A population study on the effect of metallicity on ZAMS to the merger

Deeptendu Santra; Sourav Roy Chowdhury

REVIEW 3 major objections 6 minor 139 references

A population study on the effect of metallicity on ZAMS to the merger

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A population-synthesis model that assigns each zero-age main-sequence star its own metallicity produces black-hole and neutron-star binary masses that match observed gravitational-wave data better than uniform-metallicity models do.

desk verdict A modest COSMIC extension with a real code release, but the headline mass ranges rest on an ad hoc per-star metallicity mapping that needs a control run before the claims can stand. read the letter →

arxiv 2411.11902 v2 pith:H7SIAOGI submitted 2024-11-15 astro-ph.HE astro-ph.CO

Sourav Roy Chowdhury , Deeptendu Santra This is my paper · ORCID

classification astro-ph.HEastro-ph.CO

keywords binarypopulationsynthesisindividualmetallicitymass-redshift-metallicityrelationblackholeshole-neutronstarbinariessub-hertzgravitationalwaveszero-agemainsequenceLISALGWAsensitivity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Most binary population synthesis models assign one metallicity to an entire stellar cluster, even though metallicity controls stellar winds, remnant masses, and which stars become black holes. This paper relaxes that assumption by giving every zero-age main-sequence star, and even each component of a binary, its own metallicity through a mass–redshift–metallicity relation, then evolving a million binaries at redshift $z \approx 4$ with the COSMIC code. The central claim is that the resulting first-generation binary black holes (total masses $8$–$86\,M_\odot$) and black hole–neutron star systems ($6$–$31\,M_\odot$) reproduce the observed gravitational-wave mass distribution far more closely than uniform-metallicity runs do. The paper also computes sub-hertz characteristic strains for these inspirals, showing they fall mainly below the projected sensitivity of planned observatories LISA and LGWA.

What carries the argument

The load-bearing object is the fiducial mass–redshift–metallicity relation of Eq. (1), $\log_{10}(Z/Z_\odot) = p\log_{10}(M_\odot/M) + q\exp(-rz)$, with $p=0.5$, $q=0.67$, $r=0.5$, which assigns a metallicity to every zero-age main-sequence star from its mass and the cluster redshift. Around it the paper modifies the binary population synthesis code COSMIC to store metallicity as a two-element vector, so primary and secondary stars keep independent chemical compositions that propagate through metallicity-dependent wind prescriptions, ignition tables, Eddington-limited mass transfer, and remnant calculations. The final mass distribution of compact remnants is the output that carries the comparison with observations.

What would settle it

A future sub-hertz or third-generation gravitational-wave survey at $z\approx4$ that finds first-generation BBH total masses consistently outside the $8$–$86\,M_\odot$ range would refute the model's central prediction, as would spectroscopic measurements showing that the mass–metallicity slope at these masses is far from $p=0.5$.

Watch

Extended reading notes

Core claim

The paper's discovery is that replacing a cluster-wide metallicity with star-by-star metallicities changes the predicted demographics of compact-object mergers in a way that brings them into line with observations. Overlaid on LIGO–Virgo–KAGRA event data, the simulated masses of first-generation BBHs and BH–NS binaries show much higher concordance than a single-metallicity catalogue, according to the paper. The model produces BBH total masses from $8$ to $86\,M_\odot$ and BH–NS masses from $6$ to $31\,M_\odot$ at $z\approx4$, with the heaviest black hole reaching about $43\,M_\odot$, and it finds that the majority of these inspiralling systems radiate in the sub-hertz band with characteristic strains that lie below the sensitivity curves of LISA and LGWA over a four-year observation.

Load-bearing premise

The whole prediction rests on assuming that a galaxy-scale mass–redshift–metallicity relation applies separately to each star, and even separately to the two members of a binary inside one cluster, with an arbitrarily chosen slope of p=0.5; if that per-star mapping is wrong, the reported mass ranges are not meaningful.

Editorial extensions

If this is right

If the per-star metallicity mapping is right, uniform-metallicity population synthesis misestimates compact-object merger masses, and star-by-star metallicity assignment becomes the benchmark for interpreting gravitational-wave catalogs.
The predicted BBH total-mass range $8$–$86\,M_\odot$ and BH–NS range $6$–$31\,M_\odot$ at $z\approx4$ give concrete search targets for LIGO–Virgo–KAGRA and next-generation detectors.
Because the predicted sub-hertz strains lie below LISA and LGWA sensitivity curves, these first-generation inspirals are unlikely to be individually resolved and would instead contribute to the stochastic gravitational-wave background.
The code's 'individual' and 'reduced_mass' metallicity modes bracket the extremes of cluster chemical inhomogeneity, giving future studies a way to test the sensitivity of merger demographics to the metallicity prescription.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The model implies that a single cluster can be chemically inhomogeneous down to the scale of individual binary components; a stronger test would compare the resulting metallicity spread with resolved observations of star-forming regions at $z\approx4$.
Applying the same mass–redshift–metallicity mapping at higher redshift ($z>6$) or to second-generation mergers would test whether the $8$–$86\,M_\odot$ range widens as the exponential redshift term saturates.
Replacing Eq. (1) with a distribution that includes scatter around the relation would presumably broaden the predicted mass ranges; that broadening is a quantitative measure of how strongly the central claim depends on the $p=0.5$ slope.
The reduced-mass shared-metallicity variant offers a cheap way to approximate inhomogeneous clusters in unmodified population-synthesis codes, a transferable trick for other simulation frameworks.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: this is a modest but real code contribution wrapped in an overclaimed headline. The genuinely new thing is modifying COSMIC to accept per-component metallicities from Eq. (1), then producing a z~4 sub-hertz inspiral strain catalog for the resulting BBH and BH-NS binaries. That is a legitimate extension of population synthesis practice, and the authors are honest that the predicted strains fall below LISA and LGWA sensitivity. Credit where due: the code is public, the method is described clearly enough to reproduce, and Appendix A tests a shared-metallicity alternative using the reduced mass, which shows they thought about the physical objection.

