# CEE

## EOS paper

Skeleton of paper with draft intro and methods sections: http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos.pdf.

#### Relevant papers

3D simulations:

- Reichardt, De Marco, Iaconi+ 2020
- Conclude that final separation unaffected by EOS (ideal or MESA) BUT actually in one of their simulations there is quite a large difference, with the tabular EOS producing a larger final separation by 16%.
- Find that recombination energy release greatly increases the unbound mass
- Unbound mass curves almost independent of EOS up until first periastron passage, and diverge thereafter, with tabular EOS resulting in roughly 50% more unbound mass in both sets of simulations, using a definition of unbound that includes thermal energy but not recombination or radiation energy (Fig. 2)
- Find that released helium recombination energy is thermalized (released at too high an optical depth to radiate away)
- In contrast, find that about half of released hydrogen recombination energy would be radiated away
- Provide references for early papers: Lucy 1967, Roxburgh 1967, Han, Podsiadlowski & Eggleton 1994 and Harpaz 1998
- Provide good summary of the recent literature and controversy over whether released recombination energy would radiate away
- Point out in Sec. 2.0 that the helium mass fraction can vary quite a bit from on star to another, and this could potentially affect the results a lot
- Provide useful information about the MESA EOS in Sec. 2.1 (we could refer to this summary in our paper to avoid having to repeat it)
- End of Sec. 4.1 talk about ionization fronts staying at roughly constant radius, as opposed to e.g. moving inwards "counter to some expectations".
- Fig 4 and 5 showing spatial and time dependence are particularly useful (I have done a similar thing but I did not do a spherical average, ignored overlapping a regions, and also had an extra plot for the tracers. Also, so far I was not planning to include the unbound mass plot for the ideal gas EOS run.)
- Fig 6 is also interesting, purpoting to show the release of recombination energy (which is negative for ionization). However, I think it is flawed because it implicitly assumes that the gas does not move radially
- Sec. 5 tries to estimate how much of the released recombination energy might be lost by convection+radiation (since the simulation cannot include those effects)

- Lau, Hirai, Gonzalez-Bolivar+ 2022
- Simulate CEE involving a 12 Msun RSG primary (focus on case with q=0.25)
- Compare 3 sims: (1) Full EOS; (2) ideal gas; (3) ideal gas + radiation energy and pressure (but no recombination at all)
- Find that the Run (1) unbinds about 114% more mass than Run (3) and 233% more mass than Run (2) (assuming KE+PE+TE energy density definition for unbound)
- Find that recombination energy of helium contributes importantly to envelope unbinding, whereas recombination energy of hydrogen is mostly released into gas that has already become unbound
- Find that the "final" separation in Run (1) is 34% larger than that of Run (2) and the final separation of Run (3) is 14% larger than that in Run (2)
- Simulations are not very well converged with resolution (Fig. 9)
- Also not converged with respect to softening length at late times (Fig. B1)
- Fig. 13: Present spherically averaged color plots of ionization state at a given radius and time —> focus on regions where two ionization states (e.g. HeII and HeIII) coexist, as these regions are where gas is "actively recombining". Density of unbound gas is overplotted.
- These plots also show contours for the tau=1, 10, 100 surfaces (spherically averaged)
- Includes much discussion about the possibility of losses of recombination energy due to convection and radiation (Secs. 4.1 and 4.4)

- Sand, Ohlmann, Schneider+ 2020
- Simulations use OPAL EOS and ideal gas EOS
- Compare ideal gas and OPAL sims and find that ideal gas unbinds ~20% and OPAL ~90% by end of the simulations (about 22% vs 78%, respectively, at time corresponding to the end of the ideal gas simulation), according to the bulk KE + PE density criterion for unbound gas
- Show that the evolution of the released recombination energy during the simulation resembles the unbound mass evolution
- The difference in unbound mass becomes larger after about 400 days, whereas the first periastron passage is at about 600 days.
- Get convection (at some level)
- "recombination energy acts behind the spiral shocks where the gas cools, boosting the expansion"
- Determine tau=1 surface in postprocessing and equate this with location of photosphere (not stated whether they use MESA opacity tables to do this)
- Find that most of the hydrogen ionization happens below the photosphere, but this number goes from 99% at t=296 days to 94% at t=1000 days to 80% at the end of the simulation (t=2500 days)
- Similar results for runs with 2x smaller or 1.5x larger companion mass
- "We find that the spiral-in is deeper by 17%–23% when not including recombination energy compared to the final separations in the simulations that include recombination energy. This can be explained by the fact that without recombination energy release the expansion of the envelope is slower and the transfer of orbital energy terminates later when little mass is within the orbit of the cores."
- "We cannot follow the evolution for longer with confidence with our current numerical methods, because the energy-error rate exceeds the recombination-energy-release rate in the system and we can no longer decide whether a further envelope unbinding is physical or caused by numerical errors"

