# Recombination Update(7/31)

isothermal flow and Bondi problem:

https://www.wolframcloud.com/objects/yxamyz/isothermal-fixed_x.nb

# 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

# CEE energy budget project

## New Work

- Working closely with Luke to prepare for the paper. We are hoping to get a first draft by next Monday

- Updates on energy note

https://www.pas.rochester.edu/~yishengtu/CEE_gp_meeting_07312018/Energy_note_07312018.pdf (most up-to-date)

The major updates for energy note are

- High resolution data updates (section 6.1) Many thanks to Luke, Baowei and Jonathan!
- Comparison between theoretical calculation and simulation values. (section 5.2 and 6.2)
- Spacial energy plots added self-gravity of the gas
- Plots about energy and mass within the orbital radius of the particles (section 5.4 and 5.6)
- momentum (not very useful for now)

- Updates on energy figure

This is a separate note intended to analyze the energy figure (figure 2 in energy_note_06262018 and figure 2, 3, 4 in current version)

Some of the plots in this note are not up to date as the energy note. The table is also not as up-to-date as the energy note In this note, figure 1, 5, 6 compares results from our simulation to that of Ohlmann's.

- Updates on energy movies. The movies last time excluded the gas-self gravity. This updated version includes this term.

This movie is the normalized energy movie. The normalization term is the larger term of the absolute value of potential energy and kinetic energy (include internal) https://www.pas.rochester.edu/~yishengtu/CEE_gp_meeting_07312018/D143_energy_movie_Z.gif

This movie is the absolute value of the energy in log scale. I am still trying to figure out a better way to present the actual values of energy density but so far this is what I could think of ..

https://www.pas.rochester.edu/~yishengtu/CEE_gp_meeting_07312018/D143_energy_movie_Z_abs.gif

## Next step

- May want to justify the similarities between de-resolved data and full resolution data since some of the data could be hard to obtain with full-resolved data.
- More work on the paper with Luke

# Update 7/31

- Need to move out of 476 for a week or two. What should we do with computers/where should we store miscellany?

- Parameter space paper essentially done. If we want input from Ruth, we should set up a time to talk with her. I'll give it a final once-over, then submit.

- First cut of intro and methods for radiation pressure paper. Introduction may need to go a little deeper into a discussion of the wind itself - could use some input here. Also, I've pulled most of the methods from the parameter space paper.

- HD209458b status: These two frames compare almost the same amount of physical time:

The wind is building much more slowly. Based on Owen & Alvarez 2015, we're well into the cooling-limited regime here. This seems relatively borne out by the heating and cooling happening:

Doing a calculation similar to that for the radiation pressure blowoff (but I believe more accurate - fewer unknown factors here), without cooling, we would expect the mass between the ambient and R_{p} to be completely unbound in CT ([min flux, med flux, max flux]), compared to CT for our heavier parameter space planet (which is on the high side, but not too far off - plus, we're not launching all of the mass considered here). This suggests it will take ~50x longer to launch the wind with HD209458 There's no explicit dependence on planet radius, but changing the radius also changes the density (which is why these differ, in addition to the additional planet mass). Louden et al. reconstructed a lower total ionizing flux (a factor of ½) than we're using, but we could increase the flux to get a stronger wind.

- I believe charge exchange should be working now, with the stellar wind also implemented as required. I have the stellar wind set to maintain in the -x, y boundaries (y because there's the rotational component of the interaction). Waiting for the most recent test to start (requires more RAM than available on debug partition).

# To Do

- Still contemplating the blowoff threshold. Eric has suggested cooling as a possible mechanism; I'd also like to include some sort of ablation, since the outside layers can absorb a lot more energy than required to unbind them before they're no longer shielding the inner gas (this is partially because we assume the gas absorbs at line center, no matter its radial velocity - this may be more important than we were initially thinking).

- Finalize charge exchange. Will test against analytic 1D solution; anything else we can test against?

- Continue HD209458b radiation pressure.

# Bondi Flow/Accretion Subgrid Model Questions

** The equations for Bondi flow admit 4 classes of solution only two of which are physical**

- A solution with u(r) = 0 at r = infinity. (AB'C' in Bondi 1954 Fig 2)

- A solution with u(r) = 0 at r = 0. (A'BC in Bondi 1954 Fig 2)

Note both are of type ii in Bondi's formulation.

From first principles we expect the global solution (not just what happens in the kernel to be solution 1. We have a spherically collapsing cloud which has

.That solution however must be matched as cleanly as possible with what happenes within the kernel (whose radius is

) with the kernel values being given asSo the question becomes are we expecting that within the kernel we may switch from solution type 1 to solution type 2?

Physically this can only occur if a shock has formed at the "surface" of the accreator which has then expanded such that

.So given the values of velocity and location, we can calcualte x0 and y0, which give us lambda and lambda_c. This then divides the x0-y0 space into super/subsonic and super/subcritical regions.

- In the yellow region, you can integrate inward (or outward) without ever becoming subsonic.
- In the cyan region you can integrate inward (or outward) without ever becoming supersonic.
- In the left supercritical region,s you should be ok - as you should be able to integrate inward - though not outward
- The right supercritical region presents a problem - as the integral inward will diverge. It is these regions which have no steady state solution and require something like the 'shock assumption'

And for reference, here's the same figure ignoring Gamma

Not the line dividing sub/super critical follows x0^{2}*y0*z0=lambda=lambda_c - as z0 = 1 by definition.

And here's the same plot but for a range of

.