Spectroscopy of binary black hole ringdown using overtones and angular modes

Abstract

The black hole uniqueness and the no-hair theorems imply that the quasinormal spectrum of any astrophysical black hole is determined solely by its mass and spin. The countably infinite number of quasinormal modes of a Kerr black hole are thus related to each other and any deviations from these relations provide a strong hint for physics beyond the general theory of relativity. To test the no-hair theorem using ringdown signals, it is necessary to detect at least two quasinormal modes. In particular, one can detect the fundamental mode along with a subdominant overtone or with another angular mode, depending on the mass ratio and the spins of the progenitor binary. Also in the light of the recent discovery of GW190412, studying how the mass ratio affects the prospect of black hole spectroscopy using overtones or angular modes is pertinent, and this is the major focus of our study. First, we provide ready-to-use fits for the amplitudes and phases of both the angular modes and overtones as a function of mass ratio $q\in[0,10]$. Using these fits we estimate the minimum signal-to-noise ratio for detectability, resolvability, and measurability of subdominant modes/tones. We find that performing black-hole spectroscopy with angular modes is preferable when the binary mass ratio is larger than $q\approx 1.2$ (provided that the source is not located at a particularly disfavoured inclination angle). For nonspinning, equal-mass binary black holes, the overtones seem to be the only viable option to perform a spectroscopy test of the no-hair theorem. However this would require a large ringdown signal-to-noise ratio ($\approx 100$ for a $5\%$ accuracy test with two overtones) and the inclusion of more than one overtone to reduce modelling errors, making black-hole spectroscopy with overtones impractical in the near future.