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COMMON ENVELOPE SIMULATIONS

Plotted pressure and temperature profiles from frame 0 of simulation and compared with previous results.
Plotted sound speed profile from frame 0 of simulation and compared with that of fiducial RGB Run 143.
Plotted free electron fraction, gamma1 and mu profiles from frame 0 of simulation and compared with MESA profiles.
Added gamma3 (MESA) to plot from last blog showing gamma1.
Planning for Paper 5 on EoS.

Initial conditions
1. The pressure profile from frame 0. Orange=Run 143 (fiducial ideal gas EoS), Green=Run 207 (MESA EoS). Profiles match perfectly, as expected (pressure profile was inputted in a data file).
2. The sound speed profile from frame 0. Red=Run 143 (fiducial ideal gas EoS), Black=Run 207 (MESA EoS). Profiles are slightly different. Consistent with P and rho profiles being the same between simulations, but gamma1 differing. Since c_s propto gamma1^½ and gamma1 reduces by no less than a factor of about 4/5, we get no less than a factor of about 0.9 in c_s. So the difference in c_s profiles is very small.
3. RGB Pressure profile from MESA. As shown in the last blog but now with the new curve showing the simulation initial condition.
4. RGB Temperature profile from MESA. As shown in the last blog but now with the new curve showing the simulation initial condition.
5. RGB Various profiles from MESA. As shown in the last blog but now with new curves for electron fraction, mean molecular mass mu and gamma1=(dlnP/dlnrho)_S showing the simulation initial condition.
6. Yisheng's plot of initial profile (temperature) in cgs units.
7. Yisheng's plot of initial profile (specific internal energy) in cgs units.
Derivation of expression for mu in terms of X, Z, average number of nucleons per metal species A, and electron fraction
Plan for EoS project, presentation given during meeting

mu was computed using an analytic formula which assumes a mean atomic mass for metal species of 16 (the result is not sensitive to this number).
It is not possible to compute the recombination energy (total or from each species individually)
Since the hydrogen, helium and metals fractions are CONSTANT in the envelope (and are assumed to be constant for the duration of the simulation), then to compute mu we would need the ionization fraction of each species, e.g. n_HII/n_HI, n_HeII/n_HeI, n_HeIII/n_HeII, and the same for all the metal species included in the EoS.
These ionization fractions can be estimated using the Saha equation but this would not take fully into account the EoS. This was the method used by Reichardt+2020 to compute the recombination energy—but they neglected ionization and recombination of metals.
Can the ionization fractions for each species as well as mu be obtained directly as part of the MESA EoS? If not, we need to use the Saha equation.

Use Saha equation to estimate the ionization fractions and recombination energy and make some plots.
Migrate new code to Stampede and test (produce 1 frame for each run).
Prepare the new fiducial run (increased resolution, etc.) and new EoS run (Runs R1 and R2 in the Plan for EoS project presentation above), and perform test runs.