The soft spots are not fatal to the paper as a code methods note, but they gut the physical conclusions. Eq. (1) is a galaxy-scale mass–redshift–metallicity relation, and applying it to individual ZAMS stars—let alone assigning the primary and secondary different metallicities, as in Figure 1—is an ad hoc mapping with no stellar-physics justification. The slope p=0.5 is set "for simplicity," and that parameter largely decides which stars become black holes. There is no uniform-metallicity control run anywhere in the main analysis, and the claim of "much higher concordance" with LVK masses rests on an overlay in Figure 5, not on any quantitative statistic. The stress-test note has it right: the 8–86 Msun and 6–31 Msun ranges are essentially products of the chosen mapping unless that mapping is independently validated.

To be fair, the authors do not hide their choices. They flag the arbitrary p, and they note the code does not evolve metallicity during stellar evolution. The absence of a control run is an addressable omission, not a sign of sloppiness. The citation pattern looks fine; they build on prior work rather than ignoring it. What is missing is an out-of-sample test: run the same initial conditions with a uniform Z matched to the same star-forming environments, and show that Eq. (1) actually improves agreement with LVK masses in some measurable sense.

The paper is for population synthesis practitioners and people doing sub-hertz GW forecasts. I would not cite the mass ranges as a result, but I might cite the code capability it demonstrates. It deserves a serious referee, not a desk reject, because the code contribution is real and the underlying question—heterogeneous metallicity within a cluster—is worth airing. I would send it out with a recommendation for major revision: add the control run, quantify the LVK concordance claim, and either justify the per-star mapping or demote the headline mass ranges to illustrative status. The authors can do that; the material is in the paper already, half-done.

Referee Report

3 major / 6 minor

Summary. The paper modifies the COSMIC binary population synthesis code to assign metallicities to individual ZAMS stars through Eq. (1), an empirical mass-redshift-metallicity relation with slope p=0.5, instead of using a single cluster metallicity. It simulates 10^6 binary systems at z~4, retains those forming first-generation BBHs and BH-NS binaries, reports BBH total masses of 8-86 Msun and BH-NS masses of 6-31 Msun, overlays these on LVK mass measurements, and computes sub-Hz characteristic strains for LISA and LGWA. The central conclusion is that the individual-metallicity treatment yields much higher concordance with observed gravitational-wave events.

Significance. If the central claim were robust, the paper would make a useful contribution by showing that intra-cluster metallicity dispersion can materially shift compact-object masses relative to single-metallicity population synthesis, and by quantifying the sub-Hz detectability of eccentric first-generation binaries. The strengths are the public code release, the explicit COSMIC extension, and the inclusion of a shared-metallicity variant in Appendix A as a partial check. However, the headline concordance claim is not yet supported: the metallicity assignment is an uncalibrated and physically unmotivated mapping, and the paper provides no quantitative comparison to observations and no uniform-metallicity control run.

major comments (3)

[Section II A, Eq. (1)] Eq. (1) is the load-bearing element of the paper: it sets the metallicity of every ZAMS star, and through COSMIC's metallicity-sensitive winds, remnant masses, and binary interactions it determines the reported BBH (8-86 Msun) and BH-NS (6-31 Msun) ranges. The relation is a galaxy-scale mass-metallicity relation (Ma et al. 2015), where 'mass' means galaxy stellar mass, not the mass of an individual star; replacing that mass with the ZAMS stellar mass and choosing p=0.5 'for simplicity' imposes a physically unvalidated anti-correlation between stellar mass and metallicity. Please calibrate the per-star mapping against cluster abundance data (e.g., SMC/LMC star abundances) or at minimum show that the headline mass ranges are insensitive to p (e.g., p=0.2, 0.8) and to the functional form of Eq. (1).
[Section II A, Fig. 1; Appendix A] The code assigns different metallicities to the primary and secondary of a binary, although coeval cluster stars form from a shared gas reservoir. This creates a spurious anti-correlation between component mass and metallicity, which is directly responsible for pushing massive progenitors to low Z. Appendix A defines a shared-metallicity 'reduced_mass' variant, but it is used only for scatter plots and qualitative statements about 'consistent evolutionary trends'; it is not used to recompute the BBH/BH-NS mass ranges, the strains, or the LVK comparison. The shared-metallicity run should be either adopted as the fiducial model or reported quantitatively so the reader can see how much of the claimed effect is an artifact of per-component metallicity assignment.
[Section III B, Fig. 5; Conclusion] The conclusion that the simulated final mass distribution 'exhibits much higher concordance with observational data' is unsupported. Figure 5 overlays LVK mass measurements on the simulated distribution without error bars, a selection-function model, or a quantitative concordance statistic, and there is no comparison against a uniform-metallicity COSMIC run. I recommend adding a formal comparison (e.g., KS/AD test with and without the LVK selection function) and a control run with a single cluster metallicity within the claimed range (e.g., Z=0.002-0.004) to establish that the improvement is due to the individual-metallicity prescription rather than to the overall low-metallicity scale.

