New Work
- I wrote a script in IDL which calculates the Kepler orbit given the initial velocities, and used it to show that the orbit obtained was just what would be expected if the point particles were not feeling the gas gravity, further confirming the above conclusion.
- This problem with the code was corrected by Baowei and Jonathan.
- The base case (run 084 from last blog) was rerun now with the code corrected, with the goal of reproducing the basic results from Ohlmann+16a.
Summary of New Results
- The simulation now looks "reasonable" at the beginning (first ~dynamical time) but then deviates from the results of Ohlmann+16a.
- I realized while writing this blog that the problem is caused by the mistaken re-introduction of the secondary (hence the introduction of a third particle with mass equal to that of the secondary) on restarts. In fact, there was a switch in the problem.data file called "secondary_already_present" to deal with restarts, but I had forgotten to change it to .true. before restarting.
Results
I) Circular orbit as in Ohlmann16a
Damp088) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm
(comet compute 1728 cores, 2 cores per task to increase memory per task)
( cm, , 5 levels AMR)
Restarted from run Damp062, at s, just after Damping stopped, to s
2d density
2d density and velocity
2d density and velocity (zoomed)
2d temperature (zoomed)
2d particle velocity (zoomed)
2d particle position (zoomed)
2d Particle mass (zoomed)
Particle trajectories, (with circles representing softening radius)
Particle separation with time
Particle trajectories up to mistaken introduction of third particle
Particle separation with time up to mistaken introduction of third particle
Discussion
- What has happened is that another secondary got introduced on each restart. This happens at frame 107. It also happens at frame 92 but this won't matter much because I had to redo that frame only on bluehive because there had been an I/O problem at that frame on comet. So the simulation is correct up to frame 106, or elapsed time t = 2.12e6 - 1.5e6 = 6.2e5 s = 7.2 days, about 1 dynamical time, but is wrong after that.
- Results up to the kink seen in the plot of separation vs time are very close to those of Ohlmann+16a (see below). The introduction of the third point particle occurs before the kink. So the results so far are consistent with those of Ohlmann+16a. (If one looks closely there is another point in the plot of separation vs time that is a little off, and this is due to the one frame that was done on bluehive where the 3rd particle also appeared.)
Next Steps
Once I've edited the problem.data file to make "secondary_already_present=.true.", I will redo the simulation from frame 106. I will then again compare the result with Ohlmann+16a
Figure 1.
Here are the other figures from that paper for reference:
Figure 2
Figure 3
Figure 4
Update on common envelope simulations
Recap of Last Post
- In the last post I presented a simulation of a RG translating across the grid.
- I also presented a common envelope simulation but later realized that the initial velocities of the primary and secondary were wrong (about a factor of 2 too small). I corrected the script to calculate the initial velocities and tested it against the Sun-Earth system.
New Work
I corrected the initial velocities and simulated the following cases:
- RG star of mass 1.956 Msun including 0.369 Msun core (point mass), with secondary point mass of 0.978 Msun (half the RG mass), at initial separation 49 Rsun, just outside of the RG outer radius of about 48 Rsun. Very close to parameters of Ohlmann+16a.
- As above but larger separation of 60 Rsun instead of 49 Rsun.
- As above but even larger separation of 98 Rsun instead of 49 Rsun.
- As the first case but now make secondary mass equal to only 0.001 Msun so that problem reduces to "1-body".
- Replace RG with a point particle of the same mass and run in low resolution with uniform background to test orbital dynamics.
- Same but with original point masses of the first case, i.e. the RG core and the secondary, without RG envelope.
Summary of New Results
- We do not achieve a circular orbit in the CE sims. In each case the orbit is looser than it should be. The binary separation grows with time and the speed of the secondary reduces with time.
- When the RG is replaced by a point mass then the correct circular orbit is obtained (in low res with a uniform ambient medium).
- If the RG envelope is excluded and the point masses representing the core and secondary are made to orbit in a uniform ambient medium, we obtain almost the identical (non-circular) orbit as for the full CE simulation.
- The natural explanation for these results is that the point masses can feel each other's gravity, the gas can feel the gravity of the point masses, but the point masses do not feel gravity from the gas! This feature must obviously be included in the next set of runs.
Results
I) Circular orbit as in Ohlmann16a
Damp084) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm
(comet compute 1728 cores, 2 cores per task to increase memory per task)
( cm, , 5 levels AMR)
Restarted from run Damp062, at s, just after Damping stopped, to s
2d density
2d density and velocity
2d density and particle velocity
2d density edge-on
2d Temperature
2d Particle position
2d Particle mass
II) As above but wider orbit (binary separation of 60Rsun instead of 49Rsun)
Damp086) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm
(bluehive standard 120 cores)
( cm, , 5 levels AMR)
Restarted from run Damp062, at s, just after Damping stopped
2d density
2d density and velocity
III) As above but even wider orbit (binary separation of 98Rsun instead of 49Rsun)
Damp087) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm
(comet compute 1728 cores, 2 cores per task to increase memory per task)
( cm, , 5 levels AMR)
Restarted from run Damp062, at s, just after Damping stopped
2d density and velocity
IV) As above but very low mass secondary (0.001Msun instead of 0.978Msun)
Damp085) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm
(stampede normal 1024 cores)
( cm, , 5 levels AMR)
Restarted from run Damp062, at s, just after Damping stopped
2d density andparticle velocity
V) As above but RG represented by a point mass, so two point masses orbiting on uniform background
Kepler083) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient density and pressure set to 1d-10
( cm, , 0 levels AMR)
(Started from t=0)
2D projected particle positions
particle velocities
2D projected particle positions, edge-on
VI) As (V) above but only mass of RG core is included in primary point mass, so same point masses as in
Kepler083core) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient density and pressure set to 1d-10
(stampede normal 1024 cores)
( cm, , 0 levels AMR)
(Started from t=0)
2D projected particle positions
particle velocities
Comparison between and (VI)
Particle velocities
COMMENTS: Clearly, the secondary does not feel the gravity of the RG envelope. Thus, point masses do not feel gravity of the gas. This obviously needs to be corrected for the next set of runs.
Next Steps
Once this problems is resolved, we need to redo run in particular. If everything is in order, we can then plot the orbital separation as a function of time, and compare the result with Ohlmann+16a
Figure 1.
Here are the other figures from that paper for reference:
Figure 2
Figure 3
Figure 4
Aside from resolution and other details, the biggest difference between our setup and that of Ohlmann+ is that their RG is initiated with 95% corotation with the orbit, whereas ours is not rotating initially.
Other points worth mentioning
- My quota on bluehive has been reduced from 24 TB to 16 TB. I will look to reduce it more in the next two weeks. My quota on blue streak has been reduced from 5 TB to 2 TB.
- There is a nice paper by MacLeod et al. about accretion onto the secondary during the common envelope that I'm reading at the moment. Aside from being interesting, it is quite pedgogically written. I'm doing a literature review to prepare for the upcoming conference.
Update on CE project
Recap of Last Post
- In the last post I presented the first runs that included a secondary point mass. I had forgotten to initialize the primary with an orbital velocity.
- I had also presented the first runs that attempted to translate the star across the grid. I had been implementing this incorrectly, as I had been adding the velocity every time step rather than just at the start of the run, and also not giving any velocity to the point mass.
New Work
This time I've tried the following:
- Translating the RG across the grid at 100 km/s. This is important because otherwise in the binary, there would be no way of knowing whether effects on the RG were caused by the secondary or by motion through the ambient medium. We want to make sure the RG is stable as it moves through the ambient medium.
- Evolving the RG from t=0 (now without translating) with a nested grid that minimizes resolution outside the RG. The point is to save computation time since there is no need to have high resolution outside the star.
- I've also written a script in IDL that calculates the required initial velocities for a given set of orbital parameters (masses, binary separation, eccentricity, orientation of the orbit on the x-y plane), and makes a simple animation of the orbit, showing the positions and velocities as a function of time in CM coordinates.
Summary of New Results
- I was able to translate the star across the grid. After about a dynamical time, it begins to become unstable on the trailing side.
- The simulation with low resolution in the ambient medium runs about 4-5 times faster than the previous sims which allowed for AMR in the ambient medium. However, the star becomes unstable earlier, and relatively large density contrasts develop in the ambient medium near the star.
