High-overtone fits to numerical relativity ringdowns: Beyond the dismissed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>8</mml:mn></mml:math> special tone

Abstract

In general relativity, the remnant object originating from an uncharged black hole merger is a Kerr black hole. This final state is reached through the emission of a late train of radiation known as the black hole ringdown. In linear perturbation theory around the final state, the ringdown morphology is described by a countably infinite set of damped sinusoids---the quasinormal modes---whose complex frequencies are solely determined by the final black hole's mass and spin. Recent results advocate that ringdown waveforms from numerical relativity can be fully described from the peak of the strain onwards if quasinormal mode models with ${N}_{\mathrm{max}}=7$ overtones (beyond the fundamental mode) are used. In this work we extend this analysis to models with ${N}_{\mathrm{max}}\ensuremath{\ge}7$ up to ${N}_{\mathrm{max}}=16$ overtones by exploring the parameter bias on the final mass and spin obtained by fitting the nonprecessing binary black hole simulations from the SXS catalog. To this aim, we have computed the spin weight $\ensuremath{-}2$ Kerr quasinormal mode frequencies and angular separation constants for the $(l=m=2,n=8,9)$ co- and counter-rotating overtones, which all approach a Schwarzschild algebraically special mode at low spins. We provide tables of the values obtained for these modes, which are in agreement with previous results. From the systematic variable-${N}_{\mathrm{max}}$ analysis, we find that ${N}_{\mathrm{max}}\ensuremath{\sim}6$ overtones are on average sufficient to model the ringdown from the peak of the strain, although about 21% of the cases studied require at least ${N}_{\mathrm{max}}\ensuremath{\sim}12$ overtones to reach a comparable accuracy on the final state parameters. Considering the waveforms from an earlier or later point in time, we find that a very similar maximum accuracy can be reached in each case, occurring at a different number of overtones ${N}_{\mathrm{max}}$. We also provide new error estimates for the SXS waveforms based on the extrapolation and the resolution uncertainties of the gravitational wave strain, which dominate over the errors obtained from the quasilocal measures of the final mass and spin. Finally, we observe substantial instabilities on the best-fit amplitudes of the tones beyond the fundamental mode and the first overtone, that, nevertheless, do not impact significantly the mass and spin estimates.