Binary Black Hole Spins: Model Selection with GWTC-3

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors The authors investigate how the spins of observed binary black hole mergers can provide insights in spin prescriptions used in stellar evolution models. The authors use several toy model spin prescriptions for stars and then apply a Bayesian Hierarchical inference to compute likelihoods for each model based on observational properties of binary black holes, including spins, chirp mass, and mass ratio. Though studies calculating likelihoods for population synthesis models from gravitational-wave data are not new, and the spin (and kick) prescriptions are simple toy models, the authors are honest about these caveats and their study does find some new insights, particularly the calculation of likelihoods for this specific set of model assumptions, that are interesting for publication. I recommend publication after addressing my comments below.   There's some critical assumptions that the authors make that could strongly impact the black hole spin results that the authors find. Most importantly:

1. The authors use the tidal spin up  model from Bavera et al (2021), described in section 2.3. This model creates a simple prescription to fit BH spins based on detailed MESA model outcomes.  However, these MESA models are based on simulations that assume the "delayed" Fryer model to calculate the remnant mass. This is an important assumption, because the chosen remnant mass prescription decides the amount of mass that is lost/ejected from the star and, in turn, also the amount of angular momentum that is lost during the supernova (and thus impact the final spin). The authors instead use stellar evolution models with the "rapid" Fryer (2012) prescription, which is inconsistent with the assumptions of the Bavera (2021) fit. This will likely significantly impact the expected (and correct) BH spin distribution.
2. Similarly, the Bavera (2021) model is based on efficient angular momentum loss (i.e. low BH natal spins). Whereas some of the other models that the authors assume, are based on inefficient angular momentum loss. For this reason, it doesn't make physically sense to combine these prescriptions (they contradict each other). The authors, however, do combine such prescriptions (as described in their section 2.3) 
3. The Maxwellian kick distributions used in this study (sigma150 and sigma265) are motivated by results from X-ray binary observations. However, the BBH mergers studied by the authors have significantly higher BH masses compared to X-ray binaries. The literature typically assumes in this case that the kicks are drawn from Maxwellian distributions with a reduction based on the fraction of fallback from the Fryer prescriptions (which would be consistent with X-ray binaries that can still have high kicks).

  [1,2,3]: Could the authors provide in the text some context or comments to address the points above to make sure readers won't get confused by these assumptions.   4. Moreover, regarding model F and F_B21: 4a I do not see model "F" (dotted line) in Figure 4. 4b Can the authors deliberate on why in their analysis, adding a small spin population (F_B21) gives such a vastly different log-likelihood compared to model F? (especially since Fig 4 seems to not show any differences between the models?).   5. particularly Fig 1 & 2 could suffer from sampling uncertainties that alone could explain the deviations between models. Could the authors show or discuss the sampling (i.e. Poisson) uncertainties or do a simple bootstrapping to check this doesn't impact their results   6. Fig 1: what does the y-axis mean here? How are the binaries weighted in this plot? Are all metallicities weighted equally? (particularly for model GM20)   7. Fig 2, 3,.. etc.: please explain what "PDF" here is. I assume this is some (observed?) rate per mass bin ? It should be something of the order dN/dx (x = parameter).It's unclear now what the y-axis means, especially since the values exceed unity. Are the distributions normalized?    8. The caption in Figure 1 is confusing. The authors mention on line 108 natal kicks:  "We model natal kicks of neutron stars and BHs according to three different models, as shown in Fig. 1:" , but Figure 1 caption mentions the systemic velocities instead (the velocity of the center of mass of the binary after the second SN)   9a. l126: "which angular momentum transport is relatively inefficient." -> does this model in practice assign spins of a=0.85 to almost all BHs? (since I suspect most BBHs will have the condition M_CO < m_1?)   9b. It would be really helpful (also to answer many of the questions in this report) to somewhere show a figure like Fig 1, but for the different BH spin prescriptions. E.g., showing the individual BH spins (chi_BH1 and chi_BH2) versus the CO mass or ZAMS mass for the stars in the simulation.   10: l106, the authors write: "This realistically represents the upper limit for BH natal kicks". But they refer to a Maxwellian distribution. Can the authors (i) emphasize what they mean with upper limit for BH kicks here (what value? or is it a distribution?), and how they come to the conclusion that this is a "realistic representation"?     11: l119: "which bracket the current uncertainties on BH spins". -> can the authors explain what they specifically mean with bracket the current uncertainties (especially given the above). The authors also do not consider the spin flip scenario and other spin misalignment scenarios, so it might be a limited set of toy models.   12: l101: "This model naturally produces low-kicks for electron-capture, stripped and ultra-stripped supernovae" -> can the authors emphasize whether the BHs in the author's simulations go through these type of SNe, or whether the small kicks in Fig 1 just result from their assumption of BH fallback. Can the authors emphasize whether the fallback fraction assumed in the Fryer Rapid simulations is taken into account for m_ej?   13: l267: " In contrast, model GM20 has a stronger preference for low-mass BHs(...) The reason for this difference is that all BHs in tight binary systems receive slow natal kicks in model GM20 (Fig. 1). This happens because stars in tight binary systems lose their envelope during mass transfer episodes; hence, the mass of supernova ejecta (mej) is small, triggering low kicks in model GM20" -> but why does this lead to more low mass BHs?   14: It might be good if the authors write a little note on how much their specific population synthesis simulation (the default choices for MOBSE) could impact the results. Do the authors expect their method/results to hold for all/most population synthesis simulations?      small notes:     a: l18: "lead to more accurate constraints on the mass and spin distribution of these systems"  -> more accurate than what?   b: l25: "we can safely exclude that all BHs are maximally spinning"; is "we" referring to the authors or to "the field" ?   c: l125 "to some evolutionary tracks by the Geneva group" -> can you be more precise what "some" refers to here?   d: l317: "(for spin models σ150 and σ265)" -> for SN kick models? e: l320: has non-negligible support -> has no support?   Comments on the Quality of English Language

