COMMON ENVELOPE SIMULATIONS

EoS stuff

Work done

  1. Explored effect on recombination energy of including temperature dependence of partition function.
  2. Made pdf with all the initial profile plots, for easy reference in the future.
  3. Went back and did a bit more reading on the EoS, particularly the OPAL EoS which is used everywhere in the initial RGB profile ​Rogers+ 1996, ​Rogers+Nayfonov 2002.
  4. Some reading, including this preprint, which is relevant for our EoS CE project: ​Hirai+ 2020.
  5. Figured out that we were missing the recombination energy from recombination of two hydrogen atoms to produce a hydrogen molecule, which is included in the MESA EoS and discussed in Hirai+ 2020. So included that contribution in the plots.

Results

  1. The temperature dependence of the partition function cannot explain the decrement in the internal energy near the surface (see last blog post). Therefore it must be caused by other physics included in the EoS but not captured by the contributions included (thermal+thermal radiation+recombination) or, another possibility is that the Saha equation does not accurately predict the recombination energy near the surface, perhaps because local thermodynamic equilibrium cannot be assumed. In any case, the profile gets modified near the surface (r >~ 45 Rsun up to the outer radius of 48.1 Rsun) because of the matching onto the ambient, so we are not too concerned about this region. However, during the simulation there will also be regions where it doesn't quite work…is this a problem for what we want to do?—update: I now realize that the decrement is caused by the neglect of the latent recombination energy due to recombination of H atoms into molecular H2! See the last item of Results and discussion below…
  2. Here is the pdf with all the various profile plots for easy reference: ​eos_figs.pdf.
  3. The Hirai paper mentioned above also has the same idea as me of including the recombination energy of H or not, of He or not, etc. in the simulation…but they do not use a tabular EoS. Rather, they use an analytic solution to approximate the tabular EoS.
  5. Although the number density of H2 molecules is completely negligible, this component of the recombination energy H+H —> H2 is not negligible, and in fact dominates at temperatures below 104 K (see Fig 17 in the above pdf). When we include all the contributions, excluding recombination energy of metals, the results for the internal energy density agree to within 0.6% everywhere. If we include recombination energy of metals as well, we do a bit worse, especially at radius below 12 Rsun, where the percent difference becomes as high as 1.4% (over predicts the internal energy by up to 1.4%).

Discussion

  1. We have confirmed that by adding the thermal energy contributions of gas and of radiation and the recombination energy from hydrogen and helium, one gets back the MESA internal energy profile (the discrepancy is on the order of half a percent at most).
  2. We can now say that it is reasonable to estimate the recombination energy contribution using the sum of hydrogen and helium recombination energies computed from the Saha equation.
  3. We need not worry about the temperature dependence of the partition functions, as ignoring it produces results in good agreement with MESA.
  4. Recombination energy of metals can safely be neglected, it seems, but recombination energy of H+H —> H2 cannot be neglected, though it was not considered in ​Reichardt+ 2020.
  5. As mentioned in the last blog post, one can see from the above pdf that the latest version of MESA (12778) gives results that are completely consistent with the version used (8845) (the slight differences apparently come from the small mismatch in the times of the snapshots). One could run the simulation with higher time resolution and better match the snapshot, and then use the snapshot from the latest version of MESA. Or it could be simply mentioned that the results are completely consistent and just use the original MESA 8845 RGB profile for consistency with earlier papers. It does not make a difference so might as well do the latter.
  6. I also ran into a problem when doing test runs, which is that one cannot add much refinment around the secondary at t=0 because by doing this one asks for more resolution than contained in the initial profile. It is easy to increase the resolution in the ambient, but the extra refinement region (i.e. particle buffer) around the secondary could overlap the envelope if the separation between the secondary and RGB radius is smaller than the particle buffer size. To increase the resolution in the envelope profile, one needs to rerun MESA at higher spatial resolution. Since we know from the AGB paper (see Fig B1) that the orbital evolution is insensitive to the resolution around the secondary before the first periastron passage, it is unnecessary to refine around the secondary at a high level right from t=0. So I did not bother rerunning MESA to get higher spatial resolution in the profile. However, if we, for example, want to add even one level of AMR in the outer envelope from t=0 in the future, we would need to rerun MESA with higher spatial resolution and reproduce the initial condition. Something to keep in mind.

Next steps

  • Reproduce EoS tables using mean atomic weight of metals as 17.35 instead of 18 (differences will be minor but might as well).
  • Migrate new code to Stampede and test (produce 1 frame for run 207 and make sure it agrees with bluehive result).
  • Prepare the new fiducial run with gamma=5/3 EoS (increased resolution, etc.) and perform test runs (This was named Run R1 in the ​Plan for EoS project presentation).
  • Prepare new EoS run where recombination energy is completely thermalized (Run R2) and perform test runs.
  • Prepare new EoS run where recombination energy is completely radiated away (Run R3—this will involve a bit of coding in astrobear—how to proceed?) and perform test runs.

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