Good things always come in 3s: trimodality in the binary black-hole chirp-mass distribution supports bimodal black-hole formation

TL;DR

The paper addresses the question of whether a bimodal black-hole (BH) mass spectrum can explain the observed trimodal distribution of BBH chirp masses reported by LVK. It implements a novel bimodal remnant-mass prescription, derived from recent SN explodability criteria, within the COMPAS rapid binary population-synthesis framework and tests its robustness across 20+ variations in binary physics and cosmic star-formation history. The results show that the bimodal model naturally yields a three-peak (trimodal) intrinsic chirp-mass distribution that survives cosmic evolution and selection effects, while traditional non-bimodal models fail to reproduce the feature; merger rates are lowered by a factor of a few, improving agreement with LVK constraints. The study also uncovers an unexpected formation channel where luminous blue variable winds suppress binary interaction before the first BH forms, contributing to the central peak. These structural features offer a potential standard-candle-like probe for core-collapse physics and binary evolution, with implications for using BBH chirp masses to constrain stellar physics and cosmology as detectors improve.

Abstract

The latest GWTC-4 release from the LIGO-Virgo-KAGRA (LVK) collaboration nearly doubles the known population of double compact object mergers and reveals a new trimodal structure in the chirp-mass distribution of merging binary black holes (BBHs) below 30 Msun. Recent detailed stellar evolution models show that features in the pre-collapse cores of massive stars produce a bimodal black hole (BH) mass distribution, which naturally extends to a trimodal BBH chirp-mass distribution. Both distributions depend only weakly on metallicity, implying universal structural features which can be tested with LVK observations. Using a new compact-remnant mass prescription derived from these models, we perform rapid population synthesis simulations to test the robustness of the predicted chirp-mass structure against uncertainties in binary evolution and cosmic star formation history, and compare these results with the current observational data. The trimodal chirp-mass distribution emerges as a robust outcome of the new remnant-mass model, persisting across variations in binary and cosmic physics. In contrast, traditional BH formation models lacking a bimodal BH mass spectrum fail to reproduce the observed trimodality. The updated models also predict lower BBH merger rates by a factor of a few, in closer agreement with LVK constraints. Intriguingly, the central chirp-mass peak, dominated by unequal-mass BBHs, originates from a previously underappreciated formation pathway in which strong luminous blue variable winds suppress binary interaction before the first BH forms. If isolated binary evolution dominates BBH formation below 30 Msun, the relative heights of the three chirp-mass peaks offer powerful observational constraints on core collapse, BH formation, binary evolution, and cosmic star formation. These universal structural features may also serve as standard sirens for precision cosmology.

Figures (14)

