# 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.

# Review: Conserving angular momentum over accretion

Enforcing mass and linear momentum conservation means that angular momentum will generally *not* be conserved over the accretion step. We can see this by first noting that (by mass conservation) the sum of the mass to be accreted from the kernel (LHS) is equal to the mass of the sink particle after the accretion takes place (RHS; post-accretion quantities are denoted by a prime):

Similarly, momentum conservation says that:

Note, this last equation gives the velocity of the center of mass of the accreted material, which must equal the velocity of the sink particle, given momentum conservation.

From here, we might be tempted to write:

However, we already know that the mass of the sink and velocity of the sink are

and , respectively. Thus we have to write:and ask for what R' is this equation valid. Rearranging this equation (and calling the LHS

), we can write:In general,

and will not be perpendicular, thus there will be no solution for .What if we instead let

equal the center of mass of the accreted material? Then, the equation for angular momentum conservation becomes:

Equality then requires that

, which also will not generally be true.
Thus, the sink angular momentum cannot strictly be set equal to the *accreted* angular momentum, if the angular momentum is to be conserved across the accretion step. Instead, we need an additional vector which can absorb the difference in the angular momentum. This is the reason behind devising a 'spin' angular momentum vector for the sink particle. With the spin vector, the *total* angular momentum across the accretion step can be conserved.

**Using a spin angular momentum vector to conserve angular momentum**

As discussed above, the sink angular momentum following accretion (

) is set by the accreted mass and linear momentum from the kernel. It is given by:

As shown above, this angular momentum vector will generally differ from the total angular momentum accreted from the kernel (

):

Thus, we can't simply set the particle's spin axis equal to *total* angular momentum across accretion is conserved. We call this vector the particle's spin. The spin can be found by enforcing conservation of the total angular momentum across the accretion step:

This equation shows that the updated total angular momentum of the sink = the old total angular momentum + the accreted angular momentum. By rearranging this equation, we can solve for

, which absorbs any excess angular momentum over :

# Simulation Update

- Ionization-only test: Matches exactly the results from our original ionization tests (way back when) up to the final frame at 4ish hours (~0.205 time units). Since this simulation is running in 3D, it doesn't go as far as the potentially troublesome simulation, but I think it's safe to go back to 2D.

The long term behavior still appears to not be what we expect — given the behavior of the 1D simulation (see below), it may be due to a higher flux than expected being used.

1D test: With the HotJupiter branch line transfer module, we get a stable ionization equilibrium (did rerun to make sure none of the parameters had been changed). With the radiation pressure implemented, the ionization front moves across the simulation domain to the right, indicating something incorrect happening. However, the momentum is a constant 0, so it doesn't appear to be radiation pressure-related.

- Investigated neutral tail coming from the first planet. Velocity vectors show it's originating almost entirely well outside of the planet boundary.

- Have simulations queued for parameter space. For production runs, using total of 150 frames for 15 computational times (5.25 days, or ~30 planetary crossing times).

Rotating Frame | |||

Run # | M_{P} (M_{J}) | Flux (phot/cm^{2}/s) | Status |

1 | 0.07 | 2x10^{13} | 117 frames complete, running |

2 | 0.263435 | 2x10^{13} | 107 frames complete, queued to restart |

3 | 0.263435 | 2x10^{17} | Unqueued |

4 | 0.07 | 2x10^{17} | Unqueued |

Non-rotating Frame | |||

Run # | M_{P} (M_{J}) | Flux (phot/cm^{2}/s) | Status |

1 | 0.07 | 2x10^{13} | Unqueued |

2 | 0.263435 | 2x10^{13} | Unqueued |

3 | 0.263435 | 2x10^{17} | Unqueued |

4 | 0.07 | 2x10^{17} | Unqueued |

Was missing the TABLES from the non-rotating version, not sure why I wasn't getting any error output.