minor comments (6)

[Section II A, Eq. (1)] The text says 'm is the progenitor mass' but the equation uses M; please define the notation consistently.
[Fig. 2] The x-axis label appears as 'M2(Msun)' and the y-axis as 'M2(Msun)'; the primary mass axis should be labeled M1.
[Section II B] It is unclear whether all 10^6 initial binaries are placed at a single redshift z=4 or drawn from a redshift distribution; Section II A says clusters lie at a fixed redshift, while Section II B mentions a star formation history starting at 10 Gyr. Please clarify.
[Section II C, Eq. (7)] The strain normalization, including the harmonic weighting with m=1 in Eq. (8), should be benchmarked against a standard circular-inspiral case (e.g., Peters 1964), because the normalization directly affects the conclusion that the strains lie below the LISA and LGWA sensitivity curves.
[Appendix A] The reduced-mass choice in Eq. (A1) is one of several possible mass proxies for a shared-metallicity system; a brief test using the primary mass or the geometric mean would make the alternative model more convincing.
[Section IV] The sentence 'the sensitivity predicted by our model is of the order O(10^{-2}) for LISA and LGWA' is unclear, since the characteristic strains in Fig. 6 appear to lie below the detector curves; please rephrase.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Eq. (1) is an external empirical input, and the LVK comparison is post-hoc, not a fit.

full rationale

The derivation chain is not circular. Eq. (1) is the only input that couples stellar mass to metallicity; it is adopted from the external galaxy-scale relation of Ma et al. [98], with p=0.5 chosen 'for simplicity' rather than fitted to the LVK detections. The remnant masses and binary properties are then produced by the independent COSMIC population-synthesis machinery (wind prescriptions, remnant-mass fits of Fryer et al., common-envelope physics), so the output mass ranges are not equal to the input function by construction. The LVK comparison in Fig. 5 is a post-hoc overlay, not a calibration step; no LVK datum enters Eq. (1) or any other simulation parameter, so no fitted input is being renamed as a prediction. The self-citations (refs. 8, 10, 13) are background remarks on magnetars and primordial black holes and are not load-bearing for the metallicity prescription or the mass predictions. The reduced-mass shared-metallicity variant in Appendix A is an alternative scenario and is not used to produce the headline mass ranges or the concordance claim. The genuine limitations—Eq. (1) is a galaxy-scale relation applied to individual ZAMS stars, the slope p is arbitrary, and 'much higher concordance' is asserted without a quantitative statistic or a uniform-Z control—are physical-soundness and validation issues, not circularity. Consequently no circular step is identified.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the adopted mass-redshift-metallicity relation, the COSMIC physics package, and the initial mass and orbital sampling choices. No new particles, forces, or dimensions are introduced. The free parameters are the coefficients of the metallicity relation and the selection thresholds; the most fragile is p=0.5, which is chosen without external justification.

free parameters (5)

p (mass-metallicity slope) = 0.5
Set for simplicity in Eq. (1). No calibration or sensitivity study is given, yet this slope directly sets the metallicity assigned to each ZAMS mass.
q (redshift normalization) = 0.67
Adopted from reference [98]. Sets the metallicity scale for z~4 clusters, so the central mass output depends on it.
r (redshift exponent) = 0.5
Adopted from reference [98]. Controls the redshift decline of metallicity and is not varied.
Zmax (metallicity ceiling) = 0.01
Hard upper cutoff for low-metallicity ZAMS populations, adopted from references [102,103]. Acts as a selection threshold that shapes which binaries are admitted.
m (harmonic multiplier in Eq. 8) = 1
Chosen without sensitivity study. Sets the maximum harmonic number used in the strain and SNR sums.

