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Piling up in the darkness: Features of the BBH mass distribution from isolated binaries

Published online by Cambridge University Press:  15 October 2026

Cristiano Ugolini Open the ORCID record for Cristiano Ugolini [Opens in a new window]
Cristiano Ugolini*
Affiliation:
Gran Sasso Science Institute (GSSI), L’Aquila (Italy), Viale Francesco Crispi 7 INFN, Laboratori Nazionali del Gran Sasso, 67100 Assergi, Italy
*
email: cristiano.ugolini95@gmail.com
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Abstract

After the third LIGO–Virgo–KAGRA observing run, the number of detected binary black hole (BBH) mergers became sufficient to identify statistical features of the population. We explore how different prescriptions for the final fate of massive stars and key binary-evolution processes shape isolated binaries and their remnants. Using sevn, we evolved $10^{7}$ binaries across 15 metallicities, 3 core-collapse supernova models, 4 PPISN models, and 6 common-envelope (CE) prescriptions, for a total of 990 runs ($9.9 \times 10^{9}$ systems). Both single- and binary-star physics shape the BH mass distribution: single-star processes control the high-mass tail ($M_{\rm BH} \geq 45\,M_{\odot}$), while binary evolution produces pile-ups in specific intervals. In particular, the bump at $\sim 35\,M_{\odot}$, often attributed to PPISNe, also emerges from binaries evolving only through stable mass transfer, without CE. Finally, we test a top-heavy IMF, finding it boosts merger numbers and alters the abundance of systems with a given primary BH mass.

Keywords

Binary stellar evolutionSupernovaeBlack Hole AstrophysicsGravitational Waves

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Type
Poster Paper
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Proceedings of the International Astronomical Union , Volume 21 , Symposium S398: Compact Objects and Binaries in Dense Star Clusters , September 2025 , pp. 304 - 308
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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.
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© The Author(s), 2026. Published by Cambridge University Press on behalf of The International Astronomical Union

1. Introduction

The three observing runs of the LIGO-Virgo-KAGRA (LVK; LIGO Scientific Collaboration and Virgo Collaboration et al. 2020; Abbott et al. Reference Abbott2021; Abbott et al. Reference Abbott2023) collaboration revealed a population of stellar black holes (BHs) more massive than those known from X-ray binaries (Miller-Jones et al. Reference Miller-Jones2021). By GWTC-3, 90 BBH mergersFootnote † enabled inference of the BH mass spectrum, favoring a Power Law + Peak model with a Gaussian excess at upper M Subscript normal upper B normal upper H Baseline tilde 34 normal upper M Subscript circled dot $M_{\rm BH}\sim34\,{{\rm M_{\odot}}}$ (Abbott et al. Reference Abbott2023; Callister & Farr Reference Callister and Farr2024). This feature may trace specific evolutionary pathways (Abbott et al. Reference Abbott2021).

Theoretical models of BBH formation remain uncertain (see review by Spera et al. Reference Spera, Trani and Mencagli2022). Two main channels are proposed: (i) isolated binaries (e.g. Mapelli Reference Mapelli2016a; Spera et al. Reference Spera, Mapelli, Giacobbo, Trani, Bressan and Costa2019; Iorio et al. Reference Iorio2023) or (ii) dynamical assembly in dense clusters (e.g. Rodriguez et al. Reference Rodriguez, Morscher, Pattabiraman, Chatterjee, Haster and Rasio2015; Mapelli Reference Mapelli2016b; Arca Sedda et al. Reference Arca Sedda, Mapelli, Benacquista and Spera2023). Both are affected by uncertainties in winds, rotation, and SN physics (e.g. Burrows et al. Reference Burrows, Radice and Vartanyan2019; Ugolini et al. Reference Ugolini, Limongi, Schneider, Chieffi, Carlo and Spera2025). Pair-instability processes, dividing into PISNe and PPISNe (Fowler & Hoyle Reference Fowler and Hoyle1964), shape the upper BH mass limit (Woosley Reference Woosley2017). While the 35 normal upper M Subscript circled dot $35\,{{\rm M_{\odot}}}$ bump has been attributed to PPISNe (Belczynski et al. Reference Belczynski2016), recent works emphasize binary interactions such as SMT and CE (van Son et al. Reference van Son2022; Dorozsmai & Toonen Reference Dorozsmai and Toonen2024).

Here we explore how single-star and binary evolution combine to shape the BH mass spectrum using SEVN (Spera et al. Reference Spera, Mapelli, Giacobbo, Trani, Bressan and Costa2019; Iorio et al. Reference Iorio2023). Section 2 summarizes the setup, Section 3 presents the impact of CE efficiency, and Section 4 discusses IMF effects.

