Landscape of stellar-mass black-hole spectroscopy with third-generation gravitational-wave detectors

TL;DR

This paper assesses the potential of third-generation gravitational-wave detectors, like the Einstein Telescope and Cosmic Explorer, to perform black-hole spectroscopy and test gravity in the strong-field regime using stellar-mass black hole mergers.

Contribution

It provides a detailed analysis of the expected event rates and measurement precisions for black-hole spectroscopy with upcoming advanced detectors, incorporating population models and mode analysis.

Findings

Einstein Telescope can measure two quasinormal modes within 1% uncertainty for at least 1 event per year.

Operating with Cosmic Explorer significantly improves measurement accuracy and event rates.

Detector configuration, such as arm length and network setup, influences the precision and number of detectable events.

Abstract

Gravitational-wave black-hole spectroscopy provides a unique opportunity to test the strong-field regime of gravity and the nature of the final object formed in the aftermath of a merger. Here we investigate the prospects for black-hole spectroscopy with third-generation gravitational-wave detectors, in particular the Einstein Telescope in different configurations, possibly in combination with Cosmic Explorer. Using a state-of-the-art population model for stellar-origin binary black holes informed by LIGO Virgo-KAGRA data, we compute the average number of expected events for precision black-hole spectroscopy using a Fisher-matrix analysis. We perform our analysis on the dominant mode (2, 2, 0) and a set of subdominant modes [(3, 3, 0), (2, 1, 0), (4, 4, 0)] using amplitude and phase fits corresponding to the aligned spin configurations. We find that Einstein Telescope will measure two independent quasinormal modes within O(1)% (resp. O(10)%) relative uncertainty for at least O(1) (resp. O(500)) events per year, with similar performances in the case of a single triangular configuration or two L-shaped detectors with same arm length. A 15-km arm-length configuration would improve rates by roughly a factor of two relative to a 10-km arm-length configuration. When operating in synergy with Cosmic Explorer the rates will improve significantly, reaching few-percent accuracy for O(100) events per year.