assumptions (6)

domain assumption Eq. (1) mass-redshift-metallicity relation applies to individual ZAMS stars at z~4
The entire metallicity initialization rests on this empirical form, yet it is a galaxy-scale relation applied per star and per binary component, with an arbitrary slope p.
domain assumption Salpeter IMF and uniform mass-ratio distribution describe the ZAMS binary population
Standard binary population synthesis choices, but not validated for z~4 low-metallicity clusters.
domain assumption Sana et al. (2012) initial orbital distributions apply at z~4
Orbital period and eccentricity sampling is adopted from local star-forming regions and applied unchanged at high redshift.
domain assumption COSMIC wind, common-envelope, natal-kick, and remnant-mass prescriptions are accurate
The outputs inherit all COSMIC v3.6.1 physics, including Fryer delayed remnant masses and PPISN fits, without independent revalidation.
domain assumption A ZAMS mass floor of 8 solar masses for both components fully captures CO-forming binaries
The minimum mass cutoff excludes lower-mass neutron star progenitors and may bias the mass and metallicity distributions.
standard math Peters-Mathews harmonic GW formalism (Eqs. 2-7) applies to these inspiralling eccentric binaries
Standard weak-field gravitational wave emission model, used for both characteristic strain and SNR integration.

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Cite this review

Pith. "Pith review of A population study on the effect of metallicity on ZAMS to the merger." pith.science (2026). https://pith.science/paper/H7SIAOGI

@misc{pith2026241111902,
  author       = {Pith},
  title        = {Pith review of: A population study on the effect of metallicity on ZAMS to the merger},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H7SIAOGI}},
  note         = {Machine review of arXiv:2411.11902}
}

abstract

The formation channels of compact object binaries are crucial for interpreting gravitational wave observations and enhancing early multi-messenger alerts. Despite the key role of stellar metallicity in progenitor evolution, many models assume a uniform value for all stars in a cluster. In this study, we investigate the impact of a heterogeneous stellar metallicity distribution on the formation of compact object binaries and their resulting gravitational wave signatures. We extend the COSMIC binary population synthesis code to incorporate a fiducial mass-redshift-metallicity relation for individual Zero-Age Main Sequence stars of a stellar cluster. Focusing on low-metallicity environments at redshift $z \approx 4$, we analyse the gravitational-wave signals from binary black holes and black hole-neutron star systems in the sub-hertz regime. The resulting binary black holes have total masses from $8$-$86\,M_\odot$, while black hole--neutron star systems range from $6$-$31\,M_\odot$. We assess the detectability of the characteristic strains against the sensitivity curves of planned sub-hertz observatories.

Figures

Figures reproduced from arXiv: 2411.11902 by the authors.

**Figure 3.** FIG. 3. Distribution of the eccentricity, orbital period and [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 6.** FIG. 6. Characteristic strain against the frequency of COs [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: FIG. 5. Distribution of primary and secondary masses of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 7.** Figure 7: FIG. 7. The distributions of the primary ( [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

139 extracted references · 69 canonical work pages

[1]

B. P. Abbottet al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 119, 161101 (2017)

2017
[2]

B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Astrophys. J. Lett.848, L12 (2017). 8

2017
[3]

Abbott et al

R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Astrophys. J.896, L44 (2020)

2020
[4]

individual

We note that the number of BBH formed is much higher than the BH-NS binaries. In addition, BH masses in BH-NS binaries are significantly lower than in BBH binaries. In our simulation, the maximum mass of the BH reaches ≈ 43 M⊙. The progenitor stars that evolve into NSs exhibit a maximum initial mass≈ 23 M⊙. The results indicate that in certain instances t...
[5]

https://www.gw-openscience.org/eventapi/html/ GWTC/
[6]

Maselli, S

A. Maselli, S. Marassi, and M. Branchesi, Astron. As- trophys. 635, A120 (2020)

2020
[7]

B. P. Abbottet al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016)

2016
[8]

S. R. Chowdhury and M. Khlopov, Universe 7, 10 (2021)

2021

Show all 139 references

[9]

Abdikamalov, G

E. Abdikamalov, G. Pagliaroli, and D. Radice, Gravita- tional waves from core-collapse supernovae, inHandbook of Gravitational Wave Astronomy (Springer Singapore,
[10]

Ciolfi and L

R. Ciolfi and L. Rezzolla, Mon. Not. Roy. Astron. Soc.: Lett. 435, L43 (2013)

2013
[11]

Sasaki, T

M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, Phys. Rev. Lett.117, 061101 (2016)

2016
[12]

Mukherjee and J

S. Mukherjee and J. Silk, Mon. Not. Roy. Astron. Soc. 506, 3977 (2021)

2021
[13]

S. R. Chowdhury and M. Khlopov, Phys. Rev. D110, 063037 (2024)

2024
[14]

S. E. Woosley, S. Blinnikov, and A. Heger, Nature450, 1476 (2007)

2007
[15]

Wang, S.-P

Y.-Z. Wang, S.-P. Tang, Y.-F. Liang, M.-Z. Han, X. Li, Z.-P. Jin, Y.-Z. Fan, and D.-M. Wei, Astrophys. J.913, 42 (2021)

2021
[16]

S. R. Chowdhury, A. Basak, M. Khlopov, and M. Kras- nov, (2025), arXiv:2507.21332 [gr-qc]

2025 arXiv
[17]

Marchant and J

P. Marchant and J. Bodensteiner, Annu. Rev. Astron. Astrophys. 62, 21 (2024)

2024
[18]