- Kramer, Schneider, Ohlmann+ 2020
- Simulations use OPAL EOS and one comparison simulation with ideal gas EOS
- Sec. 3.3: The run with 0.08 Msun companion and 1 Msun primary (tip of RGB) unbinds about 78% of the envelope (OPAL) compared to 7% (ideal gas)
- "Companions of even lower masses can certainly not eject the envelope when only tapping the orbital energy reservoir" — seems overly restrictive since simulations could evolve for much longer

- Moreno, Schneider, Roepke+ 2021(preprint)
- Simulations use OPAL EOS
- Emphasize the "internal energy" criterion which tells them the envelope is almost completely unbound at the end of the simulation
- Claim that recombination energy is very important for unbinding the envelope but provide no evidence for this statement

- Ivanova & Nandez 2016
- Identify some differences between 1D and 3D simulations
- Strive to understand the transition between early phase (3D models) and late phase (1D models)
- "The steady recombination outflow may dispel most of the envelope in all slow spiral-in cases, making the existence of a long-term self-regulated phase debatable, at least for low-mass giant donors."
- Find that in some cases their can be a "recombination runaway" where recombination leads to expansion leads to cooling leads to more recombination
- In other cases get a "steady recombination outflow"
- Then can get "shell-triggered ejection" which is partly powered by recombinaton energy (see also Clayton+2017)

- Nandez & Ivanova 2016
- "We can clarify that there is no recombination energy stored in the ejected material at the end of the simulations."
- "The role of the recombination energy for the CEE with a low-mass RG donor is not that it is necessary for the overall energy budget, as none of the considered systems were expected to merge by the standard energy formalism, but because the recombination occurs exactly at the time when the shrunk binary is no longer capable of transferring its orbital energy to the expanded envelope."
- Modify energy formalism to include recombination energy and energy taken away by the ejecta

- Nandez, Ivanova & Lombardi 2015
- "Taking [recombination energy] into account helps to avoid the formation of the circumbinary envelope found in previous studies"
- Use misleading definition of unbound that includes all internal energy density — classify > 0 energy density as "ejecta"
- Find that for the ideal gas + radiation EOS, 50% of the envelope becomes unbound but for the MESA EOS the entire envelope is ejected
- "Indeed, ionized material forms the circumbinary envelope initially. Recombination then takes place there, while the circumbinary envelope continues to expand. This results in the ejection of the circumbinary envelope and effectively of all the CE material."
- "If instead the recombination energy had been released too early, the simulations would have ended up with unexpelled circumbinary envelope as in previous studies"

- Chapter 9 of Ohlmann 2016 (phd thesis)
- Their setup very similar to the one we are using (2 Msun RGB with R = 48 Rsun + 1 Msun companion and initial separation similar to ours, but they have 95% corotation to begin with)
- Contains a critique of Nandez+2015
- Very little difference in the separation curves between ideal gas and OPAL EOS simulations
- More mass is unbound (KE+PE density unbound criteria) in the simulation with the OPAL EOS (Fig. 9.3 — compare blue and yellow curves)
- Includes spatial analysis of where recombination energy is released and whether it contributes to unbinding (Fig. 9.5)
- As in our simulation their high ambient temperature causes material near the surface to be ionized from t=0
- Shows spatial evolution of ionization states in Fig. 9.6

