  The ringdown is the late part of the post-merger signature emitted during the
coalescence of two black holes and comprises of a superposition of
quasi-normal-modes. Within general relativity, because of the no-hair theorems,
the frequencies and damping times of these modes are entirely determined by the
mass and angular momentum of the final Kerr black hole. A detection of multiple
ringdown modes would potentially allow us to test the no-hair theorem from
observational data. The parameters which determine whether sub-dominant
ringdown modes can be detected are primarily the overall signal-to-noise ratio
present in the ringdown signal, and on the amplitude of the subdominant mode
with respect to the dominant mode. In this paper, we use Bayesian inference to
determine the detectability of a subdominant mode in a set of simulated
analytical ringdown signals. Focusing on the design sensitivity of the Advanced
LIGO detectors, we systematically vary the signal-to-noise ratio of the
ringdown signal, and the mode amplitude ratio in order to determine what kind
of signals are promising for performing black hole spectroscopy.