H. Sana, S. E. de Mink, A. de Koter, N. Langer, C. J. Evans, M. Gieles, E. Gosset, R. G. Izzard, J.-B. L. Bouquin, and F. R. N. Schneider, Science 337, 444 (2012)

2012
[19]

C. L. Fryer, K. Belczynski, G. Wiktorowicz, M. Do- minik, V. Kalogera, and D. E. Holz, Astrophys. J.749, 91 (2012)

2012
[20]

Marchant et al., Astron

P. Marchant et al., Astron. Astrophys. 650, A107 (2021)

2021
[21]

Zevin andS

M. Zevin andS. S.Bavera, Astrophys. J.933, 86 (2022)

2022
[22]

Moe and R

M. Moe and R. D. Stefano, Astrophys. J. S.230, 15 (2017)

2017
[23]

J. S. W. Claeys, O. R. Pols, R. G. Izzard, J. Vink, and F. W. M. Verbunt, Astron. Astrophys.563, A83 (2014)

2014
[24]

F. A. Evans, M. Renzo, and E. M. Rossi, Mon. Not. Roy. Astron. Soc.497, 5344 (2020)

2020
[25]

Hjorth, Phil

J. Hjorth, Phil. Trans. R. Soc. A.371, 20120275 (2013)

2013
[26]

Chatterjee, C

S. Chatterjee, C. L. Rodriguez, V. Kalogera, and F. A. Rasio, Astrophys. J. Lett.836, L26 (2017)

2017
[27]

Yoon and N

S. Yoon and N. Langer, Astron. Astrophys.443, 643 (2005)

2005
[28]

Tøffner-Clausen, and T

C.Larsen, H.C.G.Larsen, C.C.Pedersen, P.N.Thom- sen, J. Tøffner-Clausen, and T. M. Tauris, Nature625, E18 (2024)

2024
[29]

B. M. Ziosi, M. Mapelli, M. Branchesi, and G. Tormen, Mon. Not. Roy. Astron. Soc.441, 3703 (2014)

2014
[30]

Mapelli, Mon

M. Mapelli, Mon. Not. Roy. Astron. Soc. 459, 3432 (2016)

2016
[31]

Mandel and S

I. Mandel and S. E. de Mink, Mon. Not. Roy. Astron. Soc. 458, 2634 (2016)

2016
[32]

Mapelli, M

M. Mapelli, M. Spera, E. Montanari, M. Limongi, A. Chieffi, N. Giacobbo, A. Bressan, and Y. Bouffanais, Astrophys. J. 888, 76 (2020)

2020
[33]

Y.-H. Lin, C. Scarlata, V. Mehta, E. Skill- man, M. Hayes, K. B. W. McQuinn, L. Fortson, K. Chworowsky, and L. Clarke, Astrophys. J.951, 138 (2023)

2023
[34]

L. Boco, A. Lapi, M. Chruslinska, D. Donevski, A. Si- cilia, and L. Danese, Astrophys. J.907, 110 (2021)

2021
[35]

Giacobbo, M

N. Giacobbo, M. Mapelli, and M. Spera, Mon. Not. Roy. Astron. Soc. 474, 2959 (2017)

2017
[36]

Spera, M

M. Spera, M. Mapelli, and A. Bressan, Mon. Not. Roy. Astron. Soc. 451, 4086 (2015)

2015
[37]

J. S. Vink, L. E. Muijres, B. Anthonisse, A. de Koter, G. Gräfener, and N. Langer, Astron. Astrophys.531, A132 (2011)

2011
[38]

Kowalska-Leszczynska, T

I. Kowalska-Leszczynska, T. Regimbau, T. Bulik, M. Dominik, and K. Belczynski, Astron. Astrophys. 574, A58 (2015)

2015
[39]

U. N. Di Carlo, M. Mapelli, Y. Bouffanais, N. Giacobbo, F. Santoliquido, A. Bressan, M. Spera, and F. Haardt, Mon. Not. Roy. Astron. Soc.497, 1043 (2020)

2020
[40]

Cerviño and J

M. Cerviño and J. M. Mas-Hesse, Astron. Astrophys. 284, 749 (1994)

1994
[41]

Martins and A

F. Martins and A. Palacios, Astron. Astrophys. 645, A67 (2021)

2021
[42]

Paxton, L

B. Paxton, L. Bildsten, A. Dotter, F. Herwig, P. Lesaf- fre, and F. Timmes, Astrophys. J. S.192, 3 (2010)

2010
[43]

Szécsi, The Evolution of Low-Metallicity Massive Stars, Ph.D

D. Szécsi, The Evolution of Low-Metallicity Massive Stars, Ph.D. thesis, Universität Bonn (2016)

2016
[44]

Siess, R

L. Siess, R. G. Izzard, P. J. Davis, and R. Deschamps, Astron. Astrophys. 550, A100 (2013)

2013
[45]

O. R. Pols, C. A. Tout, P. P. Eggleton, and Z. Han, Mon. Not. Roy. Astron. Soc.274, 964 (1995)

1995
[46]

