Analysis and simulations of binary black hole merger spins — The question of spin-axis tossing at black hole formation

Abstract

The origin of binary black hole (BH) mergers remains a topic of active debate, with effective spins (${\chi }_{\mathrm{eff}}$) measured by the LIGO-Virgo-KAGRA (LVK) Collaboration providing crucial insights. In this study, our objective is to investigate the empirical ${\chi }_{\mathrm{eff}}$ distribution (and constrain individual spin components) of binary BH mergers and compare them with extensive simulations, assuming that they originate purely from isolated binaries or a mixture of formation channels. We explore scenarios using BH kicks with and without the effect of spin-axis tossing during BH formation. We employ simple yet robust Monte Carlo simulations of the final core collapse forming the second-born BH, using minimal assumptions to ensure transparency and reproducibility. The synthetic ${\chi }_{\mathrm{eff}}$ distribution is compared to the empirical data from LVK science runs O1–O3 using functional data analysis, kernel density estimations, and three different statistical tests, accounting for data uncertainties. We find strong indications for spin-axis tossing during BH formation if LVK sources are dominated by the isolated binary channel. Simulations with spin-axis tossing achieve high p-values (up to 0.882) using Kolmogorov–Smirnov, Cramer-von Mises, and Anderson–Darling tests, while without tossing, all p-values drop below 0.001 for isolated binaries. A statistically acceptable solution without tossing, however, emerges if $\sim 72\pm 8\text{\%}$ of detected binary BH mergers result from dynamical interactions causing random BH spin directions. Finally, for an isolated binary origin, we find a preference for mass reversal in $\sim 30\text{\%}$ of the progenitor binaries. Predictions from this study can be tested with LVK O4+O5 data as well as the 3G detectors, Einstein Telescope and Cosmic Explorer, enabling improved constraints on formation channel ratios and the critical question of BH spin-axis tossing.