• Figure 1: The binary black-hole chirp-mass $\xspace \mathcal{M}$ distribution from observations and from some of the model predictions from this work. The observed distribution (top plot) includes the high-confidence events from all GWTC data releases to date. We show only the region between 5 and 30 $\xspace M_{\odot}\xspace$, where the impact of our bimodal BH mass model is more relevant, which includes 52 observed BBHs with median chirp mass in this range. The black curve is the sum of the posteriors of these systems (see text); the blue shaded region shows the 90% confidence interval obtained from bootstrapping this curve. The predicted distributions (bottom plot) highlight a subset of the results from our population synthesis setup, including the more traditional BH formation models (green lines) and two that used the bimodal BH formation model described in section \ref{['sec:black_hole_mass_models']} (red and dark red lines). These are described in detail in subsequent sections. The sharp peak at 6 $\xspace M_{\odot}$ in the observed distribution comes from just two BBH mergers.
• Figure 2: Core-collapse outcome landscape from the bimodal BH model. The outcome of core collapse is shown in colors as a function of $Z$, $\xspace M_{\mathrm{CO}}$ at He depletion, and MT history, for the bimodal BH mass models explored in this work. MT history refers to the timing (Case A, B, or C) of the first binary interaction in which the core-collapse progenitor was a donor, or 'No MT' if the progenitor was never a MT donor, shown in the four sub-plots. We include three variations to this model, Optimistic, Balanced, and Pessimistic, corresponding to how the model is extrapolated outside of the range $Z \sim [0.1 Z_{\odot}, Z_{\odot}]$. The interpolation region is highlighted in darker colors to emphasize that this is the region where we are more confident in the models. In the extrapolation region, we show in lighter colors the outcomes for only the Balanced extrapolation mode, which we treat as the default. See text for details.
• Figure 3: BH and BBH mass distribution from direct collapse, fallback, and chemically homogeneous formation channels, under the $M_\mathrm{rem}$: Bimodal, Balanced model for a simulation of $10^7$ binaries. Left panel: distribution of masses of all BHs formed in the simulation. Colors and hatching indicate systems which formed via direct collapse (orange) or fallback (yellow), or if they experienced CHE (dark blue), regardless of the explosion mechanism. The vertical dotted line at 14 $\xspace M_{\odot}$ indicates the boundary that we use to distinguish low-mass (LM) and high-mass (HM) BHs, forming from the bimodal BH prescription. Middle panel: same as the left plot, but including only components of merging BBHs. Right panel: BBH source-frame chirp masses $\xspace \mathcal{M}_{\mathrm{S}}$, prior to convolution with a cosmic SFH. Colors indicate whether both components are low-mass BHs (LM+LM, lime), both are high-mass BHs (HM+HM, sea green), one of each (LM+HM, green), or if either component formed through CHE (dark blue). Bin edges lie at integer values of the ordinate.
• Figure 4: Chirp mass $\xspace \mathcal{M}_{\mathrm{S}}$ vs period at BBH formation $\xspace P_{\mathrm{BBH}}$ under the $M_\mathrm{rem}$: Bimodal, Balanced model. The chirp mass is the outcome of the population synthesis, not including convolution with a cosmic SFH. Marginalized histograms of each parameter are shown at the top and right. Colors correspond to metallicity bins, with $Z_{10}:= \log_{10}(Z)$. Filled scatter points and histograms show binaries that experienced a common envelope event during their evolution; those that experienced only stable mass transfer are depicted in hollow points and histograms (stacked on top of the filled histograms). Colored contours in the scatter plot bound the regions containing the highest 90% of the KDE volume for each metallicity bin, determined using a 2D Gaussian KDE with bandwidth = $0.25\,\xspace M_{\odot}\xspace$ for the chirp mass and 0.001 dex in $\xspace P_{\mathrm{BBH}}$/d. Characteristic inspiral times $\xspace T_\mathrm{insp}$ for circular BBHs are over-plotted in the scatter plot to guide the eye. Eccentric BBHs can have much shorter $\xspace T_\mathrm{insp}$ for the same period, however most BBHs here are circular at formation. The scatter points have been down-sampled by a factor of 5 to improve clarity, but the histograms show the full output of the simulation.
• Figure 5: Masses of the primary ($\xspace M_{\mathrm{BH,1}}$) and secondary ($\xspace M_{\mathrm{BH,2}}$) component in BBH under the $M_\mathrm{rem}$: Bimodal, Balanced model. Primary and secondary are defined here as the more and less massive component at birth, $M_\mathrm{ZAMS,1} > M_\mathrm{ZAMS,2}$, so we directly see which systems experienced mass ratio reversal ($\xspace M_{\mathrm{BH,1}}\xspace < \xspace M_{\mathrm{BH,2}}\xspace$) and which did not. Colors correspond to metallicity bins, and filled and hollow points depict systems that went through CEE and SMT formation channels, respectively. Colored contours bound the regions containing the highest 90% of the KDE volume for each metallicity bin, determined using a 2D Gaussian KDE with bandwidth = 0.2 $\xspace M_{\odot}$. The green dashed line highlights where $\xspace M_{\mathrm{BH,1}}\xspace=\xspace M_{\mathrm{BH,2}}\xspace$. Black dot-dashed lines show curves of constant chirp mass $\xspace \mathcal{M}_{\mathrm{S}}$ (labeled in $\xspace M_{\odot}$).