Results
I) Translation across the grid at 100 km/s
Damp069) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm
(bluehive standard 120 cores)
( cm, , 5 levels AMR)
(Restarted from run Damp062, at s, after Damping stopped, to s
2d density (continuous)
2d density (1 loop)
2d density and velocity (continuous)
2d density and velocity (1 loop)
For comparison, from a previous post, here is the same run without translating
Damp062) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient dyne/cm
( cm, , 5 levels AMR)
(bluehive standard 120 cores up to frame 7 and then about 2 days on comet compute 864 cores, 2 cpus/task up to frame 150 )
2d density (continuous)
2d density (1 loop)
COMMENT: The star becomes unstable on the trailing side sooner than it takes to become unstable when it is not in motion.
II) Evolve RG with low resolution outside the star
Damp070) Periodic hydro BCs, Periodic Poisson BCs, ambient dyne/cm
(bluestreak standard 8192 cores, about 3-4 days computation time)
( cm, , 5 levels AMR)
(As Damp059 except that resolution reduced in ambient medium, with 2 buffer cells per level)
2d density (continuous)
2d density (1 loop)
For comparison, from a previous post, here is the same run without constraining refinement outside RG
Damp059) Periodic hydro BCs, Periodic Poisson BCs, ambient dyne/cm
(bluestreak standard 8192 cores, about 15 days computation time up to s)
( cm, , 5 levels AMR, run up to s)
2d density (continuous)
2d density (1 loop)
Damp078) Extrapolated hydro BCs, Multipole Expansion Poisson BCs, ambient
(bluehive standard 120 cores, about 34 hours computation time)
( cm, , 5 levels AMR)
(As Damp070 except that different BCs, and now 8 buffer cells per level)
2d density (continuous)
2d density (1 loop)
2d density with mesh (continuous)
2d density with mesh (1 loop)
COMMENT: The star becomes unstable sooner than it takes to become unstable when low resolution is not imposed on the ambient medium. But there is a tradeoff as the computation time is reduced by a factor of 4-5.
III) Circular binary orbit with 1 solar mass secondary (as Ohlmann+16a)
(comet compute 1728 cores, 2 cores per task to increase memory per task, a little over 1 day computation time)
( cm, , 5 levels AMR)
2d density (continuous)
2d density (1 loop)
2d density (2x zoom, continuous)
2d density (2x zoom, 1 loop)
2d density (4x zoom, continuous)
2d density (4x zoom, 1 loop)
2d density (Edge-on, continuous)
2d density (Edge-on, 1 loop)
2d density (Edge-on, 2x zoom, continuous)
2d density (Edge-on, 2x zoom, 1 loop)
2d density (Edge-on, 4x zoom, continuous)
2d density (Edge-on, 4x zoom, 1 loop)
Discussion
The RG is still not quite stable enough after damping is turned off and it is allowed to evolve for a few dynamical times. The situation worsens somewhat when the star is translated across the grid. It is worth comparing with Ohlmann+ to see what differences may be important between their setup and ours. Here is a table comparing the two setups:
The most obvious difference is the density of the ambient medium being much larger in our setup. I am currenlty trying to reduce this ambient density to see if it will help to improve the stability of the RG.
The other curious thing is that they used a very small box in their relaxation run, and they used periodic BCs. Does this explain the oscillations they were getting?
Next steps
- Experiment with lower ambient densities
- Longer binary runs
First common envelope trial runs
Recap of Last Post
The last post I had presented runs of an isolated RG that was quasi-stable after applying the damping prescription of Ohlmann+17, using the freefall timescale of s as the dynamical timescale.
New Work
This time I've tried the following:
- Translating the star across the grid
- Adding a secondary
Summary of New Results
- Translating the star did not work because I was doing it incorrectly I now realize.
- Adding the secondary seems to produce reasonable results, except I realize now that I forgot to initialize the primary with the required velocity.
Results
I) Isolated RG runs from last blog
Damp059) Periodic hydro BCs, Periodic Poisson BCs, ambient dyne/cm
(bluehive standard 120 cores up to 33 then bluestreak 8192 cores, 2 cpus/task)
( cm, , 4 levels AMR)
2d density
- Note: this has been extended in time since the last post, but I haven't used this run for the simulations presented below. Instead I've used run "Damp062" below with extrapolated hydro BCs and multipole expansion Poisson BCs.
Damp060) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient
( cm, , 4 levels AMR)
(Damp060 stampede normal, about 2 days with 1024 cores, 1 cpu/task for half and then 512 cores, 1 cpu/task for half)
2d density
Damp062) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient
( cm, , 5 levels AMR)
(Bluehive standard 120 cores up to frame 7 and then about 2 days on comet compute 864 cores, 2 cpus/task up to frame 150 )
2d density
II) Translating the RG across the grid
- Two methods were tried: 1) add 30 km/s to every point; and 2) add 30 km/s to only those points that belong to the star, defined by a threshold density.
Damp064) Restarts Damp062 from
(Bluehive standard 120 cores)
2d density
- Translating every point at once leads to a numerical instability and the code crashes
Damp067) Restarts Damp062 from
(Bluehive standard 120 cores)
2d density
2d zoomed density
- Translating only points with g/cm allows the code to run but results look unphysical. Also, code becomes unreasonable slow.
III) Adding a secondary
- A secondary of mass Msun was added at binary separation Rsun, so just oustide the outer radius of the RG Rsun.
- The secondary was given an initial tangential velocity of km/s for run Damp066, and km/s for run Damp068. The latter velocity should result in a circular orbit according to my analytical calculation.
- The IACCRETE variable was specified to be "KRUMHOLZ_ACCRETION"
- The softening length for the spline softening was specified to be the same as that used for the RG.
Damp066) Restarts Damp062 from
(Bluehive standard 120 cores)
2d density
2d zoomed density
Damp068) Restarts Damp062 from
(Comet compute 1728 cores, 2 cores/task)
2d density
2d zoomed density
Discussion and Next Steps
- Translating the star needs to be done by giving a velocity to the central point mass and envelope only at the start.
- When introducing the secondary, I forgot to give the primary an initial velocity. I will redo run Damp068 giving the primary the appropriate inital velocity.
- At the same time I am working on improving the stability of the RG. I will be experimenting with buffer zones, which Baowei has shown me how to implement. The gain in efficiency should allow me to impose a higher max resolution.
- Must put label "X" on particles…
Update on RGB star for CE sims
Introduction
The last blog post I was struggling to avoid a cubical ("boxy") and thus unstable star. This boxiness is worse with AMR but reduces with damping.
However, we cannot keep damping turned on indefinitely. I had found that changing the BCs can make a difference.
It occurred to me that using periodic BCs may avoid this problem. Periodic BCs were used by Ohlmann+17.
I experimented again with different BCs in Sections I and II.
In Section II below I vary the value of the damping time scale
according to the prescription of Ohlmann+17, using the free-fall time s as the dynamical timescale , rather than the more conservative sound-crossing time of . Here is ramped up to over , and then left undamped for another . In Section III I try a run that includes AMR and the Ohlmann damping prescription (still running).
Results
- For the small-box simulations without AMR of Section II below, the periodic/periodic hydro/Poisson BCs seem to help to keep the star spherical,
though they increase the computation time by a factor of a few compared to extrapolating/multipole expansion BCs.
- For AMR and a twice larger box, the BCs seem to matter much less (see comparison of Ib and If below).
- It donned on me that maybe the ambient pressure is just too high at dyne/cm , and that this leads to boxiness. This value had led to a more stable star than dyne/cm in the small-box low res uniform grid sims. But with AMR we can still resolve the outer scale height if the ambient pressure is .
- So I did some runs with dyne/cm , and the results were encouraging. Not only is the star more spherical, but the computation time is typically reduced by a factor of a few.
- The star is still not perfectly spherical nor perfectly stable for the dyne/cm runs below, but clearly reducing the ambient pressure is the correct thing to do.
Next steps
- Run III(a) is ongoing. In the meantime, it will be worth doing the same run but with Extrapolating/multipole expansion BCs, which should be faster. If the results are similar, I will stick with the Extrapolating/multipole expansion, which are probably more physical than periodic/periodic and reduce the computation time.
- Simultaneously I will try the same run but with ambient pressure reduced to dyne/cm and dyne/cm to see if further improvements can be made. Clearly the pressure must be as low as possibly while still adequately resolving the scale height at the surface.
- Then it would be worth increasing the box size and resolution to be more comparable with those of Ohlmann+17. At this point we would have to make a final choice for the ambient pressure and dynamical time scale.
- After this, if everything looks good, we need to test the stability of the star as it translates along the grid. Finally we can introduce the secondary (point particle).
