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

The origin of binary black hole (BH) mergers remains a topic of active debate, with effective spins (chi_eff) measured by the LIGO-Virgo-KAGRA (LVK) Collaboration providing crucial insights. In this study, our objective is to investigate the empirical chi_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_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 ~72+/-8% 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 ~30% 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.