Detectability of the subdominant mode in a binary black hole ringdown

TL;DR

This paper investigates the conditions under which subdominant black hole ringdown modes can be detected using Bayesian inference, focusing on signal-to-noise ratio and mode amplitude ratios with implications for testing the no-hair theorem.

Contribution

It provides a systematic analysis of the detectability of subdominant ringdown modes in simulated signals using Bayesian methods, informing future black hole spectroscopy efforts.

Findings

Detectability depends strongly on signal-to-noise ratio and mode amplitude ratio.

Certain combinations of parameters are promising for black hole spectroscopy.

Results are based on the design sensitivity of Advanced LIGO detectors.

Abstract

The ringdown is the late part of the post-merger signature emitted during the coalescence of two black holes and comprises of a superposition of quasi-normal-modes. Within general relativity, because of the no-hair theorems, the frequencies and damping times of these modes are entirely determined by the mass and angular momentum of the final Kerr black hole. A detection of multiple ringdown modes would potentially allow us to test the no-hair theorem from observational data. The parameters which determine whether sub-dominant ringdown modes can be detected are primarily the overall signal-to-noise ratio present in the ringdown signal, and on the amplitude of the subdominant mode with respect to the dominant mode. In this paper, we use Bayesian inference to determine the detectability of a subdominant mode in a set of simulated analytical ringdown signals. Focusing on the design sensitivity of the Advanced LIGO detectors, we systematically vary the signal-to-noise ratio of the ringdown signal, and the mode amplitude ratio in order to determine what kind of signals are promising for performing black hole spectroscopy.