Multipole moments on the common horizon in a binary-black-hole simulation

Abstract

We construct the covariantly defined multipole moments on the common horizon of an equal-mass, nonspinning, quasicircular binary-black-hole system. We see a strong correlation between these multipole moments and the gravitational waveform. We find that the multipole moments are well described by the fundamental quasinormal modes at sufficiently late times. For each nonzero multipole moment with $\ensuremath{\ell}\ensuremath{\le}6$, at least two fundamental quasinormal modes of different $\ensuremath{\ell}$ are detectable in the best model. These models provide faithful estimates of the true mass and spin of the remnant black hole. We also show that by including overtones, the $\ensuremath{\ell}=m=2$ mass multipole moment admits an excellent quasinormal-mode description at all times after the merger. This demonstrates the perhaps surprising power of perturbation theory near the merger.