I) Damping with AMR
a) Reflecting hydro BCs, Multipole expansion Poisson BCs, s, ambient dyne/cm (Damp044)
2d density
2d density and velocity
b) Extrapolating hydro BCs, Multipole expansion Poisson BCs,
2d density
2d density and velocity
c) Extrapolating hydro BCs, Multipole expansion Poisson BCs,
2d density
2d density and velocity
d) Extrapolating hydro BCs, Multipole expansion Poisson BCs,
2d density
2d density and velocity
e) Extrapolating hydro BCs, Multipole expansion Poisson BCs,
2d density
2d density and velocity
f) Periodic hydro BCs, Periodic Poisson BCs,
2d density
2d density and velocity
Comparison with (a) on left and (b) on right
2d density
2d density and velocity
Comparison with (b) on left and (f) on right
2d density
2d density and velocity
II) Damping with evolving tau
- Damping prescription as in Ohlmann+17, using s (about equal to the freefall time, while the sound-crossing time is about s).
a) Reflecting hydro BCs, Multipole expansion Poisson BCs, ambient
2d density
2d density and velocity
b) Extrapolating hydro BCs, Multipole expansion Poisson BCs, ambient
2d density
2d density and velocity
c) Extrapolating hydro BCs, Periodic Poisson BCs, ambient
2d density
2d density and velocity
d) Periodic hydro BCs, Periodic Poisson BCs, ambient
2d density
2d density and velocity
e) Extrapolating hydro BCs, Multipole expansion Poisson BCs, ambient
2d density
2d density and velocity
f) Periodic hydro BCs, Periodic Poisson BCs, ambient
2d density
2d density and velocity
III) Damping with AMR and evolving tau
a) Periodic hydro BCs, Periodic Poisson BCs, ambient dyne/cm (Damp059 bluehive standard 120 cores up to 33 then bluestreak 8192 cores)
2d density
2d density and velocity
UPDATE, May 9, 2017
- Run III(a) above is almost but not quite complete now (120 of 150 frames). It is running on bluestreak
III) Damping with AMR and evolving tau
a) Periodic hydro BCs, Periodic Poisson BCs, ambient dyne/cm
(Damp059 bluehive standard 120 cores up to 33 then bluestreak 8192 cores, 2 cpus/task up to s )
( cm, , 4 levels AMR)
2d density
b) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient
( cm, , 4 levels AMR)
(Damp060 stampede normal, about 2 days with 1024 cores, 1 cpu/task for half and then 512 cores, 1 cpu/task for half)
2d density
c) Extrapolated hydro BCs, Multipole expansion Poisson BCs, ambient
( cm, , 5 levels AMR)
(Damp062 Bluehive standard 120 cores up to frame 7 and then about 2 days on comet compute 864 cores, 2 cpus/task up to frame 150 )
2d density
Discussion
- Ohlmann+17 also tried an adaptive cubic grid and found results that were almost identical to results using their HEALPix grid. But their simulations employed a moving mesh "with an adaptive refinement ensuring similar cell masses."
Next Steps?
- Increase box size further to cm ( with 6 levels of AMR or with 5 levels of AMR?).
- Increase max resolution by a factor of two.
Computing Issues
- Current runs take about two days on XSEDE/comet (or a little less on stampede) with the max number of cores, plus a few days in the queue, so say 1 week per run. Each frame produces a chombo file of about 20 GB.
- Is it better to use and 5 levels AMR or and 4 levels of AMR?
- Would I gain much by forcing only the center and surface of the star to have max refinement instead of the whole star?
- How does the result depend on choice of machine used, e.g. bluestreak vs stampede?
- When running jobs that need more than the default memory, is it necessary to run with half the cores?
Upcoming Conferences
The Physics of Evolved Stars: The Role of Binarity
Nice, France, July 10-13, 2017
Accepted for a poster. Possibility of sharing a talk slot.
The Impact of Binaries on Stellar Evolution
Garching, Germany, July 3-7, 2017
Accepted for a poster.
update on RGB
The past few weeks I've been trying to make progress on obtaining a stable giant. Details are available here but a summary is presented below.
I) Boundary conditions
- I changed the Poisson BCs from (a) periodic to (b) multipole expansion and performed some tests. This prevents the star from oscillating. It is worth noting that Ohlmann et al. 2017 used periodic BCs and obtained oscillations.
Comparison with (a-periodic) on left and (b-multipole expansion) on right
2d density
2d density and velocity
- Note that without periodic gravity, inflows from the centres of the boundary walls tend to produce "boxiness" of the star. In the hope of reducing this boxiness, I tried several variations on the hydro BCs. In the end, none of these efforts resulted in a large improvement and it seems that simply putting reflecting hydro BCs works as well or better than anything (slightly better than extrapolating, at least for a fixed grid).
Comparison with (a-extrapolating) on left and (b-reflecting) on right
2d density
2d density and velocity
II) Damping
- I implemented velocity damping (see also last blog post), with a constant damping time s (about dynamical times) or, in a few cases, s. The latter value can prevent the boxiness, even in a small box with only moderate resolution. I performed some tests with larger boxes and found the results to be basically consistent with those of the smaller box runs.
Extrapolated BCs, multipole expansion Poisson BCs
2d density
2d density and velocity
2d pressure
1d density
1d pressure
Extrapolated BCs, multipole expansion Poisson BCs
2d density
2d density and velocity
2d pressure
1d density
1d pressure
Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
2d density
2d density and velocity
Comparison with (a-large box extrapolating) on left and (b-large box reflecting) on right,
(i) Constant ambient pressure and density
2d density
2d density and velocity
III) Hydrostatic atmosphere
- With a hydrostatic atmosphere (rather than a constant pressure and density ambient medium), we might expect it to be easier to obtain a steady state. Long story short, the low densities and sharp gradients at the boundaries lead to large spurious velocities that tend to increase the computation time (or cause the code to crash).
Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
2d density
2d density and velocity
2d density (extended color bar)
2d density and velocity (extended color bar)
IV) AMR
- I performed two AMR runs (with s velocity damping and either extrapolated hydro BCs or reflecting hydro BCs).
- Inside of cm, the refinement level was forced by hand to be equal to the highest level.
a) Extrapolating hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(i) Constant ambient pressure and density (Damp047, 27 hrs on comet compute, 576 cores)
2d density
2d density and velocity
b) Reflecting hydro BCs, Multipole expansion Poisson BCs, Velocity damping with
(NOTE THAT THIS HAS ONLY RUN FOR 2/3 OF THE TIME AS (a))
(i) Constant ambient pressure and density (Damp044)
2d density
2d density and velocity
Conclusions
- "Boxiness" of the star owing to inflows from the centres of the boundaries has been a problem both because a cubical star is unphysical and because it eventually leads to instabilities at the star "corners."
- Small improvements can be made by varying the BCs. For Poisson, we may choose periodic or multipole expansion. For hydro, either extrapolating or reflecting.
- More complicated hydro BCs (e.g. fixing the ghost zones or the region exterior to some pre-defined sphere to be equal to the initial ambient values) probably do not generate enough improvement (sometimes not any) to be worth the extra computational cost.
- From past blog posts, we know that reducing the ambient pressure by a factor of a few may also help to reduce the boxiness (though the pressure scale-height at the surface will be smaller, thus not as resolved).
- What works best against boxiness and instability at the surface is velocity damping, which has now been implemented successfully. Using s keeps the star completely stable (at least for a uniform fixed grid), while s leads to a significant reduction in boxiness.
- The boxiness/inflow problem becomes worse with AMR, but the star remains remarkably stable after a few dynamical times with s damping.
- Using a hydrostatic envelope (instead of a constant density-pressure ambient medium) reduces the boxiness, but causes instabilities to develop at the corners of the grid, which then propagate inward. The code tends to crash, and I could not get it to run at all in AMR.
Next steps
- Given the above conclusions, it is probably best to stick with a constant density and pressure ambient medium.
- The logical next step is to try the prescription outlined in Ohlmann et al. 2017 which starts with a small and gradually ramps it up to .
- This should be done concurrently for 1) a fixed uniform grid simulation, 2) AMR simulation.
Update: Trying AMR, extending the profile, exploring fluctuations, including velocity-damping
I) Invoking AMR (with smooth
Motivation:
Ultimately runs will be done with AMR so it is worth trying AMR at this stage and comparing with uniform grid runs.
Setup:
I introduced AMR with 5 levels of refinement for a run with dyne/cm , with refinement 'level 0' resolution equal to grid cells, in a box of physical dimension cm. This implies the equivalent of for level 5, which translates to a physical resolution equal (in principle) to that of Run (3) from the last blog post, which used grid cells for a box of dimension cm. So in a sense, this run combines the higher resolution of Run (3) with the larger box of Run (4). This run should in principle take about 10 days to complete on bluehive, but it did not actually complete (see below).
