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

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 ($\ddot{I}{‡}_{\mathrm{eff}}$), 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 $\ddot{I}{‡}_{\mathrm{eff}}$ distribution skewed toward positive values, with a median of zero excluded at approximately $90\%$ confidence. We find no significant $q-\ddot{I}{‡}_{\mathrm{eff}}$ correlation in the $35{\mathrm{M}}_{\odot }$ peak population, suggesting that lower-mass systems ($m_1<20{\mathrm{M}}_{\odot }$) likely drive the $q-\ddot{I}{‡}_{\mathrm{eff}}$ 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.

Accepted Version in Classical and Quantum Gravity Special Edition: Gravitational Wave Physics and Astrophysics Ten Years After GW150914. Codes are Publicly Available on GitHub: https://github.com/SoumendraRoy/35Msun_GWTC3. A Frozen Version of the Codes with Produced Data are Also Available on Zenodo: https://zenodo.org/records/15778343