Spectroscopic analysis of stellar mass black-hole mergers in our local universe with ground-based gravitational wave detectors

Motivated by the recent discoveries of binary black-hole mergers by the Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO), we investigate the prospects of ground-based detectors to perform a spectroscopic analysis of signals emitted during the ringdown of the final Kerr black hole formed by a stellar mass binary black-hole merger. Although it is unlikely that Advanced LIGO can measure multiple modes of the ringdown, assuming an optimistic rate of 240 Gpc-3 yr-1, upgrades to the existing LIGO detectors could measure multiple ringdown modes in ∼6 detections per year. New ground-based facilities such as Einstein Telescope or Cosmic Explorer could measure multiple ringdown modes in over 300 events per year. We perform Monte Carlo injections of 106 binary black-hole mergers in a search volume defined by a sphere of radius 1500 Mpc centered at the detector, for various proposed ground-based detector models. We assume a uniform random distribution in component masses of the progenitor binaries, sky positions and orientations to investigate the fraction of the population that satisfies our criteria for detectability and resolvability of multiple ringdown modes. We investigate the detectability and resolvability of the subdominant modes l=m=3, l=m=4 and l=2, m=1. Our results indicate that the modes with l=m=3 and l=2, m=1 are the most promising candidates for subdominant mode measurability. We find that for stellar mass black-hole mergers, resolvability is not a limiting criteria for these modes. We emphasize that the measurability of the l=2, m=1 mode is not impeded by the resolvability criterion.