Paxtonet al., Astrophys

B. Paxtonet al., Astrophys. J. S.208, 4 (2013)

2013
[47]

C.A.WhyteandP.P.Eggleton,Mon.Not.Roy.Astron. Soc. 214, 357 (1985)

1985
[48]

M. U. Kruckow, T. M. Tauris, N. Langer, M. Kramer, and R. G. Izzard, Mon. Not. Roy. Astron. Soc. 481, 1908 (2018)

2018
[49]

C. A. Nelson and P. P. Eggleton, Astrophys. J.552, 664 (2001)

2001
[50]

S. S. Bavera et al., Nature Astronomy7, 1090 (2023)

2023
[51]

Belczynski, V

K. Belczynski, V. Kalogera, and T. Bulik, Astrophys. J. 572, 407 (2002)

2002
[52]

Fragos et al., Astrophys

T. Fragos et al., Astrophys. J. S.264, 45 (2023)

2023
[53]

J. R. Hurley, C. A. Tout, and O. R. Pols, Mon. Not. Roy. Astron. Soc.329, 897 (2002)

2002
[54]

J. J. Eldridge and E. R. Stanway, Mon. Not. Roy. As- tron. Soc. 462, 3302 (2016)

2016
[55]

Stevenson et al

S. Stevenson et al. , Nature Communications 8, 14906 (2017)

2017
[56]

Toonen, A

S. Toonen, A. Hamers, and S. Portegies Zwart, Compu. Astrophys. Cosmo. 3, 6 (2016)

2016
[57]

M. A. Sedda et al., Mon. Not. Roy. Astron. Soc.526, 429 (2023)

2023
[58]

M. A. Sedda, M. Mapelli, M. Benacquista, and M. Spera, Mon. Not. Roy. Astron. Soc. 520, 5259 (2023)

2023
[59]

Langer, Annu

N. Langer, Annu. Rev. Astron. Astrophys. 50, 107 (2012)

2012
[60]

C. L. Rodriguez, S. Chatterjee, and F. A. Rasio, Phys. Rev. D 93, 084029 (2016)

2016
[61]

M. A. Sedda et al., Mon. Not. Roy. Astron. Soc.528, 5119 (2024)

2024
[62]

Banerjee, Mon

S. Banerjee, Mon. Not. Roy. Astron. Soc. 503, 3371 (2021)

2021
[63]

Mandel and A

I. Mandel and A. Farmer, Phys. Reports955, 1 (2022)

2022
[64]

Breivik et al., Astrophys

K. Breivik et al., Astrophys. J.898, 71 (2020). 9

2020
[65]

individual

applies delay-time models to a single stellar popu- lation, while [66] analyses integrated GW spectra from model clusters with varied compact binary populations. Post-merger BH retention depends on gravitational re- coilkicks, whicharemitigatedinisotropicconfigurations- enabli...

1954
[66]

W. G. J. van Zeist, J. J. Eldridge, and P. N. Tang, Mon. Not. Roy. Astron. Soc.524, 2836 (2023)

2023
[67]

J. C. Bray and J. J. Eldridge, Mon. Not. Roy. Astron. Soc. 480, 5657 (2018)

2018
[68]

J. J. Eldridge, E. R. Stanway, and P. N. Tang, Mon. Not. Roy. Astron. Soc.482, 870 (2019)

2019
[69]

Fragione and S

G. Fragione and S. Banerjee, Astrophys. J. Lett.913, L29 (2021)

2021
[70]

M. C. Miller, Astrophys. J.581, 438 (2002)

2002
[71]

C. L. Rodriguez, M. Zevin, C. Pankow, V. Kalogera, and F. A. Rasio, Astrophys. J. Lett.832, L2 (2016)

2016
[72]

C. L. Rodriguezet al., Phys. Rev. D100, 043027 (2019)

2019
[73]

Tagawa, Z

H. Tagawa, Z. Haiman, I. Bartos, B. Kocsis, and K. Omukai, Mon. Not. Roy. Astron. Soc. 507, 3362 (2021), https://academic.oup.com/mnras/article- pdf/507/3/3362/40323047/stab2315.pdf

2021
[74]

Reitzeet al., Bull

D. Reitzeet al., Bull. Am. Astron. Soc.51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]

2019 arXiv
[75]

Ajithet al., JCAP 2025, 108

P. Ajithet al., JCAP 2025, 108

2025
[76]

Maggiore et al

M. Maggiore et al. , J. Cosmo. Astropart. Phys 2020, 050 (2020)

2020
[77]

Robson, N

T. Robson, N. J. Cornish, and C. Liu, Class. Quantum Grav. 36, 105011 (2019)

2019
[78]

Salmon et al., Astrophys

B. Salmon et al., Astrophys. J.799, 183 (2015)

2015
[79]

Coughlin et al

S. Coughlin et al. , Cosmic-popsynth/cosmic: v3.6.0 (2025)

2025
[80]

Sesana, Phys

A. Sesana, Phys. Rev. Lett.116, 231102 (2016)

2016
[81]

