The landscape of massive black-hole spectroscopy with LISA and Einstein Telescope

TL;DR

This paper assesses the potential of LISA and Einstein Telescope to perform black-hole spectroscopy on massive binary black hole mergers, highlighting the expected measurement precision and the influence of different seed models on detectability.

Contribution

It provides a comprehensive simulation-based analysis of black-hole spectroscopy prospects with future gravitational wave detectors across various black hole seed scenarios.

Findings

LISA can measure dominant QNM frequencies within 0.1% uncertainty for heavy seed scenarios.

At least 3 QNM parameters can be estimated within 1% error during LISA's mission.

Einstein Telescope can measure 3 QNM parameters with ~10% error in a few to ten events per year for light seed scenarios.

Abstract

Measuring the quasi-normal mode~(QNM) spectrum emitted by a perturbed black-hole~(BH) --~also known as BH spectroscopy~-- provides an excellent opportunity to test the predictions of general relativity in the strong-gravity regime. We investigate the prospects and precision of BH spectroscopy in massive binary black hole ringdowns, one of the primary science objectives of the future Laser Interferometric Space Antenna~(LISA) mission. We simulate various massive binary BH population models, featuring competing prescriptions for the Delays between galaxy and BH mergers, for the impact of supernova feedback on massive BH growth, and for the initial population of high redshift BH seeds (light versus heavy seeds). For each of these scenarios, we compute the average number of expected events for precision BH spectroscopy using a Fisher-matrix analysis. We find that, for any heavy seed scenario, LISA will measure the dominant mode frequency within ${\cal O}(0.1) \%$ relative uncertainty and will estimate at least 3 independent QNM parameters within $1 \%$ error. The most optimistic heavy seed scenarios produce $\mathcal{O}(100)$ events with $1 \%$ measurability for 3 or more QNM quantities during LISA's operational time. On the other hand, light seed scenarios produce lighter merger remnants, which ring at frequencies higher than LISA's sensitivity. Interestingly, the light seed models give rise to a fraction of mergers in the band of Einstein Telescope, allowing for the measurement of 3 QNM parameters with $\sim 10 \%$ relative errors in approximately a few to ten events/yr. More precise BH spectroscopy in the light seed scenarios would require instruments operating in the deciHertz band.