- Prust & Chang 2019
- Study a system almost identical to our own (looking at two cases: 95% corotation or no initial spin like us) — their initial separation is slightly greater than us (52 Rsun compared to 48 Rsun), and they mention that their star is slightly bigger compared to Ohlmann+16a (the latter is almost identical to ours)
- For internal energy density criterion, they get some ~65% of the envelope mass ejected by the end of the simulations (240 days)
- For the KE+PE density criterion, they find that the it is only about 8% ejected (but rising) by 240 days: Unlike Ohlmann+16a but like us, they find a decreasing trend (before a rising trend) — see their Fig. 6
- They do not try an ideal gas (gamma=5/3) model
- Their final separation (no initial corotation) is 3.2 Rsun at 240 days — apparently still decreasing slowly by the end of the simulation (see Fig. 7)

1D simulations

- Ivanova, Justham & Podsiadlowski 2015
- Importance of helium vis-a-vis hydrogen recombination energy
- Detailed study of usefulness of recombination energy in unbinding envelope in their 1D simulations
- Find that ~90% of helium recombination energy is used to unbind the envelope, while for hydrogen it is less clear

Analytical modeling

- Ivanova+ 2013
- Argue that much of the hydrogen recombination energy does not get released until after envelope ejection
- Argue that the subsequent release of this energy can explain LRNe
- Argue that the luminosity comes from the recombination front, i.e. photosphere ~= recombination front
- For the latter they cite Popov (1991) (see text after eq 7 in Popov 1991, in that model R_i is the radius of the front, dimensionless radius of the front is x_i). See also Kasen+Woosley(2009).
- The location of this recombination front is expected to be "almost constant," in contrast with the CE ejecta, which moves out at a speed which is of order the escape speed
- This also implies importance of helium vis-a-vis hydrogen recombination energy in assisting envelope ejection (see Lau+22)

Papers focusing on whether recombination energy is lost owing to radiation or convection+radiation before it can contribute to unbinding

- Soker & Harpaz 2003
- Sabach, Hillel, Schreier & Soker 2017
- Grichener, Efrat & Soker 2018
- Soker, Grichener & Sabach 2018
- Ivanova 2018

Other recent CE papers not directly relevant

- Ondratschek, Roepke, Schneider+ 2021(preprint)
- "able to follow the evolution to complete envelope ejection" — 99% unbound by "kinetic energy criterion"

- Law-Smith, Everson, Ramirez-Ruiz+ 2020(preprint)
- Clayton, Podsiadlowski, Ivanova+ 2017
- Sequel to Ivanova+2015, now extending simulations to include episodic dynamical mass ejections

- Ricker, Timmes, Taam & Webbink 2019

### Status of runs

Summary:

**Run 277: MESA EOS (completed up to frame 322 or 75 days on Frontera)****Run 282: Ideal gas gamma=5/3 EOS (completed up to frame 343 or 79 days on Frontera)****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 graph and compare the two methods of computing the released recombination energy and check that they agree at all times
- Combine tracer figures and make colors non-overlapping
- Normalized energy (red/blue) plot for Run 282
- Continue to extend Runs 277, 282 and 283
- 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

# CEE

## Conferences

- Will submit blurb for the upcoming LANL meeting (date still not finalized), as requested of all participants by the organizer, Chris Fryer.

## Jet paper

- Submitted to MNRAS and astro-ph by Amy

## EOS paper

### Meeting?

A meeting before the end of Feb seems like a good idea. Times?

### Writing

Made progress on Intro and Methods sections

### Status of runs

- 277 and 282 are now running on Frontera
- Run 283 was not running properly (slow and chombos huge) ⇒ resubmitted using old executable (Baowei) and old module settings

Summary:

**Run 277: MESA EOS (completed up to frame 288 or 67 days on Frontera)****Run 282: Ideal gas gamma=5/3 EOS (completed up to frame 295 or 68 days on Frontera)****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)

### New analysis

#### Energy terms

We can calculate the released recombination energy two ways:

- Using the Saha equation and tracers to see how the ionic state has changed, calculate the corresponding energy released, and integrate over all gas (see notes from last post),
- Assume an ideal gas (with mean particle mass mu and temperature T taken from the simulation) and integrate to get the total thermal energy and subtract this from the internal energy to get the recombination energy. The negative of the net change in the recombination energy is equal to the released recombination energy.