Results:
2d density slice full box
2d pressure slice full box
2d density slice central
2d pressure slice central
1d density central
1d pressure central
2d density fluctuations slice $6.6\times10^{-9}$ to $6.8\times10^{-9}$ g/cm$^3$
2d pressure fluctuations slice $9.98\times10^{6}$ to $1.04\times10^{7}$ dyne/cm$^2$
1d density fluctuations $10^{-8.3}$ to $10^{-8.0}$ g/cm$^3$
1d pressure fluctuations $10^{6.95}$ to $10^{7.1}$ dyne/cm$^2$
- The run got killed, initially because the time allotment was exceeded. But after restarting the run, it again got killed, possibly because of a problem in the calculation (unclear). But clearly the run has become unphysical by this time anyway. 80 of 101 frames completed up to a time of s.
- The pressure remains remarkably stable. The core pressure retains its initial value marginally better than Run (3), which had high resolution in a smaller box. Global oscillations are similar in amplitude and frequency to Run (4) (the larger box run), as would be expected, but seem to be less regular. This is best seen in the 1D pressure movie. This is not surprising given that the AMR grid is non-uniform, and refined patches are not spatially distributed in a regular manner.
- The density, on the other hand, becomes unstable on a time scale of about 1 dynamical time. The star first develops small indentations at the points on the surface closest to the boundary and then develops a boxy morphology with the orientation aligned with the grid. Finally, the instabilities develop at the corners of the boxy stellar profile in the 2d slice.
- The oscillations in the pressure stabilize somewhat after about half the simulation time (a few dynamical times). In the 1d plots that zoom in on the boundary, there seems to be at least two changes to the profiles of density and pressure: first at about 1 dynamical time ( s) and then again at a few dynamical times, when the density is seen to become unstable in the 2d density plot.
Discussion:
- The fact that the density becomes unstable but the pressure distribution remains stable is consistent with what we found happens last blog post when the resolution is reduced (comparison plots of Run C). So it seems likely that somewhere in the box, there is a lack of resolution that leads to the instabilities in density. The instability seems to be strongest at the "corners" of the boxy profile that develops, which suggests that the resolution is too low to resolve these sharp corners.
- It is worthwhile looking at the low-level fluctuations for the previous simulations as a comparison:
For the small box run we have (in 1d plots purple=smoothed pressure, green=unsmoothed pressure):
2d density slice boundary $6.6\times10^{-9}$ to $6.8\times10^{-9}$ g/cm$^3$
2d pressure slice boundary $9.98\times10^{6}$ to $1.04\times10^{7}$ dyne/cm$^2$
1d density boundary $10^{-8.3}$ to $10^{-8.0}$ g/cm$^3$
1d pressure boundary $10^{6.95}$ to $10^{7.1}$ dyne/cm$^2$
For the large box run we have (in 1d plots purple=smoothed pressure):
2d density slice boundary $6.6\times10^{-9}$ to $6.8\times10^{-9}$ g/cm$^3$
2d pressure slice boundary $9.98\times10^{6}$ to $1.04\times10^{7}$ dyne/cm$^2$
1d density boundary $10^{-8.3}$ to $10^{-8.0}$ g/cm$^3$
1d pressure boundary $10^{6.95}$ to $10^{7.1}$ dyne/cm$^2$
Conclusions:
The AMR fails to resolve the sharp density gradients that appear at certain points, causing the simulation to crash. Instead of developing 'clean' global pressure waves, like in the uniform grid simulations, the waves have a complex structure, with many small-scale fluctuations embedded within them. This probably helps to damp regular global osciallations that develop in the uniform grid models.
II) Adding an isothermal atmosphere (with smooth
Motivation:
The profiles used in previous runs are characterized by a constant ambient density and pressure.
The pressure profile was smoothed at the star-ambient boundary, but not the density profile.
Adding a thick hydrostatic atmosphere for which the density and pressure decline with radius may be more realistic.
In its simplest form, such an atmosphere would be isothermal, continuous in pressure, density and their respective gradients across the star-ambient boundary, and in hydrostatic equilibrium if self-gravity is neglected. The derivation of the profile, with plots, is available in the file profile_atmosphere.pdf.
Setup:
The atmosphere is added by simply modifying the density and pressure profiles inputted. It is ensured that these new profiles are defined over the entire box, so there is no need for any ambient values (either defined explicitly or imposed implicitly by astrobear).
Results:
Below are movies from two runs with the same physical resolution but different box size:
a) small box (with smooth
2d density slice extended color bar
2d pressure slice extended color bar
2d density slice old color bar
2d pressure slice old color bar
1d density
1d pressure
b) large box (with smooth
2d density slice extended color bar
2d pressure slice extended color bar
2d density slice old color bar
2d pressure slice old color bar
1d density
1d pressure
- Clearly, boundary effects lead to sharp gradients in density, which probably is what causes the code to crash in (b).
- Morphologies appear unphysical, if one looks at small densities and pressures, but at the density/pressure range we were looking at before, the density slice remains quite circular and stable until a few dynamical times, when the density becomes suddenly unstable.
Conclusions:
These runs are somewhat less stable than the constant ambient density/pressure runs above, as sharp gradients develop more easily, probably as a result of reflection from the boundary. If this problem could be overcome, then this idea of an atmosphere may be more useful, because it seems to succeed (at least transiently) in transfering the disturbances to very low density and pressure where they are negligible.
New results (post-March23 meeting):
c) small box (with smooth , Multipole expansion BCs for Poisson solver, and run time seconds)
2d density slice extended color bar
2d pressure slice extended color bar
2d density slice old color bar
2d pressure slice old color bar
2d density slice extended color bar with velocity (scaled)
1d density
1d pressure
d) small box (with smooth
2d density slice extended color bar with velocity (scaled)
2d density slice extended color bar with velocity (unscaled)
2d density slice old color bar
1d density
III) Implementing damping (with smooth
Motivation:
We wish for the star to be stable. As we have seen this is rather difficult to achieve. We must then resort to damping the motions by, in effect, adding a damping source term to the momentum equation. We follow the idea discussed by Ohlmann+17. That is to add a term of the form
,
where
is a parameter.
Setup:
The most direct way to implement this form of damping would be to add the extra term directly to the momentum equation. However this would involve changing the code at the lowest level. For the time being we try an alternative prescription, whereby we set
,
with
,
since
,
which leads to
.
However, it was unclear to me exactly how to implement this in the code, so I tried two different methods below.
Preliminary Results:
a) small box, with resolution
2d density 2d pressure 1d density 1d pressure 2d hydrostatic equilibrium 2d sound speed 2d Mach number
b) small box, with resolution
2d density
2d pressure
1d density
1d pressure
2d hydrostatic equilibrium
2d sound speed
2d Mach number
c) small box, with resolution
2d density
2d pressure
1d density
1d pressure
2d hydrostatic equilibrium
2d sound speed
2d Mach number
…and the fiducial run for comparison (small box,
2d density
2d pressure
1d density
1d pressure
2d hydrostatic equilibrium
2d sound speed
2d Mach number
Note that the fractional hydrostatic equilibrium
does not include the gravity of the point source (I must correct this).
d) small box, with resolution
2d density
2d density and velocity
2d pressure
1d density
1d pressure
e) small box, with resolution
2d density
2d density and velocity
2d pressure
1d density
1d pressure
f) small box, with resolution
2d density
2d density and velocity
2d pressure
1d density
1d pressure
g) small box, with resolution
2d density
2d density and velocity
2d pressure
1d density
1d pressure
Mapping a modified RGB profile to the grid: Increasing time, resolution, or box size, and smoothing P at the surface
Mapping a modified RGB profile to the grid: Increasing time, resolution, or box size, and smoothing P at the surface
Recall from the last post that the RGB star was most stable for case (D),
which was the case where the ambient pressure is set to AstroBear.
I now extend the study in four ways:
1) Increase the run time from seconds (about 1 dynamical time) to seconds and then again to seconds.
2) Make the pressure profile smooth at the transition from the MESA profile to the ambient value,
as the discontinuity in the pressure gradient could be causing unwanted effects.
3) Increase the resolution from to without changing the box size.
4) Increase the box dimension from cm (with ) to cm (with ).
Below I present the results of each of these experiments in turn. 2D plots are slices through the center of the Y-axis, while 1D plots show an extra slice through the center of the Z-axis.
