Inferring black-hole orbital dynamics from numerical-relativity gravitational waveforms

TL;DR

This paper explores how to infer the orbital dynamics of binary black holes from gravitational wave signals, addressing gauge ambiguities and proposing methods to estimate orbital phase and angular momentum direction from numerical relativity data.

Contribution

It introduces a method to estimate the binary's orbital phase and angular momentum direction from gravitational waveforms, accounting for gauge ambiguities in numerical relativity simulations.

Findings

The gravitational-wave signal can approximate the orbital angular momentum direction.

A new quantity $ ext{ extPhi}(t)$ effectively estimates the orbital phase.

The approach aids in waveform injections into gravitational-wave detector data.

Abstract

Binary-black-hole dynamics cannot be related to the resulting gravitational-wave signal by a constant retarded time. This is due to the non-trivial dynamical spacetime curvature between the source and the signal. In a numerical-relativity simulation there is also some ambiguity in the black-hole dynamics, which depend on the gauge (coordinate) choices used in the numerical solution of Einstein's equations. It has been shown previously that a good approximation to the direction of the binary's time-dependent orbital angular momentum $\mathbf{\hat{L}}(t)$ can be calculated from the gravitational-wave signal. This is done by calculating the direction that maximises the quadrupolar $(\ell=2,|m|=2)$ emission. The direction depends on whether we use the Weyl scalar $\psi_4$ or the gravitational-wave strain $h$, but these directions are nonetheless invariant for a given binary configuration. We treat the $\psi_4$-based direction as a proxy to $\mathbf{\hat{L}}(t)$. We investigate how well the the binary's orbital phase, $\phi_{\rm orb}(t)$, can also be estimated from the signal. For this purpose we define a quantity $\Phi(t)$ that agrees well with $\phi_{\rm orb}(t)$. One application is to studies that involve injections of numerical-relativity waveforms into gravitational-wave detector data.