2. Methods

We employ the population-synthesis code SEVN (Spera et al. Reference Spera, Mapelli and Bressan2015), which interpolates stellar tracks from PARSEC v2.7.0 (Bressan et al. Reference Bressan, Marigo, Girardi, Salasnich, Dal Cero, Rubele and Nanni2012). Initial conditions follow Iorio et al. (Reference Iorio2023): primary masses are drawn from a Kroupa IMF in left bracket 8 comma 150 right bracket normal upper M Subscript circled dot $[8,150]\,{{\rm M_{\odot}}}$ , and secondaries from left bracket 5 comma 150 right bracket normal upper M Subscript circled dot $[5,150]\,{{\rm M_{\odot}}}$ . This analysis focuses on a subsample of the simulations presented in Ugolini et al. (prep), consisting of 10 Superscript 7 $10^{7}$ binaries evolved for each of 15 metallicities and 6 CE prescriptions, plus an additional run adopting a Larson IMF (Larson Reference Larson1998).

3. Effect of BSE on the 35 normal upper M Subscript circled dot $35\,{{\rm M_{\odot}}}$ peak

Figure 1.

Primary BH mass distribution of merging BBHs for different CE efficiencies alpha $\alpha$ . Upper row: alpha equals 0.5 comma 1 comma 3 $\alpha=0.5,1,3$ ; lower row: alpha equals 5 comma 10 $\alpha=5,10$ , and the always-stable MT case. Blue: SMT channel; purple: CE channel. Dashed: metal-poor ( upper Z less than or equals 5 times 10 Superscript negative 4 $Z\leq 5\times10^{-4}$ ); solid: full population. The black curve is the total over all the channels.

Multiple graphs depict the distribution of primary black hole masses in merging binary black hole systems for different common envelope efficiencies.

We assess how the CE efficiency parameter alpha $\alpha$ shape the BH mass spectrum under our fiducial ccSN+PPISN combination (delayed_Gauss+ M20). We also consider an “always-stable MT” setup, where CE can still occur only if both stars overflow their Roche lobes (treated with alpha equals 3 $\alpha=3$ when it happens).

CE parameter alpha equals 0.5 $\alpha=0.5$ . CE ejection is inefficient, so many systems merge as stars rather than form BBHs. Among survivors, the long-lasting CE phase shrinks orbits efficiently, making CE the dominant channel in the BBH sample. Indeed, the CE channel supplies tilde 54 percent sign $\sim54\%$ of BHs in the 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ bump, with CE and SMT nearly degenerate at 32– 34.5 normal upper M Subscript circled dot $34.5\,{{\rm M_{\odot}}}$ , and CE producing more BHs at 35– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ . SMT builds up BHs at tilde 13 $\sim13$ – 22 normal upper M Subscript circled dot $22\,{{\rm M_{\odot}}}$ (about 65% of SMT-formed primaries).

CE parameter alpha equals 1 $\alpha=1$ . CE shrinks orbits less than at alpha equals 0.5 $\alpha=0.5$ , thus more binaries successfully eject the envelope before merging, increasing the overall merger yield. CE contributes to 57% of the BBH in the bump. As at alpha equals 0.5 $\alpha=0.5$ , channels are degenerate at 32– 34.5 normal upper M Subscript circled dot $34.5\,{{\rm M_{\odot}}}$ ; CE contributes more at 35– 37.5 normal upper M Subscript circled dot $37.5\,{{\rm M_{\odot}}}$ .

CE parameter alpha equals 3 $\alpha=3$ . Maximum amount of BBH among all the setups. The 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ bump is now primarily from SMT ( tilde 54 percent sign $\sim54\%$ ), with CE and SMT contributing similarly at 35– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ .

CE parameter alpha equals 5 $\alpha=5$ . CE still dominates for upper M Subscript normal upper B normal upper H Baseline less than or equals 14 normal upper M Subscript circled dot $M_{\rm BH}\leq 14\,{{\rm M_{\odot}}}$ , while SMT dominates at 16– 22 normal upper M Subscript circled dot $22\,{{\rm M_{\odot}}}$ and in the 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ bump. In this bump, 65% of systems evolved without CE (pure SMT). CE systems contributing to the bump decline because prompt ejection leaves separations too wide to merge within a Hubble time.

CE parameter alpha equals 10 $\alpha=10$ . SMT shapes the higher-mass distribution. In the 32 minus 37 normal upper M Subscript circled dot $32-37\,{{\rm M_{\odot}}}$ mass-interval, 83% of merging systems never undergo CE. The total number of mergers and the general shape resemble alpha equals 0.5 $\alpha=0.5$ , but the bump is narrower for high alpha $\alpha$ (concentrated at 32– 34.5 normal upper M Subscript circled dot $34.5\,{{\rm M_{\odot}}}$ ) and broader for low alpha $\alpha$ (extending to tilde 37 normal upper M Subscript circled dot $\sim37\,{{\rm M_{\odot}}}$ ).

