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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.