Evidence for mass-dependent spin subpopulations in GWTC-4

Abstract

While the origin of merging black-hole binaries observed in gravitational waves remain uncertain, different formation channels are expected to leave distinct imprints on their observed mass and spin distributions. In this work, we focus on the mass dependence of the spin magnitudes $(\chi_1,\chi_2)$, allowing for multiple spin subpopulations whose relative fraction varies with mass. Using the binaries from the fourth LIGO--Virgo--KAGRA gravitational wave transient catalog (GWTC-4), we find strong evidence for two subpopulations, with a log Bayes factor of $\log_{10} \mathcal B = 4^{+6}_{-2}$. The data support a picture in which low-mass systems are composed almost entirely of slowly spinning black holes ($\chi \lesssim 0.2$), while high-mass systems are dominated by a broader component with moderate to rapid spins, peaking at $(\chi_1,\chi_2)\approx(0.7,0.7)$ and retaining a non-negligible tail toward asymmetric spins $(\chi_1,\chi_2)\approx(0.7,0)$. The transition between these regimes spans a broad range from $m_1 \approx 35^{+20}_{-20} \,M_\odot$ to $m_1 \approx 70^{+90}_{-25}\,M_\odot$. For the low-mass, slowly-spinning regime, a flexible model of spin orientations does not allow us to exclude identically vanishing spins, $\chi_1 = \chi_2 = 0$. Meanwhile, the high-mass, rapidly-spinning population does not neatly display the spin-magnitude asymmetry expected from hierarchical mergers, although the data do not exclude that. This kind of localized structure is generally difficult to access with standard Monte-Carlo likelihood estimators, which we replace with a regularized representation in terms of truncated Gaussian mixtures. Taken together, our results provide a new target for formation models, which should reproduce not only the mass and effective spin distributions, but also the mass-dependent structure of the individual component-spin magnitudes.