few small grammar mistakes/typos, but nothing major.  

Author Response

Dear referee,

We thank you for all your relavant comments, we reply to all of them in the attached file "Review Spin paper A.pdf".

Regards,

The author team

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In "Binary black hole spins: model selection with GWTC-3", the authors investigate impact of prescriptions on the spin parameter to understand astrophysical models of gravitational wave events. I find the work useful to interpret the future GW observations, the topic is of interest to the community, and I think it will merit publication after the authors respond to a several points listed below.

 

Comments: 

- For section 2.3, could you give a comment on the prescription for the tidal spin-up? Is it highly uncertain and some parameters are fitted to explain the GW observation, or is this process well understood? 

 

- For section 2.5, I'm not familiar with the prescription for the distributions of the eccentricity (F(e) \propto e^-0.42). Could you explain the motivation of them and whether they may influence the results of the paper?

 

- There are several papers trying to understand astrophysical models using the X_p parameter (e.g. Gompertz+21: https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.1454G/abstract, Gerosa+21: https://ui.adsabs.harvard.edu/abs/2021ApJ...915...56G/abstract, Tagawa+21: https://ui.adsabs.harvard.edu/abs/2021MNRAS.507.3362T/abstract, Gayathri+21: https://ui.adsabs.harvard.edu/abs/2021ApJ...920L..42G/abstract). Please mention these studies. 

 

- From figure 4, models Max and Max_B21 look much better than others. However, according to Table 4, the likelihood for F_B21 sigma150 is close to that for Max_B21 sigma265. Could you explain why it is? Does this mean that likelihood values are not adequate quantities to see the wellness of the fit for the spin distribution?

 

Author Response

Dear referee,

We thank you for your relevant comments and reply to them in the attached file.

Reagrds,

The author team

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I thank the authors for their corrections and answers. The author's edits and responses have resolved my major concerns with the paper/results and make the paper ready for publication. 

I have one more minor comment regarding the author's response: 
The authors address my points 4, and write "The F model yields L(F) = −∞ if we do not include the tidal spin-up correction,  regardless of the kick model. This indicates that the LVK data do not support vanishingly small BH spins for the entire BBH population " (line 344), 

However, looking at the updated figure 4  it is clear to me that  I think the correlation in this sentence goes the other way: The F model yields L(F) = - infinity, *because* the LVK has spins > 0.05, and model F does not have any support there. (In other words: one could have concluded that LVK data supports at least some BBHs to have spins >0.05, from the LVK data *alone* (no model comparison/likelihood calculation needed) - as also pointed out by earlier work such as the GWTC papers and Callister et al. (2023). I suggest the authors rephrase or make a small note about this (this = that their likelihoods are -infinity *because* the data has support outside model F).  

I would also urge the authors to consider that looking at their models vs the data, that all of their models seem to not represent the LVK data well (eg Fig 2: none of the models are a good match). I think this is worth pointing out when calculating and describing the likelihoods. In the end, likelihood calculations are comparisons between two models but doesnt tell you whether a single model is a "good model" to represent the data (only that one is better than the other) . I think adding a small note/caveat in the section describing the likelihood values would be really helpful and connect to the rest of the discussions about caveats by the authors in the paper. 

 

Comments on the Quality of English Language

no major problems. Grammar can be improved in minor places (but I assume an editor will do so) 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf