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Investigating chemically homogeneous evolution as a possible source of the 35 M⊙ peak

Published online by Cambridge University Press:  09 November 2026

Lucas M. de SáOpen the ORCID record for Lucas M. de Sá[Opens in a new window],
Lieke A. C. van Son and
Matteo Cantiello
Lucas M. de Sá*
Affiliation:
Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão, 1226, São Paulo, SP 05508-090, BrazilCenter for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 100010, USAUniversität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert Ueberle Str. 2, 69120, Heidelberg, Germany
Lieke A. C. van Son
Affiliation:
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 100010, USADepartment of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USADepartment of Astrophysics/IMAPP, Radboud University, P.O. Box 9010, NL-6500 GL Nijmegen, The Netherlands
Matteo Cantiello
Affiliation:
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 100010, USADepartment of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA
*
email: lucas.desa@uni-heidelberg.de
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Abstract

The $M_1\sim35\,\mathrm{M}_\odot$ peak has been one of the most consistent features of gravitational-wave data on binary black hole (BBH) mergers, but its astrophysical origins remain among the most elusive. We examine chemically homogeneously evolving (CHE) stars as a plausible origin. CHE stars mix efficiently due to their rapid rotation, and end their Main Sequence evolution as compact helium stars. Efficient mixing occurs only in stars whose zero-age main-sequence masses exceed about $20\,\mathrm{M}_\odot$. As a result, CHE stars can form close pairs of massive black holes without undergoing mass transfer, retaining much of their mass and making them natural candidates for BBH mergers near the $35\,\mathrm{M}_\odot$ peak. We develop large grids of CHE star simulations using MESA to create synthetic populations of BBH mergers. We qualitatively discuss how a combination of the initial mass function and Wolf-Rayet winds can conspire to produce a $\sim35\,\mathrm{M}_\odot$ peak.

Keywords

massive stellar evolutionbinary evolutionblack hole-black hole mergers

Information

Type
Contributed Paper
Information
Proceedings of the International Astronomical Union , Volume 21 , Symposium S402: Massive Stars Across Redshifts in the Era of JWST and Large Surveys , January 2025, pp. 184 - 189
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2026. Published by Cambridge University Press on behalf of The International Astronomical Union

1. Introduction

The recent release of the fourth Gravitational-Wave Transient Catalog (GWTC-4) has brought the number of detected binary black hole (BBH) mergers to over 150 (The LIGO-Virgo-KAGRA Collaboration 2025), affirming the presence of a upper M 1 tilde 35 normal upper M Subscript circled dot $M_1\sim35\,\mathrm{M}_\odot$ peak for BBHs. Although one of the most robustly inferred features of gravitational-wave (GW) data, the tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ peak still lacks a satisfactory explanation (e.g., Roy et al. Reference Roy, van Son and Farr2025, and references therein).

We explore one possible formation channel: chemically homogeneously evolving (CHE) stars. Characterized by rapid rotation rates and low metallicities, these stars have been proposed to develop meridional currents that efficiently mix material throughout the envelope (e.g., Yoon and Langer Reference Yoon and Langer2005; Yoon et al. Reference Yoon, Langer and Norman2006). As a result, they become He-enriched on the surface by the end of the Main Sequence (MS), and remain compact throughout their lives. Because the necessary rotation is assumed to develop from tidal locking in tight binaries, these factors make them good potential BBH progenitors (Mandel and de Mink Reference Mandel and de Mink2016; Marchant et al. Reference Marchant, Langer, Podsiadlowski, Tauris and Moriya2016). They are furthermore expected to lead to more massive BBHs ( upper M 1 greater than or equivalent to 20 normal upper M Subscript circled dot $M_1\gtrsim20\,\mathrm{M}_\odot$ ) because rotational mixing is only effective in more massive, radiation-dominated stars (Hastings et al. Reference Hastings, Langer and Koenigsberger2020), and because their compactness avoids mass transfer episodes, potentially allowing them to retain a larger fraction of their initial mass. Finally, CHE mostly forms equal-mass binaries (though mass ratios as low as q almost equals 0.7 $q\approx0.7$ might occur in tilde 20 percent sign $\sim20\%$ of systems, see Marchant et al. Reference Marchant, Langer, Podsiadlowski, Tauris and Moriya2016; Hastings et al. Reference Hastings, Langer and Koenigsberger2020), which is also in line with recent findings on the upper M 1 tilde 35 normal upper M Subscript circled dot $M_1\sim35\,\mathrm{M}_\odot$ peak (Roy et al. Reference Roy, van Son and Farr2025; Banagiri et al. Reference Banagiri, Thrane and Lasky2025).

2. MESA setup

We run grids of CHE star models with version 23.04.1 of the 1D stellar structure code Modules for Experiments in Stellar Astrophysics (MESA, Paxton et al. Reference Paxton, Bildsten, Dotter, Herwig, Lesaffre and Timmes2011; Paxton et al. Reference Paxton, Cantiello, Arras, Bildsten, Brown, Dotter, Mankovich, Montgomery, Stello, Timmes and Townsend2013; Paxton et al. Reference Paxton, Marchant, Schwab, Bauer, Bildsten, Cantiello, Dessart, Farmer, Hu, Langer, Townsend, Townsley and Timmes2015; Paxton et al. Reference Paxton, Schwab, Bauer, Bildsten, Blinnikov, Duffell, Farmer, Goldberg, Marchant, Sorokina, Thoul, Townsend and Timmes2018; Paxton et al. Reference Paxton, Smolec, Schwab, Gautschy, Bildsten, Cantiello, Dotter, Farmer, Goldberg, Jermyn, Kanbur, Marchant, Thoul, Townsend, Wolf, Zhang and Timmes2019; Jermyn et al. Reference Jermyn, Bauer, Schwab, Farmer, Ball, Bellinger, Dotter, Joyce, Marchant, Mombarg, Wolf, Sunny Wong, Cinquegrana, Farrell, Smolec, Thoul, Cantiello, Herwig, Toloza, Bildsten, Townsend and Timmes2023). We build our models based on the inlists and extra routines from Gottlieb et al. (Reference Gottlieb, Renzo, Metzger, Goldberg and Cantiello2024), with the sigma equals 0 $\sigma=0$ Superscript 12 Baseline normal upper C left parenthesis alpha comma gamma right parenthesis Superscript 16 Baseline normal upper O $^{12}\mathrm{C}(\alpha,\gamma)^{16}\mathrm{O}$ reaction rate from deBoer et al. (Reference deBoer, Görres, Wiescher, Azuma, Best, Brune, Fields, Jones, Pignatari, Sayre, Smith, Timmes and Uberseder2017) as our fiducial assumption. Besides varying mass, initial spin periods and metallicities, we build an updated wind scheme, with the minimum between Björklund et al. (Reference Björklund, Sundqvist, Singh, Puls and Najarro2023) and Krtika et al. (2024) for thin (OB) winds; Vink et al. (Reference Vink, Muijres, Anthonisse, de Koter, Gräfener and Langer2011) for thick (very massive star, VMS) He-poor winds; and the minimum between Sander and Vink (Reference Sander and Vink2020) (with the Sander et al. Reference Sander, Lefever, Poniatowski, Ramachandran, Sabhahit and Vink2023, temperature correction) and Vink (Reference Vink2017) for thick (Wolf-Rayet, WR) He-rich winds. We transition to thick He-poor winds following the framework by Sabhahit et al. (Reference Sabhahit, Vink, Sander and Higgins2023), and to He-rich winds by interpolating between He-poor (either thin OB or thick VMS) and He-rich WR winds within the upper Y Subscript normal s normal u normal r normal f Baseline equals 0.4 minus 0.7 $Y_\mathrm{surf}=0.4-0.7$ range. Finally, we adopt rotation-enhanced mass-loss following Heger et al. (Reference Heger, Langer and Woosley2000).

For simplicity, we run only single stellar evolution models, which we find to allow for CHE for a wide range of zero-age MS (ZAMS) masses and spins. We emulate binary evolution by assuming q equals 1 $q=1$ , tidal synchronization at ZAMS (de Mink et al. Reference de Mink, Cantiello, Langer, Pols, Brott and Yoon2009) and Jeans mode mass loss. Models are run up to core carbon depletion, after which point the star is not expected to lose any significant amount of mass or angular momentum (AM). We define CHE as maintaining upper Y Subscript normal s normal u normal r normal f Baseline divided by upper Y Subscript normal c normal e normal n normal t normal e normal r Baseline greater than or equals 0.7 $Y_\mathrm{surf}/Y_\mathrm{center}\geq0.7$ throughout the MS, and stop any runs that violate this condition or lead into a stellar merger at ZAMS by overflow through the second Lagrangian point (following Marchant et al. Reference Marchant, Langer, Podsiadlowski, Tauris and Moriya2016).

Our model grid consists of 20 values of upper M Subscript normal upper Z normal upper A normal upper M normal upper S $M_{\mathrm{ZAMS}}$ , uniformly sampled with step 10 normal upper M Subscript circled dot $10\,\mathrm{M}_\odot$ between 20 minus 120 normal upper M Subscript circled dot $20-120\,\mathrm{M}_\odot$ , and with step 20 normal upper M Subscript circled dot $20\,\mathrm{M}_\odot$ between 120 minus 300 normal upper M Subscript circled dot $120-300\,\mathrm{M}_\odot$ ; and 36 values of upper P Subscript normal upper Z normal upper A normal upper M normal upper S $P_{\mathrm{ZAMS}}$ , with step 0.05 normal d $0.05\,\mathrm{d}$ between 0.35 minus 0.90 normal d $0.35-0.90\,\mathrm{d}$ , step 0.1 normal d $0.1\,\mathrm{d}$ between 0.90 minus 2.60 normal d $0.90-2.60\,\mathrm{d}$ , and step 0.2 normal d $0.2\,\mathrm{d}$ between 2.60 minus 4.00 normal d $2.60-4.00\,\mathrm{d}$ . Each of the 720 models is evolved for 9 metallicities, upper Z divided by normal upper Z Subscript circled dot Baseline equals 1 divided by 100 comma 1 divided by 50 comma 1 divided by 20 comma 1 divided by 10 comma 1 divided by 5 comma 0.4 comma 0.6 comma 0.8 comma 1.0 $Z/{\mathrm{Z}_\odot}=1/100,1/50,1/20,1/10,1/5,0.4,0.6,0.8,1.0$ , bringing the total to 6480 models.

Next, we use these MESA models to estimate a population of merging binary black holes. To this end, we fit three-dimensional linear interpolators on upper M Subscript normal upper Z normal upper A normal upper M normal upper S $M_{\mathrm{ZAMS}}$ , upper P Subscript normal upper Z normal upper A normal upper M normal upper S $P_{\mathrm{ZAMS}}$ and Z over our MESA grids, and re-draw upper M Subscript normal upper Z normal upper A normal upper M normal upper S $M_{\mathrm{ZAMS}}$ from a Kroupa (Reference Kroupa2001) IMF, and upper P Subscript normal upper Z normal upper A normal upper M normal upper S $P_{\mathrm{ZAMS}}$ from a log-uniform distribution. Unless stated otherwise, metallicities are re-drawn from the redshift-dependent skewed-Gaussian distribution from van Son et al. (Reference van Son, de Mink, Chruliska, Conroy, Pakmor and Hernquist2023). We compute merger rates from large interpolated populations with a MESA-adapted version of CosmicIntegrator, part of the post-processing suite of the COMPAS binary population synthesis code (Neijssel et al. Reference Neijssel, Vigna-Gómez, Stevenson, Barrett, Gaebel, Broekgaarden, de Mink, Szécsi, Vinciguerra and Mandel2019; Riley et al. Reference Riley, Mandel, Marchant, Butler, Nathaniel, Neijssel, Shortt and Vigna-Gómez2021).

3. The BBH yield from CHE at fixed metallicity

From our Fiducial model grid, we find that the minimum mass at ZAMS for which CHE occurs is tilde 30 normal upper M Subscript circled dot $\sim30\,\mathrm{M}_\odot$ for metallicities below 0.2 normal upper Z Subscript circled dot $0.2\,{\mathrm{Z}_\odot}$ , and tilde 50 normal upper M Subscript circled dot $\sim50\,\mathrm{M}_\odot$ for upper Z greater than or equals 0.2 $Z\geq0.2$ . Fig. 1 shows the resulting final primary mass distribution for six different metallicity ranges, without filtering for delay time, from an interpolated tilde 10 Superscript 8 $\sim10^8$ binary population following a log-uniform metallicity distribution. The effect of increasing wind mass-loss with metallicity is immediately evident, with the high metallicity ( negative 0.3 less than or equals log upper Z divided by normal upper Z Subscript circled dot Baseline less than 0 $-0.3\leq\log Z/{\mathrm{Z}_\odot}\lt0$ ) range producing a sharp peak at tilde 10 normal upper M Subscript circled dot $\sim10\,\mathrm{M}_\odot$ , while the low metallicity ( negative 2 less than or equals log upper Z divided by normal upper Z Subscript circled dot Baseline less than negative 1.7 $-2\leq\log Z/{\mathrm{Z}_\odot}\lt-1.7$ ) range produces masses between tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ and tilde 95 normal upper M Subscript circled dot $\sim95\,\mathrm{M}_\odot$ , with a modest pile-up at the upper end. Conspicuously, all log upper Z divided by normal upper Z Subscript circled dot Baseline greater than negative 0.7 $\log Z/{\mathrm{Z}_\odot}\gt-0.7$ metallicities produce either a peak or a sharp cut-off around tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ (black vertical line in Fig. 1).

Figure 1.

Final mass distribution from an interpolated population of 10 Superscript 8 $10^8$ binaries over different metallicity intervals, for a population generated following the Kroupa (Reference Kroupa2001) IMF, a log-uniform orbital period distribution and a log-uniform metallicity distribution. The solid vertical line indicates upper M Subscript normal f Baseline equals 35 normal upper M Subscript circled dot $M_\mathrm{f}=35\,\mathrm{M}_\odot$ .

A histogram showing the distribution of final mass in a population of binaries across different metallicity intervals.

Two main effects shape the distribution in Fig. 1. First is the interplay between the minimal ZAMS mass required for CHE, m Subscript normal upper C normal upper H normal upper E Superscript normal m normal i normal n Baseline almost equals 30 normal upper M Subscript circled dot $m_{\mathrm{CHE}}^{\mathrm{min}}\approx30\,\mathrm{M}_\odot$ , at low metallicities, and the Kroupa (Reference Kroupa2001) IMF, which favors lower masses. In other words, the initial mass function of CHE stars is itself peaked slightly above the lower edge of the window, i.e., tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ . In the absence of mass loss, this means most stars will have a final mass of tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ , which leads to the lowest metallicities in Fig. 1 seeing their final masses cut off around that value.

The second effect is the strong wind mass-loss from WR and VMS winds. VMS winds dominate mass-loss at the lowest metallicities, setting the maximum final mass of tilde 90 normal upper M Subscript circled dot $\sim90\,\mathrm{M}_\odot$ visible in Fig. 1. At intermediate metallicities, WR (He-rich) winds lead to significant mass-loss even at less than 100 normal upper M Subscript circled dot $\lt100\,\mathrm{M}_\odot$ , narrowing the distribution towards the minimum progenitor mass of tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ , where mass-loss becomes weak enough to create a pile-up. At the highest metallicities, the CHE window closes at upper M Subscript normal upper Z normal upper A normal upper M normal upper S Baseline tilde 50 normal upper M Subscript circled dot $M_\mathrm{ZAMS}\sim50\,\mathrm{M}_\odot$ , but mass-loss is so intense that the distribution shifts to create a narrow peak at final masses as low as tilde 10 normal upper M Subscript circled dot $\sim10\,\mathrm{M}_\odot$ .

4. Merger rates

We draw a new tilde 10 Superscript 8 $\sim10^8$ binary interpolated population, this time sampling from the van Son et al. (Reference van Son, de Mink, Chruliska, Conroy, Pakmor and Hernquist2023) metallicity distribution. Fig. 2 shows the resulting BBH merger rates. This demonstrates that our fiducial model peaks at tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ for low redshifts ( 0 less than z less than 1 $0 \lt z \lt 1$ ). This peak shifts to higher masses with redshift. This is the result of a mass-metallicity-delay time relation: lower metallicities, with weaker winds, favor greater masses and shorter delay times. Thus, the most massive mergers form early (higher redshift) and merge quickly, while the least massive mergers form later (lower redshift) and merge later.

Figure 2.

Merger rates over mass, for different redshift bins, for an interpolated 10 Superscript 8 $10^8$ binary population, drawn from the Kroupa (Reference Kroupa2001) IMF, a log-uniform orbital period distribution and the metallicity distribution by van Son et al. (Reference van Son, de Mink, Chruliska, Conroy, Pakmor and Hernquist2023). The solid vertical line indicates upper M 1 equals 35 normal upper M Subscript circled dot $M_\mathrm{1}=35\,\mathrm{M}_\odot$ .

Line graph showing merger rates over mass for different redshift bins.

In summary, we find that the CHE channel creates a low-redshift tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ peak hailing from the interplay between the IMF and WR winds; and a high-redshift tilde 90 normal upper M Subscript circled dot $\sim90\,\mathrm{M}_\odot$ peak hailing from VMS winds. The distribution shifts smoothly from one to the other with increasing redshift. We note, however, that while our current simulations produce a reasonable match for the peak location, our merger rates are much broader in upper M 1 $M_1$ than what is supported (see Roy et al. Reference Roy, van Son and Farr2025). We conclude that our results suggest how CHE might explain a feature at 35 normal upper M Subscript circled dot $35\mathrm{M}_\odot$ , but that our particular assumptions are not fully compatible with observations.

Spins

Another important constraint is that the tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ mergers are consistent with slowly-spinning, chi less than 0.1 $\chi\lt0.1$ BHs (Roy et al. Reference Roy, van Son and Farr2025). We find our Fiducial grid, which assumes the traditional Tayler-Spruit (TS) dynamo (Spruit Reference Spruit2002), to exclusively result in chi greater than 1 $\chi\gt1$ cores. These are likely to lead to a collapsar and GRB launch, which have been found to be efficient at halting BH spins, but also at unbinding up to tilde 90 percent sign $\sim90\%$ of a WR progenitor’s mass (e.g. Gottlieb et al. Reference Gottlieb, Liska, Tchekhovskoy, Bromberg, Lalakos, Giannios and Mösta2022), which would rule out CHE as the peak progenitor. We re-run a small subset of models with the Fuller and Lu (Reference Fuller and Lu2022) AM transport prescription, which we find to exclusively produce chi less than 0.01 $\chi\lt0.01$ cores. Such a situation allows for the production of the tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ peak. However, we stress that this would eliminate CHE stars as GRB progenitors. Whether AM transport in CHE stars corresponds to either model or has a more moderate efficiency remains unclear, and the problem of spins is left to future work.

5. Conclusions

We have mapped out the conditions under which CHE could be responsible for the tilde 35 normal upper M Subscript circled dot $\sim35\,\mathrm{M}_\odot$ peak. In the absence of mass transfer, CHE results in a (thick) wind-dominated BBH merger formation channel. Crucially, CHE allows thick WR winds to affect lower progenitor masses, for which VMS winds are not activated, without mass transfer. The bump in merger rates is a reflection of the minimum mass for CHE, at which winds become negligible. We assume the BH mass directly tracks the final progenitor mass. The efficiency of rotational mixing and the nature of CHE star mass-loss are thus the most critical assumptions for CHE. Determining whether CHE stars can simultaneously satisfy the mass and spin constraints required to match the upper M 1 tilde 35 normal upper M Subscript circled dot $M_1\sim35\,\mathrm{M}_\odot$ peak observed in BBH mergers, while also accounting for GRBs, will require further study, leaving CHE as an exciting topic at the intersection between GWs, GRBs and WRs.

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Figure 0

Figure 1.Final mass distribution from an interpolated population of 108$10^8$ binaries over different metallicity intervals, for a population generated following the Kroupa (2001) IMF, a log-uniform orbital period distribution and a log-uniform metallicity distribution. The solid vertical line indicates Mf=35M⊙$M_\mathrm{f}=35\,\mathrm{M}_\odot$.

Figure 1

Figure 2.Merger rates over mass, for different redshift bins, for an interpolated 108$10^8$ binary population, drawn from the Kroupa (2001) IMF, a log-uniform orbital period distribution and the metallicity distribution by van Son et al. (2023). The solid vertical line indicates M1=35M⊙$M_\mathrm{1}=35\,\mathrm{M}_\odot$.