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The black hole uniqueness and the no-hair theorems imply that the quasinormalspectrum of any astrophysical black hole is determined solely by its mass andspin. The countably infinite number of quasinormal modes of a Kerr black holeare thus related to each other and any deviations from these relations providea strong hint for physics beyond the general theory of relativity. To test theno-hair theorem using ringdown signals, it is necessary to detect at least twoquasinormal modes. In particular, one can detect the fundamental mode alongwith a subdominant overtone or with another angular mode, depending on the massratio and the spins of the progenitor binary. Also in the light of the recentdiscovery of GW190412, studying how the mass ratio affects the prospect ofblack hole spectroscopy using overtones or angular modes is pertinent, and thisis the major focus of our study. First, we provide ready-to-use fits for theamplitudes and phases of both the angular modes and overtones as a function ofmass ratio $q\in[0,10]$. Using these fits we estimate the minimumsignal-to-noise ratio for detectability, resolvability, and measurability ofsubdominant modes/tones. We find that performing black-hole spectroscopy withangular modes is preferable when the binary mass ratio is larger than $q\approx1.2$ (provided that the source is not located at a particularly disfavouredinclination angle). For nonspinning, equal-mass binary black holes, theovertones seem to be the only viable option to perform a spectroscopy test ofthe no-hair theorem. However this would require a large ringdownsignal-to-noise ratio ($\approx 100$ for a $5\%$ accuracy test with twoovertones) and the inclusion of more than one overtone to reduce modellingerrors, making black-hole spectroscopy with overtones impractical in the nearfuture.

Spectroscopy of binary black hole ringdown using overtones and angular modes