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

Binary-black-hole dynamics cannot be related to the resulting gravitational-wave signal by a constant retarded time. This is due to the nontrivial 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 (L) over cap (t) can be calculated from the gravitational-wave signal. This is done by calculating the direction that maximizes the quadrupolar (l = 2, vertical bar m vertical bar = 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 (L) over cap (t). We investigate how well the binary's orbital phase, phi(orb) (t), can also be estimated from the signal. For this purpose we define a quantity Phi(t) that agrees well with phi(orb) (t). One application is to studies that involve injections of numerical-relativity waveforms into gravitational-wave detector data.