We want to show that these two methods give approximately the same number (at every time).

I was able to roughly show this for the 7x higher ambient density run 271. However, with the new run 277, the ambient is at a high temperature and contains a lot of recombination energy. Therefore, it becomes more important to **exclude** the ambient gas when calculating the recombination energy by method 2 above. This calculation is in progress.

There is one small caveat. The potential energy term involving self-gravity of the gas makes use of the potential Phi due to all the gas (excluding particles). We made changes to the code to recalculate Phi excluding the ambient in postprocessing. This is expected to reduce the magnitude of the gas self-gravity potential energy term by 1%. However, it reduces it by 30%, so there must be a bug.

#### Unbound mass

For the same reason, ideally we would recompute the unbound mass using the correct Phi that does not include the ambient, but this would make such a small difference it may not be worth it (could be mentioned in a footnote). Consider that the unbound mass is perhaps already underestimated because we are including self-gravity of unbound envelope gas, which is maybe too conservative (e.g. Prust+Chang 2019 exclude it).

#### Ionization and Recombination

Spatial dependence http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos_ion_277.pdf. To reduce the number of plots I am planning to plot all the tracers in one plot, but to avoid overlapping them by only showing the tracer with the highest density at that location. This should be sufficient to make the points we want to make. Overlapping leads to ambiguity because the order of overlapping affects the shades so one can no longer read off the density from the color bar, so best to avoid overlapping.

### Next steps

- Compare the two methods of computing the released recombination energy and check that they agree at all times
- Combine tracer figures and make colors non-overlapping
- Continue to extend Runs 277, 282 and 283
- 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

# CEE

## Computing

- Frontera issues for running CE code resolved by Baowei
- Stampede2 allocation is basically used up — now moving all runs to Frontera

## Jet paper

- Ready to submit I think

## EOS paper

### Status of runs

Note that the frame interval is about 0.2315 days

**Run 277: MESA EOS (completed up to frame 264 or 61 days on Stampede2)****Run 282: Ideal gas gamma=5/3 EOS (completed up to frame 268 or 62 days on Stampede2)****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)

### New analysis

#### Unbound mass

Unbound mass including envelope gas only (i.e. excluding ambient) for runs 277 (MESA EoS without radiation), 282 (gamma=5/3 ideal gas), 283 (MESA EoS without radiation or recombination energy)

- These are basically the final graphs except that the runs are all still being extended in time

#### Separation

Updated separation graph now including Run 283

#### Energy conservation

Updated energy conservation graph now including Run 283

#### Ionization and Recombination

Spatial dependence http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos_ion_277.pdf.

- Now for Run 277 (instead of old Run 271 which had a 7 times higher ambient density, slightly lower resolution and poorer energy conservation)
- Instead of worrying about transparency or truecolor plotting, I decided to make separate graphs for each ionic tracer
- Note that both the tracers and the graphs showing the ionization state at time t
**plotting only the gas density of the ionization species which is highest at that location**.- I checked and the regions of overlap are small (as expected given the exponential temperature dependence) but not completely negligible…it is just something that needs to be looked at a bit more carefully and mentioned in the text somewhere, but not a problem really. And I think unavoidable given the nature of tracers.

Analysis involving spatially integrated quantities http://www.pas.rochester.edu/~lchamandy/CE_papers/EOS/eos_ion_vol_integ_277.pdf.

- This analysis, too, considers a given species only in the region where it dominates (but separately for H and He)
- Results are consistent with those obtained for Run 271 but now I've done it for the full time resolution (1 data point per frame).

### Next steps

- Continue to extend Runs 277, 283 and 282 and also extend the existing analysis (but need to worry about energy conservation, mass leaving box, and available SUs)
- Energy terms vs time and check whether energy supplied by recombination leads to corresponding increase in thermal energy, as already done in comparison between old EOS run 271 and old ideal gas run 143.
- Explore overlapping ionization species regions to get a sense of how important they might be (< 10% difference?)
- Make progress on paper write-up and organize a meeting for all involved
- Calculate total angular momentum and check angular momentum conservation (a must I would say)