COMMON ENVELOPE SIMULATIONS

New Work

  1. Plotted separation vs time for runs 132 (Krumholz accretion) and 143 (no accretion) on the same plot, with orbits as insets.
  2. Plotted accreted mass and accretion rates for runs 132 and 143 up to t=40 days.
  3. 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.

http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/p_mult_143_132.png

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).

http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Run143/macc2_143.png

  • Below is the accreted mass as a function of time for run 132 (Krumholz accretion model) in blue, and the corresponding rate in red.

http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Run143/m2_Damp132_upto40days.png

Discussion about accretion radius in Krumholz accretion subgrid model (with Bo)

  • In the discussion following equation (17) in Krumholz+04, we read:

http://www.pas.rochester.edu/~lchamandy/Graphics/RGB/Post-sink_particle/Post-modified_Lane_Emden/Krumholz+04_extract.png.

  • 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

  1. 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.
  2. Edge-on plots of density and velocity.
  3. Read ADAF papers.
  4. Start writing paper?

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