1) Increasing the run time
Model (D) of last blog post ran for
seconds, and is labeled (A) below. Model (B) below had the same parameter values but ran for 5 times as long, with the same number of snapshots (101). Model © below was meant to run for 25 times as long as the original run and 5 times as long as run (B), but stopped just short of completion due to bluehive crashing (presumably not because of this run!). It contains 214 snapshots.A) 3d density 1d density 3d pressure 1d pressure
seconds:B) 3d density 1d density 3d pressure 1d pressure
seconds:C) 3d density 1d density 3d pressure 1d pressure
seconds:
Discussion:
- The core density and pressure decrease somewhat but then remain fairly stable.
- However, the density and pressure near the surface oscillate with time.
- This appears to be caused by a pressure wave which starts near the surface, moves inward, reflects off the core, moves outward, reflects off the box boundaries, and moves inward again toward the core. This is most evident from the 1D plots of pressure for the longer run times.
- The four-fold symmetry of the grid becomes apparent in the 3d density profile by about
seconds, or one full oscillation. This is about 2.5 dynamical times. - Both the density and pressure eventually become completely unstable at about seconds, or about 10 dynamical times.
Conclusions:
The star becomes unstable after about 10 dynamical times.
Even before this, it shows oscillations during which the density profile experiences kinking (cuspiness).
The oscillations appear to be caused by pressure waves reflecting off the core and grid boundaries.
Below we explore three possible ways to help reduce these oscillations and cuspiness:
smoothing the pressure profile near the surface, increasing the resolution, and using a larger box.
2) Smoothing the pressure profile near the stellar surface (with run time
I realized that the simplest way to smooth the pressure profile to avoid a discontinuous pressure gradient while going from the surface to the ambient
dyne/cm pressure was to make . Because the pressure spans several orders of magnitude, this prescription hardly affects the pressure near the core, and only begins to be important about 5-10 solar radii from the `surface,' where surface here means the radius at which dyne/cm . However, this prescription changes the pressure and pressure gradient near the surface, so although it avoids a sudden change in pressure gradient, hydrostatic equilibrium is not expected to be satisfied quite as accurately, at least not initially. This run took about 6 hours to complete on bluehive.3d density 1d density 3d pressure 1d pressure
3d density P non-smooth(left) vs smooth(right)
1d density P non-smooth(green) vs smooth(purple)
3d pressure P non-smooth(left) vs smooth(right)
1d pressure P non-smooth(green) vs smooth(purple)
Discussion:
- Four-fold symmetry in the density still appears but at somewhat later times, so the star is rounder than in the unsmoothed case.
- The star is somewhat larger than in the unsmoothed case.
- The core behaves similarly to the unsmoothed case.
- The frequency of oscillations is reduced compared to the unsmoothed case.
- The cuspiness produced during the oscillations is reduced compared to the unsmoothed case.
- The amplitude of oscillations remains about the same as in the unsmoothed case.
- The star oscillates between a state similar to the initial state and a state where it is larger; i.e. it pulsates.
Conclusions:
Smoothing the profile helps to avoid cuspiness and reduces the frequency of oscillations.
However, with increased pressure in the outer regions,
the star expands to be greater than its original size,
before contracting again to its original size and undergoing fairly regular oscillations between these states.
Overall, the tradeoff between less rapid less cuspy oscillations and slightly larger star is probably worth making,
so (for now at least) we adopt this smooth pressure profile prescription in the runs described below.
3) Increasing the resolution (with smooth
A natural step is to increase the resolution, as some of the effects discussed above may be caused by lack of resolution of the pressure scale height, either near the surface or near the core. Therefore, we next doubled the resolution to
, keeping the box size constant, and retaining the smoothed pressure profile. This run took about 3.5-4 days to complete on bluehive.
3d density
1d density
3d pressure
1d pressure
3d density-pressure comparison 1d density-pressure comparison
3d density 256$^3$ (left) vs 512$^3$ (right)
1d density 256$^3$ (left) vs 512$^3$ (right)
3d pressure 256$^3$ (left) vs 512$^3$ (right)
1d pressure 256$^3$ (left) vs 512$^3$ (right)
Discussion:
- The initial central density and pressure are maintained much more faithfully in the high resolution run (though they still decrease and then quasi-stabilize at slightly lower values than the initial values). This is as expected because the relatively small pressure scale height near the center is better resolved.
- The amplitude, frequency and morphology of the oscillations is very similar to the 256 run, so the oscillations are not caused by lack of resolution.
- At the end of the simulation, the 512 run is fairly circular, and symmetric in the 1D plots, while the 256 run is boxier and shows asymmetry in the 1D plots. The higher resolution thus seems to make the solution more stable. However, the 3D density profile shows that the star seems to become slightly `diamond' shaped closer to the beginning of the run, and then recovering to a more circular morphology.
Conclusions:
Increasing the resolution makes the star remain stable for a longer time (though our run was not long enough to know when the star becomes unstable, if it becomes unstable). The core density and pressure are better preserved (to within about 15% instead of to within about 40%). The star is clearly more circular by the end of the run compared with the run, though after the first 1-2 dynamical times, the morphology seems to be slightly more diamond-shaped and slightly less circular than the run (but eyeballing it isn't easy!).
4) Increasing the box size (with smooth
Since the pressure wave discussed above seems to reflect off the boundaries of the box, perhaps such waves could be reduced, in frequency and/or amplitude, by pushing out the boundaries. Therefore, we now make the grid dimension twice as large. This run took about 3 days to complete on bluehive.
3d density
1d density
3d pressure
1d pressure
3d density 256$^3$ with $L=1\times10^{13}$ cm (left) vs 512$^3$ with $L=2\times10^{13}$ cm (right)
1d density 256$^3$ with $L=1\times10^{13}$ cm (left) vs 512$^3$ with $L=2\times10^{13}$ cm (right)
3d pressure 256$^3$ with $L=1\times10^{13}$ cm (left) vs 512$^3$ with $L=2\times10^{13}$ cm (right)
1d pressure 256$^3$ with $L=1\times10^{13}$ cm (left) vs 512$^3$ with $L=2\times10^{13}$ cm (right)
Discussion:
- The frequency of the oscillations is clearly reduced, and just less than one full oscillation is completed before the end of the run (I use the word `oscillation' assuming that it will turn out to be periodic if run for longer). For the standard box size we were getting almost two full oscillations by the end of the run. So the frequency is reduced by about half. This is evidence that these waves are due to reflections off the walls.
- Moreover, the amplitude of the oscillations is drastically reduced.
- However, the star morphology is slightly `boxier' in the large grid run. This boxiness becomes apparent after about two dynamical times or about seconds. This could perhaps be due to an extra time lag between reflections from the wall and expected reflections from the corner of the grid.
- By the end of the run there is less asymmetry in the 1D density and pressure profiles in the larger box run, which seems to indicate that the star remains stable for longer.
- The decrease and quasi-stabilization of the core density or pressure are similar to the smaller box case.
Conclusions:
Increasing the grid size helps to reduce the oscillations, both in terms of frequency and especially in terms of amplitude. However, the density profile still becomes boxy, perhaps even boxier than with the smaller grid. The oscillations and boxiness are probably caused by pressure waves reflecting off the walls.
Overall discussion and conclusions:
- I adopted three measures designed to increase the stability of the star: smoothing of the pressure profile, increase of the resolution, and increase of the grid size. Smoothing the profile leads to oscillations that are less cuspy, and a density profile that is less boxy, but the star inflates more significantly during the oscillations. The core is hardly affected.
- Increasing the resolution does not change the frequency or amplitude of oscillations, but the star remains stable for longer. It also retains its round shape better though it seems to develop a diamond-shaped morphology. The core density and pressure are better maintained, likely because the scale height at the center is better resolved.
- Increasing the grid size dramatically reduces the amplitude of oscillations and also reduces their frequency approximately in proportion to the increase in grid size (doubling the grid seems to halve the frequency). However, the star still becomes boxy, and slightly boxier than for the smaller grid.
- The smoothing has already been incorporated into the runs with increased resolution or box size. Using with the larger box of cm is too demanding computationally. Therefore it is best to switch to AMR at this point.
Next steps:
I) AMR
I am now running a case with 5 levels of AMR corresponding to to resolution of a fixed grid. The simulation will take 9-10 days to complete in total, or about 2-3 more days from today. I will be presenting the results here after it finishes.
II) More realistic atmosphere
The strong pressure waves possibly rely on the ambient pressure being as large at the grid boundaries as it is at the stellar surface.
