Mapping Parameter Correlations in Spinning Binary Black Hole Mergers

Abstract

The spins of binary black holes measured with gravitational waves provide insights about the formation, evolution, and dynamics of these systems. However, interpreting these measurements-especially for heavy black holes-remains an open problem. While the imprint of spin during the inspiral phase, where the black holes are well-separated, is understood through analytic descriptions of the dynamics, no such expressions exist for the merger. Though numerical relativity simulations provide an exact solution (to within numerical error), the imprint of the full six spin degrees of freedom on the signal is not transparent. In the absence of analytic expressions for the merger and to advance our ability to interpret massive binary black hole spin measurements, here we propose a waveform-based approach. Leveraging a neural network to efficiently calculate mismatches between waveforms, we identify regions in the parameter space of spins and mass ratio that result in low mismatches and thus similar waveforms. We map these regions with a Gaussian fit, thus identifying correlations and quantifying their strength. For low-mass, inspiral-dominated systems, we recover the known physical imprint: larger aligned spins are correlated with more equal masses as they have opposite effects on the inspiral length. For high-mass, merger-dominated signals, a qualitatively similar correlation is present, though its shape is altered and strength decreases with larger total mass. Correlations between in-plane spins and mass ratio follow a similar trend, with their shape and strength altered as the mass increases. Our new methodology of waveform-based correlation mapping provides a first step toward systematically modeling spin effects in merger-dominated signals across the full intrinsic parameter-space and motivates future effective spin parameters beyond the reach of analytic methods.