The spin magnitude of stellar-mass black holes evolves with the mass

Aims. Using gravitational-wave (GW) data from the latest GW Transient Catalog (GWTC-3), we conduct a comprehensive investigation into the relationship between the masses and spin magnitudes ( χ ) of binary black holes (BBHs). Our focus is on identifying potential correlations between BBH masses and spin magnitudes, and exploring their astrophysical implications in terms of formation channels. Methods. We employed hierarchical Bayesian methods and new population models for spin-mass distributions to analyze the GW data. We further validated our results with several sanity checks. Results. Analyzing 59 GW signals, we find statistical evidence for an evolution of the spin magnitude of the BBHs as a function of the mass. We interpret the evolution in two ways. First, using a class of population models that parameterize the evolution of the spin distribution with mass, we observe a transition from a population of BBHs with lower spin magnitudes ( χ ∼ 0.2) at lower masses to higher, but less constrained, spin magnitudes for higher masses. The transition between these two distinct distributions occurs around 45 M ⊙ − 55 M ⊙ . Additionally, using population models built by mixing independent populations of BBHs, we find that the observed GW signals can be interpreted as consisting ∼98% of low-spin black holes with masses ≲40 M ⊙ and ∼2% high-spin black holes with masses ≳40 M ⊙ . Conclusions. Using different prescriptions for the interplay between BBH spins and masses, we find evidence of a mass scale at 45 M ⊙ − 55 M ⊙ , where the population distribution of spin magnitudes changes. We speculate that this result may support the hypothesis that a large fraction of low-mass, low-spin BBHs are formed through the evolution of isolated stellar binaries, whereas a smaller fraction of higher-mass, high-spin BBHs are likely formed through dynamical assembly or hierarchical mergers.