Statistical constraints on binary black hole inspiral dynamics

Abstract

We perform a statistical analysis of binary black holes in the post-Newtonian approximation by systematically sampling and evolving the parameter space of initial configurations for quasi-circular inspirals. Through a principal component analysis of spin and orbital angular momentum variables, we systematically look for uncorrelated quantities and find three of them which are highly conserved in a statistical sense, both as functions of time and with respect to variations in initial spin orientations. For example, we find a combination of spin scalar products, , that is exactly conserved in time at the considered post-Newtonian order (including spin–spin and radiative effects) for binaries with equal masses and spin magnitudes evolving in a quasi-circular inspiral. We also look for and find the variables that account for the largest variations in the problem. We present binary black hole simulations of the full Einstein equations analyzing to what extent these results might carry over to the full theory in the inspiral and merger regimes. Among other applications these results should be useful both in semi-analytical and numerical building of templates of gravitational waves for gravitational wave detectors.