# Update 4/3: Wind Tunnel Run008 (ongoing) & some plots of WT007

## Ongoing Run

### WTRun008

Initial condition: at 4*10^{12} cm of a 3M_Sun AGB star. Mach number = 2.5, rho = 3.6*10^{-6}.
Simulation Setup: the same with Run006, with region of highest resolution R_max = 30CU, Softening length (spline) is 4CU, resolved by 16 pixels.

Some plots on Run 007, will type up a note further explaining notations.

### Orbital Decay vs Time

### Growth of Bondi-Hoyle Radius

### Acceleration, constant scale

### Acceleration, scale to instantaneous BH rate

### Acceleration vs. Mach

# Update 3/26: Wind Tunnel Run 007

## Finished Runs

### WT Run 007

Same setup with Run006B: softening length resolved by 16 pixels. Region of highest refinement et to 30 CUs. Box size is set to be 2048^{3} CUs, 2^{3} as large as those of Run 006s, 4^{3} as large as Run 005s. This enables a increase of run time to 2CU.

Log density & velocity vectors movie:

As shown in the movie, although the density disturbance around the particle is almost always contained within the box, near the end of the simulation gas velocities at the boundaries are altered due to gas self-gravity. In other words the gas across the box begins to collapse onto itself. This is to be expected since the box is larger than the Jeans scale of the gas, and self-gravity introduces positive feedback to "accretion" around the point particle.

The dynamic friction also confirms this positive feedback. In the shorter timescale used before (¼ of total runtime), Run 007 does not stand out -

But the drag blows up later -

Which can be fitted by an exponential function - F = f0*Exp(t/tau) + c

Here f0 = 0.157, tau = 7.442, and c = 2.324.

Constant offset c here can represent the drag force as predicted by BHL, ignoring self-gravity.

To avoid using incorrect DF measurements due to limited box size, I am running currently Run 007B, which is the same setup as Run 007 but with a factor of 2^{3} box.

## Next Steps - parameter space? Non-dimensionalization?

I think the simulation module has become mature enough that exploring a larger portion of the parameter space becomes possible. MacLeod suggested me to non-dimensionalize the problem, to better aim at the physics. I am studying his (their) approach - there might be some difficulties in, for instance, the scalability of density. But even in cgs we can still artificially alter Mach number, density and the particle mass, etc.

# Update 3/5: Wind Tunnel Runs 006AB&D, as well as reviewing Run 005B

Work in the past two weeks has been focused on testing an AMR scheme that only forces maximal refinement within a radius of the particle. Currently the module is working fine, except that it cannot have the box be relaxed first before introducing the particle.

## Finished Runs

### WT Run 006A

Same setup with Run 004A. No accretion, highest resolution 0.5CU, softening length (spline) is resolved by 8 pixels. Radius of highest refinement is set to 40CU, which is more than twice as large as the Bondi radius 18.7CU. Significant run time improvement (order of 8) & low storage requirement (~300M per frame vs. ~4G per frame w/ normal AMR).

### WT Run 006B

Similar setup with Run 006A, except resolution is improved by a factor of two to 0.25CU, and softening length is resolved by 16 pixels. To compensate, radius of highest refinement is set to 20CU, still larger than Bondi radius. Similar run time as the previous run.

Log density movie with mesh grids:

### WT Run 006C

Similar to 006B, but with radius of refinement set at 40CU. The runtime becomes too long (longer than the normal AMR), and was left unfinished.

### WT Run 006D

Similar to 006A, low resolution, but larger radius of highest refinement - 80CU. The run time is less than 2 days, similar to the AMR case. But the result looks unreliable.

Log density movie with mesh grids and velocity vectors:

## Comparison with Run 004A

## More one Run 005B

Zoomed-in log density movie: Zoomed-in Mach number and velocity vector movie;

# Update 2/11: Wind Tunnel Runs 004AB, 005AB, and comparison to 003

## Finished Runs

Just to summarize the four recent runs -

### WT Run 004A

- Sim parameters:

- Spacial resolution: base 64
^{3}, finest 1024^{3}(4 levels) - Time Resolution: 0.005CU = 2.2e3s
- Sim time: 0.5 CU, 100 frames
- Accretion = none
- Poisson solver convergence tolerance: 1e-6
- Run time: less than a day.
- Softening Length: 8CU (16 cells)

### WT Run 004B

- Sim parameters:

- Spacial resolution: base 64
^{3}, finest 1024^{3}(4 levels) - Time Resolution: 0.005CU = 2.2e3s
- Sim time: 0.5 CU, 100 frames
- Accretion = Krumholtz
- Poisson solver convergence tolerance: 1e-6
- Run time: less than a day.
- Softening Length: 8CU (16 cells)
- Accretion Radius (particle radius): 0.5CU (1 cell)

### WT Run 005A

- Sim parameters:

- Spacial resolution: base 64
^{3}, finest 2048^{3}(5 levels) - Time Resolution: 0.005CU = 2.2e3s
- Sim time: 0.25 CU, 50 frames
- Accretion = none
- Poisson solver convergence tolerance: 1e-3
- Run time: paused after 1.5 days. Estimated next 0.25 CU takes 4.5 days.
- Softening Length: 4CU (16 cells)

### WT Run 005B

- Sim parameters:

- Spacial resolution: base 64
^{3}, finest 1024^{3}(5 levels) - Time Resolution: 0.005CU = 2.2e3s
- Sim time: 0.5 CU, 100 frames
- Accretion = Krumholtz
- Poisson solver convergence tolerance: 1e-3
- Run time: less than a day.
- Softening Length: 4CU (8 cells)
- Accretion Radius (particle radius): 4CU (8 cell)

### Run 005A log Rho movie

### Run 005A vx movie

### Run 005B log Rho movie

### Run 005B vx movie

### Different definitions of softening lengths

The softening function used by both Luke and me is spline interpolation. As noted by Ohlmann, the softened potential is steeper compared to Plummer's potential. By comparing the potential at r=0, Ohlmann argues for a factor of conversion 2.8. Then in Plummer's term my softening length is within 3 pixels. Yet Ohlmann claims that a 10 pixel resolution is necessary.

