A Mid-Thirties Crisis: Dissecting the Properties of Gravitational Wave Sources Near the 35 Solar Mass Peak

TL;DR

This paper isolates BBH mergers near the 35 M⊙ peak and infers joint distributions of $m_1$, $q$, $χ_{\rm eff}$, and $z$ to test competing formation channels. The peak occurs at $M_{\rm BH,max}=33.9^{+3.7}_{-4.2}\,M_{\odot}$ with a sharp decline beyond it, a mild preference for equal masses, a positively skewed $χ_{\rm eff}$ distribution, and redshift evolution consistent with the cosmic star-formation rate. A comprehensive comparison to PPISN, CHE, Pop III, globular clusters, and hierarchical-merger scenarios shows none can explain all observed features, yielding a genuine “mid-thirties crisis” for BBH origin theories. The work demonstrates the value of targeted, multidimensional population studies in constraining formation channels and guiding future modeling and observations with upcoming GW runs.

Abstract

One striking feature of binary black hole (BBH) mergers observed in the first decade of gravitational-wave astronomy is an excess of events with component masses around $35\,\mathrm{M}_{\odot}$. Multiple formation channels have been proposed to explain this excess. To distinguish among these channels, it is essential to examine their predicted population-level distributions across additional parameters. In this work, we focus on BBH mergers near the $35\,\mathrm{M}_{\odot}$ peak and infer the population distributions of primary mass ($m_1$), mass ratio ($q$), effective spin ($χ_{\rm eff}$), and redshift ($z$). We observe a gradual increase in the merger rate with $m_1$, rising by a factor of $3$ from $20\,\mathrm{M}_{\odot}$ to a peak around $34\,\mathrm{M}_{\odot}$, followed by a sharp, order-of-magnitude decline by $50\,\mathrm{M}_{\odot}$. This population also shows a weak preference for equal-mass mergers and has a $χ_{\rm eff}$ distribution skewed toward positive values, with a median of zero excluded at approximately $90\%$ confidence. We find no significant $q-χ_{\rm eff}$ correlation in the $35\, \mathrm{M}_{\odot}$ peak population, suggesting that lower-mass systems ($m_1<20\,\mathrm{M}_{\odot}$) likely drive the $q-χ_{\rm eff}$ anti-correlation observed in the full BBH merger catalog. The redshift evolution of the merger rate is consistent with the cosmic star formation rate. We compare our findings with predictions from a wide range of formation channels. We find that common variants of the pair-instability supernova scenario, as well as hierarchical mergers, are incompatible with the observed features of the $35\,\mathrm{M}_{\odot}$ population. Ultimately, none of the formation channels we consider can explain all or even most of the features observed in this population. The ''mid-thirties'' of black hole mergers are in crisis.

Figures (10)

