Explanation of the Mass Distribution of Binary Black Hole Mergers

TL;DR

The paper investigates the origin of the BBH mass distribution's bimodality observed in gravitational-wave data by integrating three formation channels—CHE, CE, and stable MT—within MOBSE while incorporating CHE from COMPAS and metallicity-dependent star formation. It couples population synthesis with metallicity-specific SFRD and detailed MT/CE physics to predict intrinsic and detectable BBH merger rates, finding that the low-mass peak largely arises from CE or MT (depending on the stability criterion) and the high-mass peak from CHE, with rates highly sensitive to model assumptions. The fiducial configurations reproduce the observed features around $M_{\rm BH}\sim10\,M_{\odot}$ and $\sim35\,M_{\odot}$ and yield local merger rates compatible with GW constraints; however, the distribution remains sensitive to angular-momentum loss, CE efficiency, WR winds, natal kicks, and MT stability. Overall, the work demonstrates that a multi-channel formation picture, modulated by metallicity evolution and GW selection effects, can explain both intrinsic and detectable BBH populations and provides guidance for constraining binary-evolution physics with future GW observations.

Abstract

Gravitational wave detectors are observing an increasing number of binary black hole (BBH) mergers, revealing a bimodal mass distribution of BBHs, which hints at diverse formation histories for these systems. Using the rapid binary population synthesis code MOBSE, we simulate a series of population synthesis models that include chemically homogeneous evolution (CHE). By considering metallicity-specific star formation and selection effects, we compare the intrinsic merger rates and detection rates of each model with observations. We find that the observed peaks in the mass distribution of merging BBHs at the low-mass end (10\msun) and the high-mass end (35\msun) are contributed by the common envelope channel or stable mass transfer channel (depending on the stability criteria for mass transfer) and the CHE channel, respectively, in our model. The merger rates and detection rates predicted by our model exhibit significant sensitivity to the choice of physical parameters. Different models predict merger rates ranging from 15.4 to $96.7\,\rm{Gpc^{-3}yr^{-1}}$ at redshift $z$ = 0.2, and detection rates ranging from 22.2 to 148.3$\mathrm{yr^{-1}}$ under the assumption of a detectable redshift range of $z \le$ 1.0.

Figures (5)

• Figure 1: The distribution of different formation channels for all BBH systems in the parameter space. Different formation channels are distinguished by different colors: purple, blue, and red represent BBHs formed via the CHE channel, the CE channel, and the stable mass transfer, respectively. The black straight lines indicate the mass ratios $M_{\rm 2}$/$M_{\rm 1}$. To facilitate comparison with observational data, we designate the more massive BH as $M_{\rm BH,1}$ in this context.
• Figure 2: Distribution of delay times between formation and merger (log-scale, in Gigayears). Color-coding corresponds to different formation channels, matching the scheme in Figure \ref{['fig:channel']}.
• Figure 3: The distribution of merger rate density (per unit solar mass) at redshift $z$ = 0.2 as a function of primary BH mass in BBH mergers of fiducial model. The curves and line segments represent the posterior population distributions of the power-law + Spline (PS) model and power-law + Peak (PP) model from GWTC-3 2023PhRvX..13a1048A and B-Spline model from GWTC-4 2025arXiv250818083T, along with their 90% credible intervals, indicated by the shaded regions.
• Figure 4: Distribution of merger rates across different formation channels as a function of the more massive BH mass. We displays the merger rates of different formation channels at redshift $z$ = 0.2, with purple, blue, and red colors corresponding to the CHE channel, CE channel, and stable MT channel, respectively. The total merger rate at $z$ = 0.2 also included, which shown by black curve. The light-shaded area shows the 90% sampling uncertainty as obtained from bootstrapping. Each subplot corresponds to the specific parameter configuration provided in Table \ref{['tab:uncertain']}, with the corresponding physical inputs indicated in the upper left corner.
• Figure 5: Distribution of detectable BBH mergers over chirp mass for differ channel, assuming LIGO O3 sensitivity, an SNR threshold of 8 and maximum detected redshift 1.0. The color-coding of lines (representing formation channels) and model numbering scheme follow the same conventions as Figure \ref{['fig:differ_qcrit']}. Besides, annotation labels indicate the model-specific annual detection rates (yr$^{-1}$) for each formation channel.