### Drag force: a first comparison

First guesses:

- Due to self-gravity, drag force does not asymtote to stable value?
- Dynamical friction dominates over momentum accretion?

# Update 2/7: Wind Tunnel Run004 & 005

Finished Runs

## Finished Run

### WT Run 004A

- Unless otherwise mentioned, same setup with Run003.
- From now on self gravity is enabled. Compared to Run003, this slows down the sim within order of 2, as expected.
- mu set to 0.62, average mu of the Sun. This changed the temperature, but the pressure and the sound speed is not changed. And thus Bondi radius is also unaffected.
- Slight change of timescale - one wind passing time of the box.
- I did not understand the softening length properly: it's set in CU, thought it was set in # of cells. So previously I have been using 10CU=20 cells. For this run I'm using 8CU = 16 cells. Will discuss this a bit more later.

- Simulation time = 0.5CU = 2.57 days
- Wind temp = 3.45e5K

- Sim parameters:

- Spacial resolution: base 64
^{3}, finest 1024^{3}(4 levels) - Time Resolution: 0.005CU = 2.2e3s
- Accretion = none
- Hydro solver BC: extrapolated
- Self graivty Poisson solver BC: Periodic
- Poisson solver convergence tolerance: 1e-6
- Run time: less than a day.

Run 004A logRho plot movie: Run 004A Mach number movie:

### WT Run 004B

Setup is identical with Run 004A except that Krumholtz accretion is turned on. The radius of the particle (accretion radius) is set to 1. That is the main flaw of this run: the accretion radius is deep within the softening length, meaning the density sampled for the Krumholtz procedure to estimate the Bondi accretion rate is inaccurate. This motivated Run005s': to have the accretion radius be at least as large as the softening length. Ideally of course accretion radius should be larger, so that the correctly calculated densities of surrounding gas can be sampled. Within the softening length, without graivity, pressure should become equalized, meaning the density profile would be flatter than what we expect realistically. This would surely impact the performance of Krumholtz procedure.

Due to space constraints I did not make movies of 004B, though it can be easily reproduced.

### WT Run 005A

- This is anagolous to Run004A, but with a factor of 2 higher resolution. This enables the softening length to be reduced to 4CU, while still resolved by 16 pixels. Bondi radius is around 18 CU.
- To save time Poisson solver's tolerance is set to 1e-3.
- After running for 1.5 days, first 50 frames (0.25CU) was produced. The remaining wall time is at 4.2 days and increasing. I thus decided to end the simulation. As a proof-of-concept this resolution would require an order of magnitude increase in computational resources, which is not unfeasible on Bluehive, but if possible to run it on a better computer, it would be great. Although a larger box is needed for a steady state to be reached.

# Update 12/31: Common Envelope Wind Tunnel Run 003

## Finished Run

### WT Run 003

- Gamma fixed to 5/3, AMR enabled. Order of 2 larger box.
- Setup: 3Msun AGB + 0.1Msun secondary. 10
^{12}cm separation.

- Particle mass: 1.989e32 g
- Wind temperature: 5.56862e5 K
- Wind density: 0.0001 g/cm3
- Particle radius: 8.364e9 cm = 1.0 CU = 0.120 Rsun
- Bondi radius: 1.564e11 cm = 18.7 CU = 2.249 Rsun
- Run Time: 2 TS = 2 wind passing time of the box = 8.68e5 s ~ 10 days

- Sim parameters:

- Box size 512
^{3}CU - Base grid res.: 128
^{3}, max res. 1024^{3}. - Time Scale = 4.34e5s.
- Length Scale: 1 CU = 8.364e9 cm = 0.120 Rsun
- Time Resolution: 0.01CU = 4.34e3s
- Accretion = none.
- BC: extrapolated
- Gamma: 1.67
- Softening length: 10CU (20 pixels)
- Run time: ~ 2 days

## Preliminary Results

Log density movie Mach number movie total energy (E + U) movie

- Cylinerical symmetry preserved thanks to larger softening length.
- Particle accelerates away from the (front) bow shock.
- No Krumholtz accretion. Particle mass stays constant.
- (Near) sperical region where the gas is bounded by the particle, i.e. E_int + E_kinetic<|U|, as marked by the blue line in the third movie.

I then extracted the acceleration of the particle, comparing it to the HL Rate:

The blue dashed line marks the moment when the bow shock behind (+x direction) the particle reaches the right boundary. Currently computing dynamic friction by integrating the gravity of the gas within spherical regions of 1, 2, and 4 Bondi radii, as well as that of the gravitationally bounded gas.

Although Krumholtz accretion routine did not pick up any mass, I integrated sperical regions again of 1, 2, and 4 Bondi radii, as well as the gravitationally bounded gas, to characterize the clustering of gas around the point particle.

The dotted line is the prediction of H-L accretion. Mass enclosed in all four regions all start off growing roughly linearly, before reaching a equilibrium. This can be related to the sink particle not working properly and causing a pressure buildup witin the softening radius.

The accretion rate, as normalized by the H-L rate, is shown below.

## Next Steps

- Higher resolution and smaller softening radius (preferably have it equal to the physical radius of the secondary star), hopefully get the Krumholtz accretion functional.
- Shorter run time: seems when the bow shock reaches the boundary, the boundary conditions are changed, which may be related to the stagnant accretion & dynamic friction.
- Given shorter run time, may have higher time resolution.