Detection of higher order modes of gravitational waves in third-generation (3G) ground-based detectors such as Cosmic Explorer and Einstein Telescope is explored. Using the astrophysical population of binary black holes based on events reported in the second gravitational wave catalog by Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo (GWTC-2), in conjunction with the Madau-Dickinson model for redshift evolution of the binary black hole mergers, we assess the detectability of these higher order modes using a network consisting of three 3G detectors. We find that the two subleading modes [(3,3) and (4,4)] can be detected in approximately 30% of the population with a network signal-to-noise ratio of 3 or more, and for nearly 10% of the sources, the five leading modes will be detectable. Besides, a study concerning the effect of binary’s mass ratio and its orbital inclination with the observer’s line-of-sight in detecting various modes is presented. For a few selected events of the LIGO-Virgo catalog, we identify the modes that would have been detected if a 3G detector was operational when these events were recorded. We also compute the detectability of higher modes by Voyager and find that only $\sim 6$ and 2% of the detectable population will have an associated detection of (3,3) and (4.4) modes, respectively. Observing these higher order modes in the 3G era would have a huge impact on the science possible with these detectors ranging from astrophysics and cosmology to testing strong-field gravity.

• Received 5 March 2021
• Revised 13 August 2021
• Accepted 23 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.084080