Norberg,Stars - Lecture 4, lecture note (2020) lecture notes, Durham University, PHYS1081

P. Norberg,Stars - Lecture 4, lecture note (2020) lecture notes, Durham University, PHYS1081

2020
[82]

R. M. Yates, D. Hendriks, A. P. Vijayan, R. G. Izzard, P. A. Thomas, and P. Das, Mon. Not. Roy. Astron. Soc. 527, 6292 (2023)

2023
[83]

, Astron

Crespo Gómez, A., , et al. , Astron. Astrophys. 691, A325 (2024)

2024
[84]

Chruslinska, G

M. Chruslinska, G. Nelemans, and K. Belczynski, MN- RAS 482, 5012 (2018)

2018
[85]

C. J. Neijsselet al., Mon. Not. Roy. Astron. Soc.490, 3740 (2019)

2019
[86]

Lamberts, S

A. Lamberts, S. Garrison-Kimmel, D. R. Clausen, and P. F. Hopkins, Mon. Not. Roy. Astron. Soc. Lett.463, L31 (2016)

2016
[87]

Sakstein, A

J. Sakstein, A. Pipino, J. E. G. Devriendt, and R. Maiolino, Mon. Not. Roy. Astron. Soc. 410, 2203 (2011)

2011
[88]

K. G. Shepherdet al., (2025), arXiv:2505.10206 [astro- ph.SR]

2025 arXiv
[89]

I. K. Baldry, K. Glazebrook, and S. P. Driver, Mon. Not. Roy. Astron. Soc.388, 945 (2008)

2008
[90]

Langer and C

N. Langer and C. A. Norman, Astrophys. J.638, L63 (2006)

2006
[91]

M.Mapelli,in Gravitational Waves and Cosmology (IOS Press, 2020) p. 87

2020
[92]

Belczynski, T

K. Belczynski, T. Bulik, C. L. Fryer, A. Ruiter, F. Valsecchi, J. S. Vink, and J. R. Hurley, Astrophys. J. 714, 1217 (2010)

2010
[93]

Heger, C

A. Heger, C. L. Fryer, S. E. Woosley, N. Langer, and D. H. Hartmann, Astrophys. J.591, 288 (2003)

2003
[94]

R. C. Tolman, Phys. Rev.55, 364 (1939)

1939
[95]

J. R. Oppenheimer and G. M. Volkoff, Phys. Rev.55, 374 (1939)

1939
[96]

R. S. Klessen and S. C. Glover, Annu. Rev. Astron. Astrophys. 61, 65 (2023)

2023
[97]

Astrophys.504, 373 (2009)

Calura, F., Pipino, A., Chiappini, C., Matteucci, F., and Maiolino, R., Astron. Astrophys.504, 373 (2009)

2009
[98]

Haemmerlé, L

L. Haemmerlé, L. Mayer, R. S. Klessen, T. Hosokawa, P. Madau, and V. Bromm, Sp. Sc. Rev.216, 48 (2020)

2020
[99]

R. L. Sanders, A. E. Shapley, M. Kriek,et al., ApJ902, 125 (2020)

2020
[100]

Marszewski, C.-A

A. Marszewski, C.-A. Faucher-Giguère, R. Feldmann, and G. Sun, (2025), arXiv:2505.22712 [astro-ph.GA]

2025 arXiv
[101]

X. Ma, P. F. Hopkins, C.-A. Faucher-Giguère, N. Zol- man, A. L. Muratov, D. Kereš, and E. Quataert, Mon. Not. Roy. Astron. Soc.456, 2140 (2015)

2015
[102]

Belczynski, D

K. Belczynski, D. E. Holz, T. Bulik, and R. O’Shaughnessy, Nature534, 512 (2016)

2016
[103]

De Cia, C

A. De Cia, C. Ledoux, S. Savaglio,et al., Astron. As- trophys. 611, A76 (2018)

2018
[104]

Lamareilleet al., Astron

F. Lamareilleet al., Astron. Astrophys.495, 53 (2009)

2009
[105]

E. E. Salpeter, Astrophys. J.121, 161 (1955)

1955
[106]

Srinivasan, A

R. Srinivasan, A. Lamberts, M. A. Bizouard, T. Bruel, and S. Mastrogiovanni, Mon. Not. Roy. Astron. Soc. 524, 60 (2023)

2023
[107]

https://github.com/Dsantra92/COSMIC-GW
[108]

A. M. Hopkins and J. F. Beacom, Astrophys. J.651, 142 (2006)

2006
[109]

Mazeh, D

T. Mazeh, D. Goldberg, A. Duquennoy, and M. Mayor, Astrophys. J. 401, 265 (1992)

1992
[110]

Goldman and T

I. Goldman and T. Mazeh, Astrophys. J. 429, 362 (1994)

1994
[111]

M. S. Hjellming and R. F. Webbink, Astrophys. J.318, 794 (1987)

1987
[112]

Astrophys

Davies, Ben, Oudmaijer, René D., and Vink, Jorick S., Astron. Astrophys. 439, 1107 (2005)

2005
[113]