This high ambient pressure is rather unrealistic anyway. What would be more realistic is that rather than assuming a uniform pressure ambient medium, to instead insert an extended isothermal atmosphere for which pressure and density decay with distance. The pressure and density profiles can be set by solving the equation of hydrostatic equilibrium in spherical symmetry neglecting self-gravity, which should anyway be very small for this atmosphere. The solution could be subjected to the following constraints:
1) Assume is continuous at the stellar surface (e.g. defined to be the radius at which dyne/cm ), which will give the amplitude .
2) Assume an isothermal equation of state , with a constant. This constant is obtained by requiring that is also continuous at the stellar surface.
Alternatively, but less simply, one could perhaps retain the old profile for
, and solve for (assuming hydrostatic equilibrium) assuming now that is a function of . This would then allow one to match both and at the surface.I feel it is worth trying such atmospheres before resorting to implementing an artificial forcing term to damp motions, as done in other studies such as Ohlman et al.
Mapping a modified RGB profile to the grid: modifying the surface and ambient pressure
One of the next steps identified in the last post was to try increasing the ambient pressure
to help to prevent the near-surface layers of the star from expanding outward.
There are two problems with the (modified) MESA profile near the surface
1) Due to a sudden drop in pressure as ,
the pressure scale height drops drastically,
quickly becoming unresolvable.
2) The pressure profile is not smooth at ;
i.e. is discontinuous across the surface.
This could potentially lead to numerical problems.
We comment on (2) at the end of this post; here we focus on (1). Problem (1) can possibly be addressed by increasing the ambient pressure. This would have the affect of moving the effective surface of the star (Here I have plotted the pressure vs radius (top) and pressure scale height vs radius (bottom) for both modified and unmodified profiles. Three horizontal lines in the bottom plot show the chosen scale height cutoff, while the horizontal lines in the top plot show the corresponding pressure cutoffs. For example, if we want the minimum scale height to be , then we should set the ambient pressure to dyne/cm . This would cause the pressure to equal the ambient pressure at rather than at .
) inward. It is important to be aware how the minimum pressure scale height would be affected.
Given that plot, it seems reasonable to try imposing ambient pressures of
A) set implicitly by AstroBear to a low value:
3d density
1d density
3d pressure
1d pressure
1d
3d density start and end comparison
1d density start and end comparison
3d pressure start and end comparison
1d pressure start and end comparison
B) 3d density
1d density
3d pressure
1d pressure
1d
3d density start and end comparison
1d density start and end comparison
3d pressure start and end comparison
1d pressure start and end comparison
C) 3d density
1d density
3d pressure
1d pressure
1d
3d density start and end comparison
1d density start and end comparison
3d pressure start and end comparison
1d pressure start and end comparison
D) 3d density
1d density
3d pressure
1d pressure
1d
3d density start and end comparison
1d density start and end comparison
3d pressure start and end comparison
1d pressure start and end comparison
Discussion
Density: Comparing run (B) with the fiducial run (A),
we see that the density profile ends up deviating more from that at than in run (A).
The situation seems to improve as we increase in run ©.
Low amplitude density waves are seen outside the star, but the density profile remains reasonably constant.
In run (D), density waves outside the star are of lower amplitude than in ©,
but the final density profile has been squeezed slightly in comparison with the initial profile
(the star appears slightly smaller).
The 1D density comparison shows the presence of an unphysical kink in the profile.
Here the density wave is propagating inward, and the profile has not yet stabilized.
In fact, none of the density profiles have stabilized by the end of the simulation.
Pressure: Increasing
can be seen to reduce the expansion of the star's outer layers. On the other hand, the profile in the inner part of the star gets perturbed as pressure disturbances propagate inward.We see then that imposing an ambient pressure helps to prevent the outer layers from expanding, but also causes larger inward-propagating perturbations.
The sudden transitions in
and at the stellar surface (Problem (2) above) should also be addressed. Probably some combination of increasing and smoothing the profile to satisfy mass continuity and hydrostatic equilibrium at all radii (even outside the current stellar surface) is needed. The next step is therefore to think about how to smooth the profile near the surface in a reasonable way.
Update 1
It occurred to me that another possible way to get around the problem of the scale height dropping to low values near the surface
is to simply truncate the stellar profile at some value.
I did this by truncating the profile where the pressure drops below dyne/cm .
This happens at about (so the star loses 8 of its radial extent).
The movies are shown here, with initial and final frames compared below each movie. All units are CGS:
E) set implicitly by AstroBear to a low value and cut off profile at dyne/cm :
3d density
1d density
3d pressure
1d pressure
3d density start and end comparison
1d density start and end comparison
3d pressure start and end comparison
1d pressure start and end comparison
Outgoing pressure and density waves are visible. Note also that the ambient values of pressure and density set implicitly by AstroBear are larger than in Model (A), approximately by the factor . The results are not very encouraging… and we conclude that truncating the star just below the surface does not seem to offer any signficant benefit.
Update 2
After discussing with Eric, one idea that came up was to try a model like (D)
but with the density also held constant where the pressure is held constant.
This would avoid having a small (unresolvable density scale height).
This makes the situation worse, probably because it is the pressure gradient that determines the force,
so might as well keep the density profile as realistic as possible.
F) set to dyne/cm and set to a constant in the same region:
1d
Mapping a modified RGB profile to the grid: first results
As explained in the previous blog entry,
the next step was to map the modified RGB profile to the AstroBear grid.
In this blog entry I report the initial results.
From the statement in Ohlmann+16c that it is necessary to resolve the softening length
Another constraint to satisfy is to resolve the scale height here
for the case and
here
for the case .
Note that the unphysical behaviour of near the transition radius
and noise in for are probably consequences of how the IDL routine used to differentiate
the pressure profile handles the different sampling in radius for (obtained using modified Lane-Emden) and (MESA).
This is not expected to cause a problem in AstroBear, which interpolates the inputted profile for the AstroBear grid.
For , the minimum value near is at ,
whereas for , the minimum value near is at .
With a resolution of , we resolve by at least a few cells for , which may be sufficient.
For , and resolution, is only marginally resolved by cell,
which is apparently insufficient (see results below).
We now present plots for the density from each of the following simulations:
A) Fiducial run: resolution 3d,
1d
B) Low res run: resolution ( resolution) but otherwise same as (A).
3d,
1d
C) High res run: resolution ( resolution) but otherwise same as (A) ( was attempted but protections caused the simulation to terminate).
3d,
1d
D) No iteration over core mass run: , so not fully self-consistent (see previous blogs), otherwise same as (A).
3d,
1d
E) Small softening length run: instead of , otherwise same as (A).
3d,
1d
F) No spline run: Spline softening of potential not employed in AstroBear, otherwise same as (A).
3d,
1d
G) Original MESA profile but with spline potential run: No modification to profile, but otherwise same as (A).
3d,
1d
H) Direct MESA run: No modification to profile, nor is spline softening employed, otherwise same as (A).
3d,
1d
I also made side-by-side movies of the fiducial run (on the left) and an alternative run (on the right), for easy comparison:
i) (A) and (B)
3d,
1d
ii) (A) and ©
3d,
1d
iii) (A) and (D)
3d,
1d
iv) (A) and (E)
3d,
1d
Discussion
From the above plots we can conclude:
I) The fiducial run (A) is quite stable at the center, as expected,
but there is still a slight drop in the central density during the run.
This might be alleviated by using higher resolution, but run ©, with slightly higher resolution,
shows only a marginal increase in stability.
II) In all the runs, the SURFACE of the star becomes unstable on the local dynamical time,
as expected.
III) A resolution of is needed for approximate stability at the center, as expected.
IV) The run (E) is NOT quite stable at the center when using the same resolution as for the fiducial model.
This is not surprising because both and are smaller in this model, so not as well-resolved.
V) The iteration procedure used for the particle mass to ensure that is equal to the MESA value
makes a small but noticeable difference to the stability and final profile of the star (see the 1d plot comparison in (iii) above).
If this step is not included, the density profile develops an unphysical kink at .
Next steps
Some logical next steps are:
1) Figure out a viable method for reducing and smoothing out the pressure gradient at the surface.
This will involve specifying an ambient value and/or an extension of the profiles for .
This involves coming up with some different methods, testing them, and comparing the results.
2) Once (1) is implemented, protections should no longer be a problem, so higher resolution (e.g. ) could be tested.
3) It will then be useful to make other plots to study, e.g. the degree to which hydrostatic equilibrium is being satisfied, or the local Mach number of any residual motions.
4) If the star is reasonably stable after these steps, then AMR can be implemented and tested.
5) If damping of residual motions is still needed, it can first be implemented as in Ohlmann+16c.
