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

Abstract: 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. If we assume an optimistic rate of 240 Gpc$^{-3}$yr$^{-1}$, about 3 events per year can be measured by Advanced LIGO. Further, upgrades to the existing LIGO detectors will increase the odds of measuring multiple ringdown modes significantly. New ground-based facilities such as Einstein Telescope or Cosmic Explorer could measure multiple ringdown modes in about thousand events per year. We perform Monte-Carlo injections of $10^{6}$ 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 satisfy our criteria for detectability and resolvability of multiple ringdown modes. We investigate the detectability and resolvability of the sub-dominant 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 sub-dominant 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.