Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

We study the inspiral, merger, and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from $q={M}_{2}/{M}_{1}=1$ to $q=4$). We compare numerical and post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices $(l,m)$. We find that the post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each $(l,m)$, and that the convergence of the post-Newtonian series to the numerical results is nonmonotonic. To leading order, the total energy emitted in the merger phase scales like ${\ensuremath{\eta}}^{2}$ and the spin of the final black hole scales like $\ensuremath{\eta}$, where $\ensuremath{\eta}=q/(1+q{)}^{2}$ is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-$l$ multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as $q$ increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear-estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross correlating information from different multipoles, we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.