Normal Approximate Likelihoods to Gravitational Wave Events

Abstract

Gravitational wave observations of quasicircular compact binary mergers in principle provide an arbitrarily complex likelihood over eight independent intrinsic parameters: the masses and spins of the two merging objects. In this work, we demonstrate by example that a simple normal approximation over fewer (usually, three) effective dimensions provides a very accurate representation of the likelihood, and allows us to replicate the eight-dimensional posterior over the mass and spin degrees of freedom. Alongside this paper, we provide the parameters for multivariate normal fits for each event published in GWTC-1 and GWTC-2, using the posterior samples from the catalog for each associated release. These normal approximations provide a highly efficient way to characterize gravitational wave observations when combining large numbers of events.