New Work

1. 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.
2. Drag force/secondary mass paper:
   1. Made movies for runs 149 and 151 (M2 = 0.5 Msun and M2 = 0.25 Msun)
   2. Wrote script to compute drag force
   3. Ran script to compute drag force on reduced resolution run 143 and produced various plots (see below)
   4. 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 \bm{f}_i\cdot\bm{v} and components of \bm{f}_i 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 r-component means away from the other particle, while positive \phi-component means in the sense of the orbit.
Comments: Force on secondary in frame of primary \bm{f}_2\cdot\bm{v}/v is shown by black line. Phi-component f_{2,\phi} is shown by orange line. Note that at early times, \bm{f}_2\cdot\bm{v} is dominated by f_{2,r}v_r since f_{2,r} is so large. At later times the orange and black lines coincide, so \bm{f}_2\cdot\bm{v} is dominated by f_{2,\phi} v_\phi.

We see that the \phi-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 \phi component) but the \phi 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 a(t). 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 a 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 r=a(t).
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 R_\mathrm{2,BH}(t) is comparable to a(t) and comparable to the pressure scale height H. 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 M_2 is reduced (in the limit M_2\rightarrow0, R_\mathrm{BH}\rightarrow0 since v\sim (\mathrm{G}M_1/a)^{1/2}, so independent of M_2, in that limit. This can be tested with Runs 149 and 151 which have M_2 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)