Eccentricity distributions of BH-Star binaries

[aesar77]

Hi,

I am working with detailed evolution outputs. In my pipeline, I choose systems that evolve into a black hole - main-sequence star (I consider stellar types up to 9, not only 0 and 1) at some point during their lifetime. I extract these BH-MS time intervals and construct the time-evolution data for the semimajor axis, eccentricity, and time. I calculate BH-MS lifetimes using the first and the last time elements (time[-1]-time[0]).

My purpose is to see how the semimajor axis and eccentricity evolve during the BH-MS lifetime. Now, as far as I observed, some binaries are unbound from the very beginning, at t_bhms=0, they have eccentricity > 1 and semimajor axis < 0, and status in SP is registered as 'Unbound' or 'TimesUp'. I have a few questions here.

1. The next time step, both the semimajor axis and eccentricity turn 'nan' for physically unbound systems (i.e., the eccentricity being larger than one). However, they continue to evolve; they have BH-MS lifetimes in Myr scale. Their time array continues to record time, and matches in length to the semimajor axis and eccentricity, but the latter two are filled with 'nan' after the first element. I assume that means they are no longer in a binary system, but then I think if that were the case, the simulation would just stop the evolution?
2. The systems that are physically bound at t_bhms=0 with eccentricity < 1 and semimajor axis > 0 all have zero eccentricities. I understand that they should have eccentricities close to zero, but I find it a little odd that all of them are exactly zero, and remain that way during their lifetimes, while semimajor axis values change. Is this expected?

I can provide time evolution plots or snippets from my code if necessary. Thanks!

[SimonStevenson]

Hi!

1. Some binaries will be disrupted by mass loss/kicks during the formation of the black hole. By default COMPAS will continue to evolve the companion in disrupted binaries. You can toggle this option using the program option --evolve-unbound-systems, or as you have already, select the systems that remain bound in post-processing.

2. Two possibilities I can think of here: kicks, and mass transfer:

Kicks: By default, COMPAS uses the remnant prescription from Mandel & Mueller 2020 to determine black hole masses and kicks. For black holes more massive than ~10 solar masses, this results in no kick and very little mass loss, leading to low eccentricities.

Mass transfer: We assume that any binary that undergoes mass transfer is circularised --circularise-binary-during-mass-transfer

Indeed, when I run an example population, I see a mix of systems with e = 0, and with 0 < e < 1 (mostly wider binaries that likely avoided mass transfer).

For the BH-star binaries observed by Gaia, there is the possibility (likely, at least in the case of Gaia BH3) that they are not formed through isolated binary evolution, but are rather dynamically formed.

[aesar77]

Thanks for your detailed answer!

Indeed, when I run an example population, I see a mix of systems with e = 0, and with 0 < e < 1 (mostly wider binaries that likely avoided mass transfer).

So you actually see systems with non-zero eccentricities for bound systems? I assume you used the default settings on the config file. Here are the options that I set differently from the default and think might be relevant:
--emit-gravitational-radiation: True --tides-prescription: 'PERFECT'
Do you think any of these could be the reason why I have all eccentricities zero?

And for reference, here is my plot for all bound systems' semimajor axis and eccentricity time evolution:

[SimonStevenson]

Ah yes, if you use --tides-prescription: 'PERFECT' it assumes perfectly efficient tidal circularisation, so that e=0 by construction and the rotation period is synchronised to the orbital period. This is a somewhat crude/simple approximation of how tides work. For tight binaries it might be ok. For wide binaries tides will be ineffective and should not circularise the binary. Veome Kapil has implemented a more complicated, better and more modern tidal prescription in COMPAS (though it is also a bit slower). See BaseBinaryStar::ProcessTides for the implementation of these two prescriptions.

[aesar77]

I see! Should KAPIL2025 prescriptions give more accurate distributions, then? I will implement this in my new generation.

[SimonStevenson]

If you think that tides will be important for the binaries you are interested in, then yes, I'd suggest using the KAPIL2026 (I think it got renamed from KAPIL2025 at some point) prescription. If you think tides won't be important then simply using the NONE option can be appropriate too.

[aesar77]

My purpose is to achieve the most realistic eccentricity-semimajor axis distributions for main-sequence star and black hole binaries. So, if I use 'NONE', does that mean there is no circularisation at all? Would that result in an overestimation of the higher eccentricity binaries in the population?

[SimonStevenson]

If you use --tides-prescription NONE then there is no tidal circularisation. There will still be circularisation during mass transfer (assuming you have --circularise-binary-during-mass-transfer TRUE). Your initial eccentricity distribution (--eccentricity-distribution) may also matter -- by default we assume all binaries have initially circular orbits (ZERO), which is not true for observed wide main sequence binaries (see e.g., Moe & di Stefano 2016). In terms of tides, if you are looking for the most realistic population COMPAS can give you, then yes I would suggest using the KAPIL2026 tides prescription.