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Black hole spectroscopy is the proposal to observe multiple quasinormal modesin the ringdown of a binary black hole merger. In addition to the fundamentalquadrupolar mode, overtones and higher harmonics may be present and detectablein the gravitational wave signal, allowing for tests of the no-hair theorem. Weanalyze in detail the strengths and weaknesses of the standard Rayleighcriterion supplied with a Fisher matrix error estimation, and we find that thecriterion is useful, but too restrictive. Therefore we motivate the use of aconservative high Bayes factor threshold to obtain the black hole spectroscopyhorizons of current and future detectors, i.e., the distance (averaged in skylocation and binary inclination) up to which one or more additional modes canbe detected and confidently distinguished from each other. We set up all of oursearches for additional modes starting at $t = 10(M_1+M_2)$ after the peakamplitude in simulated signals of circular nonspinning binaries. An agnosticmultimode analysis allows us to rank the subdominant modes: for nearly equalmass binaries we find $(\ell, m, n) = (2,2,1)$ and $(3,3,0)$ and, for veryasymmetric binaries, $(3,3,0)$ and $(4,4,0)$, for the secondary and tertiarymodes, respectively. At the current estimated rates for heavy stellar massbinary black hole mergers, with primary masses between 45 and 100 solar masses,we expect an event rate of mergers within our conservative estimate for the$(2,2,1)$ spectroscopy horizon of $0.03 - 0.10\ {\rm yr}^{-1}$ for LIGO atdesign sensitivity and $(0.6 - 2.4) \times 10^3\ {\rm yr}^{-1}$ for the futurethird generation ground-based detector Cosmic Explorer.

Black hole spectroscopy horizons for current and future gravitational wave detectors