Always-stable MT. CE becomes secondary (it can still occur if both stars overflow their RLs). Even the least-massive BHs are then mostly formed via SMT, yet CE still contributes tilde 38 percent sign $\sim38\%$ of primaries in the bump.

Global feature. Across models, primaries tend to accumulate at 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ : about 7% of BHs form in this interval, versus only tilde 3 percent sign $\sim3\%$ and tilde 2 percent sign $\sim2\%$ in the adjacent 27– 32 normal upper M Subscript circled dot $32\,{{\rm M_{\odot}}}$ and 37– 42 normal upper M Subscript circled dot $42\,{{\rm M_{\odot}}}$ bins, respectively. In sum, CE predominantly seeds the low-mass end, while SMT governs the 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ excess, with their balance regulated by alpha $\alpha$ .

4. Effect of a top-heavy IMF

Stars that populate the 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ bump typically have upper M Subscript normal upper Z normal upper A normal upper M normal upper S Baseline greater than or equivalent to 70 normal upper M Subscript circled dot ${ M_{\rm ZAMS}} \gtrsim 70\,{{\rm M_{\odot}}}$ , making the IMF a key factor in setting their relative abundance. To test this, we adopt a Larson IMF (Larson Reference Larson1998), usually invoked for Pop III stars but applied here across all metallicities to probe the effect of favoring massive stars. Other initial conditions follow our fiducial setup (see Section 2). Figure 2 shows the resulting distributions for alpha equals 3 comma 5 comma 10 $\alpha=3,5,10$ .

Figure 2.

Primary BH mass distribution of merging BBHs for a Larson IMF and different CE efficiencies alpha equals 3 comma 5 comma 10 $\alpha=3,5,10$ . Blue: SMT; purple: CE. Black solid: Larson IMF; black dashed: Kroupa IMF.

Three histograms compare black hole mass distributions under different conditions.

CE parameter alpha equals 3 $\alpha=3$ . As in the Kroupa IMF case, SMT contributes 54% of bump primaries and CE 46%. The Larson IMF, however, boosts the overall merger yield by tilde 67 percent sign $\sim67\%$ and nearly triples the number of systems in the 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ range. The abundance of low-mass BHs ( upper M Subscript normal upper B normal upper H Baseline less than or equivalent to 10 normal upper M Subscript circled dot $M_{\rm BH}\lesssim 10\,{{\rm M_{\odot}}}$ ) is only mildly affected.

CE parameter alpha equals 5 $\alpha=5$ . The bump is dominated by SMT (65%) with CE contributing 35%, similar to the Kroupa case, but the absolute number of bump BHs again rises by a factor tilde 3 $\sim3$ , and the total mergers increase by tilde 68 percent sign $\sim68\%$ .

CE parameter alpha equals 10 $\alpha=10$ . As in the Kroupa IMF case, 83% of bump BHs evolve without CE. The Larson IMF triples the bump population relative to Kroupa and raises the overall merger count by tilde 80 percent sign $\sim80\%$ .

In summary, adopting a top-heavy IMF greatly amplifies the 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ feature and the total merger rate, while leaving the qualitative role of CE vs. SMT largely unchanged.

5. Summary and conclusions

Large-scale population synthesis with SEVN shows that:

  • • The 32– 37 normal upper M Subscript circled dot $37\,{{\rm M_{\odot}}}$ bump arises from a combination of CE and SMT pathways. CE dominates for alpha less than or equals 1 $\alpha\le1$ , SMT for alpha greater than or equals 3 $\alpha\ge3$ .

  • • A top-heavy IMF amplifies the bump and merger rate without changing the CE/SMT balance.

  • • CE efficiency and IMF leave measurable signatures on the BH mass spectrum, offering GW observations a way to constrain them.

Future work will integrate these results into the semi-analytical BPOP model (Arca Sedda et al. Reference Arca Sedda, Mapelli, Benacquista and Spera2023) to include metallicity and star-formation histories.

Acknowledgements

The author acknowledges Mario Spera, Marco Limongi, and Manuel Arca sedda for useful discussion and comments

Supplementary material

To view supplementary material for this article, please visit https://doi.org/10.1017/S1743921325104122

Footnotes

† O4 is expected to yield at least 200 events

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Figure 0

Figure 1. Primary BH mass distribution of merging BBHs for different CE efficiencies α$\alpha$. Upper row: α=0.5,1,3$\alpha=0.5,1,3$; lower row: α=5,10$\alpha=5,10$, and the always-stable MT case. Blue: SMT channel; purple: CE channel. Dashed: metal-poor (Z≤5×10−4$Z\leq 5\times10^{-4}$); solid: full population. The black curve is the total over all the channels.

Figure 1

Figure 2. Primary BH mass distribution of merging BBHs for a Larson IMF and different CE efficiencies α=3,5,10$\alpha=3,5,10$. Blue: SMT; purple: CE. Black solid: Larson IMF; black dashed: Kroupa IMF.

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