• Figure 1: $90\%$ credible contours using the default parameter estimation (PE) prior for individual BBH mergers from GWTC-3. Top Panel: Contours in the $m_1$--$m_2$ plane. Events whose posteriors have a $50\%$ or higher probability of $m_1 > 20 \,\mathrm{M}_{\odot}$ and $3 \,\mathrm{M}_{\odot} < m_2 < 50 \,\mathrm{M}_{\odot}$ are shown in full opacity; the remaining events are shown in $25\%$ opacity. The grey region is the complement of our selected mass range. Bottom left panel: The mass ratios and effective spins of the selected events. Bottom right Panel: Redshifts of the selected events. See the https://github.com/SoumendraRoy/35Msun_GWTC3/blob/main/m1m2_cut/scripts/Plots_Main.ipynb used to generate this plot.
• Figure 2: Behavior of our mass model (colored lines), compared to the non-parametric fit of GWTC-3 (in gray) from autoreg1. In each case, we vary one parameter while keeping the others fixed at reference values: $\{\mathrm{M}_{\mathrm{tr}}=28\,\mathrm{M}_{\odot}, ~\mathrm{M}_{\mathrm{BH,max}}=34\,\mathrm{M}_{\odot}, ~\sigma=1.75\,\mathrm{M}_{\odot}, ~\alpha=2\}$. The different parameter choices for our model can reproduce the shape of the features observed in the non-parametric model. See the https://github.com/SoumendraRoy/35Msun_GWTC3/blob/main/paper_plots/codes/compare_ar1.ipynb used to generate this plot.
• Figure 3: The primary mass, mass ratio, effective spin and redshift distributions for the $35\,\mathrm{M}_{\odot}$ peak population (blue) compared to the model from gwtc-3pop (grey). The $m_1$, $q$ and $\,\chi_{\rm eff}\xspace$ distributions are evaluated at $z=0$. We normalize all $q$ distributions at $q = 1$ and all redshift ($z$) distributions at the value of $z$, where our measurement has the smallest error bar. Panels are annotated schematically with inferences for parameters controlling the shape of the corresponding curves. We compare our results to the full distribution of BBHs from the Power Law + Peak model gwtc-3pop. We find the BBH merger rate follows a flat or shallow rise with $m_1$, increasing by a factor of 3 from $20\,\mathrm{M}_{\odot}$ up to a peak at $\,\rm{M}_{\rm BH,max}\sim 34\,\,\mathrm{M}_{\odot}$, followed by a steep drop decreasing by an order of magnitude between the peak and $50\,\mathrm{M}_{\odot}$ (top left panel). The $q$ distribution shows weak preference towards equal-mass mergers compared to the full population in Golomb2024. A different pairing in gwtc-3pop shows a steeper $q$ population than ours. The $\,\chi_{\rm eff}\xspace$ distribution is skewed positively (a median of $0$ is ruled out at $\sim 90\%$ confidence). The merger rate for the $35\,\mathrm{M}_{\odot}$ peak population increases with $z$, at a rate that is consistent with the low-redshift behavior of the star formation rate (the dashed line). See the https://github.com/SoumendraRoy/35Msun_GWTC3/blob/main/m1m2_cut/scripts/Plots_Main.ipynb used to generate this plot.
• Figure 4: Left panel: Joint population distribution of mass ratio and effective spin for the $35\,\mathrm{M}_{\odot}$ peak population, evaluated at $m_1=35\,\mathrm{M}_{\odot}$ and $z=0$. Right panel: Marginal distributions for $\alpha_{\,\chi_{\rm eff}\xspace}$ (variation of the mean of $\,\chi_{\rm eff}\xspace$) Eq. \ref{['eq:alpha-eff-definition']}, and $\beta_{\,\chi_{\rm eff}\xspace}$ (variation of the width of $\,\chi_{\rm eff}\xspace$), Eq. \ref{['eq:beta-eff-definition']}. Although most of the posterior support lies at $\alpha_{\,\chi_{\rm eff}\xspace}<0$, our analysis remains consistent with no evolution, $\alpha_{\,\chi_{\rm eff}\xspace}, \beta_{\,\chi_{\rm eff}\xspace} = 0$, within the $90\%$ credible interval. We find significant posterior support at $q=0.5$ in reweighted PEs. See the https://github.com/SoumendraRoy/35Msun_GWTC3/blob/main/m1m2_cut/scripts/Plots_Main.ipynb used to generate this plot.
• Figure 5: Comparison between our results and predictions from formation channels proposed in the literature for the $35\,\,\mathrm{M}_{\odot}$ peak population. In the top-left panel the primary mass distributions from the literature are rescaled to redshift zero using the merger rate evolution model $R(z) = R_0(1+z)^{\lambda}$ with $\lambda = 3.4$MadauDickinson2014. The mass ratio distributions are normalized to a median of 1 at $q = 1$ (top right). The hatched blue region shows $q>0.8$ for the CHE channel Hastings_2020. The effective spin distributions are normalized to the peak value (bottom left). The dashed green line shows the prediction for hierarchical mergers as discussed in Section \ref{['ss: hierarchical mergers']}. While several formation channels reproduce the location of the observed $\sim35\,\mathrm{M}_{\odot}$ peak in $m_1$, none of them simultaneously provide a satisfactory match to the observed peak population in $m_1$, $q$, and $\,\chi_{\rm eff}\xspace$. See the https://github.com/SoumendraRoy/35Msun_GWTC3/blob/main/codes/scripts/Compare_formation_channels.ipynb used to generate this plot.