Plan for next step of mapping the modified RGB profile to the grid
Now that we have been able to generate a modified MESA profile, we must map it to the AstroBear grid. The steps are as follows:
1) Determine the desired cutoff radius and resolution.
2) Solve the modified Lane-Emden equation as explained in the last blog entry,
including an iteration over the mass of the gravitation-only particle.
3) Produce an input file for AstroBear with tabulated , , and values.
4) Perform multiple runs for comparison.
5) Assess the level of hydrostatic equilibrium for each run.
Let us consider item (1). For now let us consider a uniform grid. Let the resolution be .
The outer radius of the star is , and the cutoff radius is .
As in Ohlmann, the softening length for the spline potential of the gravitation-only particle is also .
(For the MESA solution will be replaced by the modified Lane-Emden solution for ,
and for will be determined by re-integrating the hydrostatic equilibrium equation
inward using , with equal to the MESA value.)
Further, we define , that is, the ratio fo cutoff radius to outer stellar radius.
The number of resolution elements over a softening length is given by ,
where is the grid element size. Finally, let the box size be .
Putting this together, we find
This formula gives the resolution required for a given
, , and . Ohlmann+16a states "…we find that a resolution of about 10 cells per softening length is required to ensure energy conservation during the in-spiral." Also, "…in a sphere of five softening lengths of the gravitation-only particle, the maximum cell radius was bound to a tenth of the softening length." This suggests using , so we set . For the RGB star, . To be consistent with our previous simulation, we may choose . As in Ohlmann+16c, we can try , , or . This results in required resolutions , , or , respectively, or, in physical units, , , or . Ohlmann+16a states "The smallest cells near the RG core have a radius of about at the beginning and about at the end of the simulation."
We now consider item (4). It would be useful, initially, to compare the following runs:
a) , .
b) , (i.e. lower resolution).
c) , (i.e. even lower resolution).
d) , , without mass iteration step in item (2), so using a slightly larger particle mass.
e) , , with mass iteration step but without modifying the MESA profile
(i.e. skipping item (2) but using the particle mass from model (a)).
f) , (i.e. smaller cutoff radius).
g) , with ambient pressure set to higher value to effectively cut off very outer layer of star where scale height cannot be adequately resolved.
Resolving the scale height
One important additional point is that one should adequately resolve not only the softening length rgb.pdf for a plot of scale height vs. radius. Modifying the MESA profile for will lead to larger scale heights there, but we must still check whether is large enough. This will likely be most problematic at the stellar surface , where . Here we will not be resolving the scale height so we would expect velocity perturbations to arise. Ohlmann+16c calculates a necessary but not sufficient expression for to ensure that Mach number fluctuations are below a specified level. Assuming the Mach number at , after the first part of a time step (see their Sect. 2.3 and Appendix A for details) one obtains
, but also the local pressure scale height . See page 3 of the past presentation,
where
is the Courant-Friedrichs-Levy constant and is the adiabatic index, so that.
E.g. for
, , and , we obtain . However, Ohlmann+16c somehow obtain the slightly larger value . In any case from this condition we require , and possibly , to avoid Mach number fluctuations greater than . However Ohlmann+16c comments "Even if the resolution requirement is met, other sources of numerical error (e.g. interpolation error, errors from the gravity solver) still introduce spurious velocity fluctuations. Thus, an appropriate relaxation procedure is necessary when mapping stellar models to hydrodynamical grids: the velocity fluctuations have to be damped."It is important to replot the scale height vs radius plot of rgb.pdf for the modified RGB profile, as well as for the case of a higher ambient pressure.
An updated README file with instructions on how to run the code, along with the relevant files, is available here.
Modified giant profiles (continued from last blog)
I continued to work on generating the modified RGB profile to use in AstroBear, as discussed in the previous blog.
As I had been confused by the mismatch between the modified Lane-Emden (MLE) solution and the MESA solution at the transition radius
, I wrote S. Ohlmann to ask about this. He explained that the pressure profile of the MLE solution is not actually used. Instead the equations for and are integrated again, this time backwards starting from some point on the MESA profile, to obtain and for . Thus, only the MLE profile for is used. (So the final profile for will not be a true polytrope, but that is okay.) This made sense but then at least the MLE profile for should almost match the MESA profile at , I realized, because both solutions satisfy hydrostatic equilibrium, after all, and by construction is almost the same for both solutions. The reason it is almost the same and not exactly the same will be discussed below.This led me to look at my code and sure enough I discovered that the solution was not properly converging. It was oscillating between two apparent solutions, which led to the error in the
profile. Therefore I set on fixing the PDE solver. The method I had been using was a shooting method (of my own design). I consulted Numerical Recipes (Press et al.) and found the relevant programs, but eventually realized I would have to start from scratch if I did it that way. I modified my own program and it now converges properly, iterating over 2 free parameters to satisfy the two boundary conditions at r=h. (It could instead be solved as a boundary value problem but that is more complicated and unnecessary.) A useful "trick" is to first run the code in low resolution, which converges in a few seconds, and then you have a good estimate of the parameters which you can use to run in high resolution.As can be seen from this new version of profile.pdf, the profiles are reasonable and match those of Ohlmann. The MLE profile for does not precisely match MESA at (as explained last blog there is no reason it should) but is now only off by about 20% for the polytrope solution with . This seems very reasonable. The only concern I had (which I kept revisiting) is that obtained from the hydrostatic equilibrium equation by first integrating to obtain , does not perfectly match MESA at the boundary. After studying various solutions (with or or ) I believe this is just because the IDL differentiation and smoothing functions used to obtain from the MESA profile is imprecise and sensitive to the number of points chosen for the smoothing, etc. I don't think this will cause problems in AstroBear. Note that the profile matches perfectly at the boundary. But this is by design: IDL was used to calculate which was then used to set the boundary condition that should equal the MESA value. Note that MESA apparently does not give the option of directly outputting .
There is, however, one slight inconsistency in the method is the following (as alluded to above). The value of AstroBear by a mass that is greater than the MESA value of . In other words, we have added the extra mass to the core, so the MESA profile for will no longer be in perfect hydrostatic equilibrium. I discussed this issue with Ohlmann who was aware of it. He says he tried setting the particle mass to some value less than and then iterating over (yet a third parameter over which to iterate). He said it did not make enough of a difference to worry about. Tomorrow morning I will try a manual iteration and report back here.
of the MESA profile is equal to the point particle mass . However, after solving the MLE, we have , where is the gas profile obtained by solving the MLE. By integrating backward and resetting , a discontinuity is avoided. But this means that the core at is being replaced inAs promised I have now tried the iteration procedure mentioned. This was done by modifying the code to include an additional parameter: profile.pdf (Figs. 14-16). I have compared these plots against those where the iteration over is not performed (Figs. 2-5). The profiles are almost indistinguishable. However, the new method including this manual iteration is more self-consistent. It is not difficult to implement nor does it require significantly extra time. Therefore I see no reason why it should not be used when constructing the profiles to be used in AstroBear. Including this last step, not included by Ohlmann, will probably not typically make an important difference. Nevertheless, it is an improvement that I think is worth noting in the paper.
which is not equal to . I obtain in the usual way from MESA but then instead of setting to equal , I set , with a fraction less than (but close to) unity. I first set to a reasonable value 0.96 given that for , we had . After a few manual iterations, I was able to get a converged solution such that . The value of turns out to be 0.963 for our fiducial profile ( polytropic index and ). I have now added the plots to the end ofModifying stellar profiles from MESA for input into AstroBear
I continued working toward getting a giant (RGB or AGB) onto the grid.
Recall that when trying to translate the MESA stellar profile to the grid, the compact core gets washed out due to the grid not being fine enough to adequately resolve the local scale height. Last time, I showed that adding a sink particle with the mass of the unresolved RGB core can help to slow down the (unphysical) expansion of the star. But the star is still unstable. This is at least partly due to the fact that the inputted stellar profile has not been modified to take into account the modification to the potential due to the replacement of the central part of the star by a point particle. As explained in Ohlmann 2016 (phd thesis), the asymptotic behaviour of the pressure gradient
as tends to 0 must be correctly reproduced ( as ) to avoid unphysical sound waves eminating from the center. This is achieved in Ohlmann 2016 by truncating the MESA profile at some radius (the higher the resolution, the smaller may be chosen to be) and replacing the inner part of the profile with the solution to a MODIFIED Lane-Emden equation that takes into account not only the potential of the gas (as in the standard LE equation), but also that of the central point particle. Doing this involves a few steps:1) Choose a truncation radius
and obtain the interior mass from the MESA profile. This is the mass of the central point particle .2) Modify the potential to account for the central point particle using a softening to prevent it from blowing up as
. Here we follow Ohlmann 2016 (see also Ohlmann et al. 2016, arXiv:1612.00008).3) For simplicity, approximate the stellar profile for
as a polytrope , with the polytropic index a parameter that Ohlmann sets to . The pressure , with constant, so for , we obtain , as for a relativistic white dwarf. Assuming mass continuity and hydrostatic equilibrium leads to the modified Lane-Emden equation derived in Ohlmann.4) Now solve the modified Lane-Emden (MLE) equation by first breaking the equation up into a system of two coupled first order PDEs and then solving the system numerically. I have done this using a 3rd order Runge-Kutta "time"-stepping routine in fortran (Brandenburg 2003). For the simplest case of code downloaded from the web.
