Detectability of the subdominant mode in a binary black hole ringdown

The ringdown is the late part of the postmerger signature emitted during the coalescence of two black holes and comprises a superposition of quasinormal modes. Within the general theory of relativity, the no-hair theorem for black holes states that the frequencies and the damping times of these modes are entirely determined by the mass and the angular momentum of the final Kerr black hole. Detection of multiple ringdown modes in the gravitational wave signal emitted during a binary black hole coalescence would allow us to validate the no-hair theorem with observations. The signal-to-noise ratio of the black hole ringdown and the amplitude of the subdominant modes to the dominant mode determine the detectability of the subdominant mode. We use Bayesian inference to investigate the interplay between these two factors towards their detectability. We systematically vary the two factors in a set of simulated analytical ringdown signals to infer the minimum signal-to-noise ratio needed in a ringdown signal for performing black hole spectroscopy. Our estimates on the minimum signal strength required to perform black hole spectroscopy as a function of amplitude ratio allows us to gain insight into the kind of signals that will be promising for black hole spectroscopy.