CE
New Analysis
2D plots showing Spatial and Temporal dependence
Helium
Hydrogen
Conclusions:
- Helium seems more important than hydrogen.
- Recombination at first but then stagnates. Heating from inspiral balances cooling by expansion?
Ionization and Recombination (Volume-integrated, showing evolution with time)
Results
Conclusions:
- Helium recombination HeIII —> HeII and HeII —> HeI are the dominant transitions
- However, after t = 25 days, there is no net release of recombination energy
Energy terms (Star gas only, excludes ambient), evolution with time
All energy terms, not accounting for fluxes out of box:
Zoom-in on change in the recombination energy:
Conclusions:
1st Figure:
- In both tabular EOS and gamma=5/3 runs, particle energy decreases at a steady (and still substantial) rate after t ~= 57 days, implying that the inpsiral does NOT stall.
- Differences between runs are very small (<10%) implying that ionization and recombination do not play a very important role up until this point in the evolution
- The release of recombination energy between about t = 6 days and t = 25 days leads to a slightly higher thermal energy compared to gamma=5/3 run (the two energy changes roughly balance one another, which makes sense).
- EOS case manages to reduce gas-particle PE terms (by puffing up envelope?) after t ~= 45 days. From t ~= 45 days to t ~= 80 days, we also see a reduction in the thermal energy in the tabular EOS run as compared to the gamma=5/3 run, which is consistent with a puffing up. But this effect has faded by the end of the simulation at t ~= 80 days. This coincides with a transition from a deeper inspiral (compared to gamma=5/3 run) to a shallower inspiral (see also separation results, below).
2nd Figure:
- The peak amount of recombination energy released is about 10%, which happens at t ~= 24 days
- Thereafter, the net recombination energy relased reduces and drops to only 1% by the end of the simulation at t ~= 80 days.
- The evolution of the recombination energy agrees well with the expectation from the ionization/recombination analysis above (using tracers and the Saha equation) FOR THE FIRST 20 DAYS. After that the tracer/Saha analysis predicts that almost 0 recombination energy is released whereas the plot of recombination energy (i.e. internal minus thermal) says that the net release of recombination energy between t ~= 20 days and t ~= 80 days is negative.
- It is important to understand the reasons for this discrepancy
Inter-particle Separation, evolution with time
Separation curve:
Conclusions:
- Mean separation continues to decrease at the ends of both simulations (though at an ever-decreasing rate of decrease)
- There is very little difference between the runs. Suprisingly, the difference between the MESA EOS run (with radiation energy removed — blue curve) and the tabular EOS run with internal energy replaced by thermal energy (green curve) is larger than the difference between MESA EOS and gamma=5/3 (red) curves.
- Comparing MESA EOS (blue) and gamma=5/3 (red) curves, the MESA EOS run shows slightly smaller separation between t ~= 25 days and t ~= 70 days and slighly larger separation thereafter
Envelope Unbinding (Volume-integrated), evolution with time (showing Star tracer mass only)
With factors of two in particle-gas potential energy terms:
Without factors of two in particle-gas potential energy terms:
Conclusions:
- Using the "internal energy" criteria (which makes no sense) would imply that the unbound mass is much higher, as found by other authors (top curve in both plots, and other authors use the equivalent of the second plot)
- Using another criteria for unbound which is more reasonable, the MESA EOS run does lead to a higher unbound mass, of order 10% larger, peaking somewhere between t ~= 25 and t~= 40 days.
- By the end of the MESA EOS simuation at t ~= 80 days, the difference is basically 0
- The MESA EOS simulation with internal energy replaced with thermal energy (green/yellow) is much more similar to the gamma=5/3 run, as would be expected. But this run generally falls between the other two. This suggests that the recombination energy is actually slighly less important than the difference between blue and red curves would suggest.
- Note that after t ~= 50 days, significant mass from the original primary is leaving the box, about the same in both runs (about 5% by t=85 days).
- Generally speaking, the unbound mass is growing steadily by the end of both simulations (irrespective of what criterion for unbound is used)
Energy conservation, evolution with time
- Energy is conserved to within ~2%, where the denominator chosen for this calculation is indicated on the plot
- If one ignores the energy loss from reducing the softening radius, it is more like ~4% for the gamma=5/3 run and <1% for the MESA EOS run
- The energy conservation inside the sphere with radius Lbox/2 (centered on the origin) is probably better: the gravitational potential due to mass outside this sphere is NOT included in the code, so envelope mass leaving this sphere reduces the gravitational PE inside the sphere, leading to an energy increase. This is likely the cause of the increase seen at the end of the simulations.
Status of runs
- Run 277: MESA EOS (analyzed up to frame 344 or 77 days, completed up to frame 377 or 87 days)
- Run 282: Ideal gas gamma=5/3 EOS (analyzed up to frame 374 or 87 days, completed up to frame 407 or 94 days)
- Run 283: MESA EOS with recombination energy removed from EOS tables (completed up to frame 218 or 50 days on Frontera)
- Run 276: MESA EOS with maxlevel increased by 1 compared to Run 277 (for convergence study — completed up to frame 47 or 11 days on Frontera)
- Run 28?: MESA EOS with maxlevel reduced by 1 compared to Run 277 (for convergence study — not yet started on Frontera)
- Run 271: MESA EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 235 or 54 days and will not extend)
- Run 143 (fiducial run of past papers): Ideal gas gamma=5/3 EOS with 7 times higher ambient (to explore role of ambient) (completed up to frame 173 or 40 days and will not extend)
Next steps
- Energy terms — include flux in total energy of primary gas tracer
- Anvil
- Continue to extend Runs 277 and 282 — but for how long?
- Extend Run 276 (high res run)
- Make progress on paper write-up
- Explore overlapping ionization species regions to get a sense of how important they might be (< 10% difference?)
- Calculate total angular momentum and check angular momentum conservation
- PostProcessing to check energy conservation within sphere of radius Lbox/2 — expect it to be better than that in full box
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