, the MLE equation reduces to the standard LE equation. I've tested my code for this case against a simpler, 1st orderSolving the MLE equation is actually much more challenging than solving the LE equation. This is because aside from
, there are now two additional parameters: the central gas density , and the characteristic radius ( can be written in terms of ). Basically, these parameters must be iterated over until a solution is found which satisfies the BOUNDARY CONDITIONS at the transition radius . (Ohlmann mentions using a non-linear root-finder to accomplish this step, but does not provide details.) I have used a simple "home-built" recipe for the iteration that leads to a converged (rapidly enough) solution.
Following Ohlmann, we use the following BCs:
i) matched to MESA profile
ii) matched to MESA profile
6) This approximate (polytrope) solution for the modified profile for
can then be combined with the MESA profile, so that for , one retains the more realistic MESA profile. Now the modified profile can be compared with that of Ohlmann.Refer to the file profile_blog1.pdf.
Figure 1 is the relevant figure from Ohlmann et al. 2016 with which results may be compared.
Figure 2 shows the mass profile of the RGB star as obtained from MESA, and the chosen transition radius
, where is the outermost radius of the star. The central mass is about , in agreement with Ohlmann.
Figure 3a shows the density
Figure 3b shows the density gradient . Note that and of the MLE solution are equal to the MESA values at . In other words, the boundary conditions have been correctly implemented. Note also that the MLE solution for agrees with Ohlmann's solution from Figure 1.
Figure 4a shows the pressure
Figure 4b shows the pressure gradient . Again, we must re-normalize at . Doing so brings the solution into close agreement with that of Ohlmann, seen in Figure 1. The re-normalization factor is close to but not precisely the same as for .
Figures 5 and 6 show the profiles for
, , , and for the case , while Figures 7 and 8 show the same for . The solutions obtained are quite similar to that obtained for the case.Figures 9, 10, and 11 show the case
. That is, with double the transition radius (and ). The MLE solutions can be compared with the green lines in Figure 1 and show good agreement.Figures 12 and 13 show the fiducial
and , but now with the boundary conditions modified so that the solution to the MLE equation has equal to the MESA value (as before) and equal to the MESA value (instead of ). We see that this results in a solution for which and do not match the MESA solution at the transition radius , as would be expected.Most of the relevant fortran, IDL and tex files for the above work including a README file can be found here.
Remarks:
Matching all quantities , , , and to the MESA solution at AND satisfying hydrostatic equilibrium is not possible to do when approximating the profile for as a polytrope. This is because there are only 2 free parameters ( and ), whereas there are 4 boundary conditions, so the problem is overdetermined. Thus, either smoothness or hydrostatic equilibrium must be sacrificed. To the best of my understanding at least, Ohlmann et al. 2016 chose to sacrifice perfect hydrostatic equilibrium to make and smooth accross the transition radius.
Some natural next steps would be:
1) Plot the quantity for the modified profile to assess the level of agreement with hydrostatic equilibrium. Do the same for the unmodified MESA profile and for the pure polytrope solution of the MLE equation.
2) Map the modified solution to the AstroBear grid and perform a run with the appropriate sink particle mass ( ) to assess the level of stability.
RGB star with sink particle
1) Understand how MESA stellar profiles translate to the grid.
It is important to make sure that the input from MESA is being gridded correctly, so compare with Ohlmann+16c https://arxiv.org/abs/1612.00008v1. See last pages of
this updated presentation. We see that the core gets cut out due to lack of resolution at the center, as expected. Though the units used are different from the Ohlman plots, I tried to lign them up. It can be seen that the initial pressure, density and specific internal energy profiles are in agreement with Ohlmann, as expected. This confirms the following:
(i) (Slide 5 & 6): The MESA density and pressure profiles that we put in are basically what we get out, except for the very center, which gets washed out due to lack of resolution (the resolution is slightly larger than 1 R_sun, which is where the profiles become flat). These profiles also agree with those of Ohlmann;
(ii) (Slide 7): A cutoff radius of 1 R_sun corresponds to a missing central core mass of about 0.4 Msun (which is the core mass used by Ohlmann);
(iii) (Slide 8): The profile for the specific internal energy looks very similar to Ohlmann's profile (though the units are different). This confirms that our code is using the same (ideal gas) equation of state as Ohlmann.
Now that this sanity check has been done, we can try introducing a sink particle at the center.
2) Introduce sink particle to replace the core. Here I've tried sink particles of the following masses:
a) 0 Msun,
b) 0.2 Msun,
c) 0.4 Msun (closest to the actual core mass),
d) 0.8 Msun,
e) 1.7 Msun,
f) 3.4 Msun,
g) 10 Msun.
Movies of density (both 2D slices and 1D profiles along x) are here. Simulations have resolution 128^{3} in a box length 140 R_sun.
Note that the star is not stable for any of the runs, but the 0.4 Msun sink particle does at least seem to help to stabilize the star compared with the case of no sink particle (see remarks below).
For the 0 Msun case (no sink particle) I've checked that the initial local sound-crossing time t_s(r) = r/c_s(r) is comparable to the time it takes for the outgoing pressure disturbance to propagate to radius r, for a few different values of r. Actually, t_s(r) is a few times larger than this expansion time, but within a factor of order unity, as expected. A plot of the initial sound-crossing time for the 0 Msun case is available here and can be compared with the expansion times in the movies showing density mentioned above. Movies of the 1D profile of the sound speed for the 0 Msun and 0.4 Msun cases are available here.
Another useful quantity is the fractional difference from hydrostatic equilibrium:
hef = | |grad P| - |rho g| |/max(|grad P|,|rho g|).
This has been plotted in the following fractional HE movies.
Remarks:
1) A sink particle with mass equal to the core mass helps to preserve the high density at the center, and slows the expansion due to hydrostatic imbalance, but also creates outgoing sound waves eminating from the center;
2) The presence of the sink particle somehow introduces unphysical 4-fold symmetry, followed by complete asymmetry. This seems to be a numerical problem that needs to be addressed;
3) Though it is not computationally optimal for this problem, it would make life simpler to change back to cgs units as the computational units here (rather than length units of R_sun, as in the current simulations). This would allow easier comparison with Ohlmann results and prevent unit conversion errors for these trial runs. I will implement this change in the next set of simulations.
Next step is to solve Ohlmann's modified Lane-Emden equation inside the truncation (cutoff) radius. The choice of truncation radius determines the core mass = m(r_truncation). Then match this solution onto the MESA profile at the truncation radius, as done by Ohlmann (density should be smooth across the transition at r_truncation). I will write a code to do this. Hopefully this will result in a more stable star.
Putting RGB star on the grid: update
1) Movies —> all units are cgs
Simulation 1: Full star on the grid, resolution 256^{3 }
a) density, variable color bar b) density, fixed color bar c) density 1D profile d) density 1D profile, zoomed
Simulation 2: Central part of star on the grid, resolution 64^{3} with 3 levels of amr, so up to 256^{3} (zoomed in by factor 50 from above movies, so most of star is "outside" the grid)
a) without mesh b) with mesh c) inner region close-up, with mesh
2) Original profiles from MESA slides
Notes on slides:
a) Slide 4 shows the scale height as a function of radius (upper plot) and pressure v. radius (lower plot). In the lower plot, the RGB star is orange. The scale height dips significantly below the local radius below r= 2e-2 Rsun. b) Slide 5 shows the density as a function of radius. The values can be compared with what is achieved in the simulations, e.g. at the center of the star.
3) Discussion
At yesterday's meeting it was decided that resolving the center is not possible, and that the most promising approach is to introduce a sink particle at the center and then modify the pressure profile accordingly to account for the modified potential, as done in Ohlmann 2016 (PhD thesis). Serendipitously, the paper on exactly this subject came out on arXiv today: https://arxiv.org/pdf/1612.00008.pdf