Kudritzki and D

R. Kudritzki and D. Reimers, Astron. Astrophys.70, 227 (1978)

1978
[114]

Belczynski et al., Astrophys

K. Belczynski et al., Astrophys. J.SS174, 223 (2008)

2008
[115]

Giacobbo and M

N. Giacobbo and M. Mapelli, Astrophys. J. 891, 141 (2020)

2020
[116]

Marchant et al., Astrophys

P. Marchant et al., Astrophys. J.882, 36 (2019)

2019
[117]

Barack and C

L. Barack and C. Cutler, Phys. Rev. D 69, 082005 (2004)

2004
[118]

S.Vagnozzi, K.Freese,andT.H.Zurbuchen,Astrophys. J. 839, 55 (2017)

2017
[119]

Vagnozzi, Atoms7, 2 (2019)

S. Vagnozzi, Atoms7, 2 (2019)

2019
[120]

Wen, Astrophys

L. Wen, Astrophys. J.598, 419 (2003)

2003
[121]

P. C. Peters and J. Mathews, Phys. Rev. 131, 435 (1963)

1963
[122]

RESUL T We now examine how our metallicity-aware population synthesisimpactsthedemographicsofcompactobjectbi- nariesandtheirobservableGWsignals

the GW frequency of these binaries at a timeTobs before the merger fo = n 32π(GMc)5/8 5c5 Tobs 3/8 [(1 + 0.27e10 0 + 0.33e20 0 + 0.2e1000 0 )(1 − e2 0)7/2]3/8.(9) III. RESUL T We now examine how our metallicity-aware population synthesisimpactsthedemographicsofcompactobjectbi-...
[123]

P. C. Peters, Phys. Rev.136, B1224 (1964)

1964
[124]

Zhao and Y

Y. Zhao and Y. Lu, Mon. Not. Roy. Astron. Soc.500, 1421 (2020)

2020
[125]

Mandel, Research Notes of the AAS5, 223 (2021)

I. Mandel, Research Notes of the AAS5, 223 (2021)

2021
[126]

Hunteret al., Astron

I. Hunteret al., Astron. Astrophys.466, 277 (2007)

2007
[127]

Brott et al., Astron

I. Brott et al., Astron. Astrophys.530, A115 (2011)

2011
[128]

Bromm, Rep

V. Bromm, Rep. Prog. Phys.76, 112901 (2013)

2013
[129]

J. J. Eldridge, E. R. Stanway, L. Xiao, L. A. S. McClel- land, G. Taylor, M. Ng, S. M. L. Greis, and J. C. Bray, PASA 34, e058 (2017)

2017
[130]

Vigna-Gómez et al

A. Vigna-Gómez et al. , Mon. Not. Roy. Astron. Soc. 481, 4009 (2018)

2018
[131]

Liu et al

B. Liu et al. , Mon. Not. Roy. Astron. Soc.534, 1634 (2024)

2024
[132]

Klencki, Jakub, Nelemans, Gijs, Istrate, Alina G., and Pols, Onno, aap638, A55 (2020)

2020
[133]

Klencki et al

J. Klencki et al. , (2025), arXiv:2505.08860 [astro- ph.HE]. 10

2025
[134]

Giacobbo and M

N. Giacobbo and M. Mapelli, Mon. Not. Roy. Astron. Soc. 480, 2011 (2018)

2018
[135]

van der Walt, S

S. van der Walt, S. C. Colbert, and G. Varoquaux, Compu. Sci. Engineer.13, 22 (2011)

2011
[136]

Virtanenet al., Nature Methods17, 261 (2020)

P. Virtanenet al., Nature Methods17, 261 (2020)

2020
[137]

J. D. Hunter, Compu. Sci. Engineer.9, 90 (2007)

2007
[138]

M.L.Waskom,JournalofOpenSourceSoftware 6,3021 (2021)

2021
[139]

Foreman-Mackey, Journal of Open Source Software 1, 24 (2016)

D. Foreman-Mackey, Journal of Open Source Software 1, 24 (2016)

2016

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

B. P. Abbottet al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 119, 161101 (2017)

2017

[2] [2]

B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Astrophys. J. Lett.848, L12 (2017). 8

2017

[3] [3]

Abbott et al

R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Astrophys. J.896, L44 (2020)

2020

[4] [4]

individual

We note that the number of BBH formed is much higher than the BH-NS binaries. In addition, BH masses in BH-NS binaries are significantly lower than in BBH binaries. In our simulation, the maximum mass of the BH reaches ≈ 43 M⊙. The progenitor stars that evolve into NSs exhibit a maximum initial mass≈ 23 M⊙. The results indicate that in certain instances t...

[5] [5]

https://www.gw-openscience.org/eventapi/html/ GWTC/

[6] [6]

Maselli, S

A. Maselli, S. Marassi, and M. Branchesi, Astron. As- trophys. 635, A120 (2020)

2020

[7] [7]

B. P. Abbottet al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 116, 061102 (2016)

2016

[8] [8]

S. R. Chowdhury and M. Khlopov, Universe 7, 10 (2021)

2021