On the detectability and resolvability of quasi-normal modes with space-based gravitational wave detectors

TL;DR

This paper analyzes the potential of space-based gravitational wave detectors like TianQin and LISA to detect and resolve multiple quasi-normal modes during black hole ringdowns, which is vital for testing the no-hair theorem.

Contribution

It provides the first detailed analysis of the detectability and resolvability of multiple quasi-normal modes with space-based detectors, including systematic error considerations.

Findings

TianQin and LISA can detect and resolve multiple quasi-normal modes.

Six fundamental modes, one overtone, and two nonlinear modes are detectable.

Systematic errors in waveform templates affect mode detection and resolution.

Abstract

The detection of quasi-normal modes during the ringdown phase is a crucial method for testing the no-hair theorem. In this paper, the detectability and resolvability of multiple quasi-normal modes using space-based gravitational wave detectors have been analyzed. The results indicate that TianQin and LISA have the potential to detect and resolve a series of modes, including six fundamental modes, one overtone, and two nonlinear second-order modes. Furthermore, the analysis of systematic errors in the waveform suggests that even modes such as (3,3,1) and (4,3,0), which are unlikely to be directly detected and resolved, need to be taken into account in the ringdown waveform templates.