A practical Bayesian method for gravitational-wave ringdown analysis with multiple modes

TL;DR

This paper introduces FIREFLY, a Bayesian algorithm that accelerates gravitational-wave ringdown analysis involving multiple modes by analytically marginalizing parameters, reducing computation time significantly.

Contribution

The paper presents a novel Bayesian method that speeds up multi-mode gravitational-wave ringdown analysis by analytically marginalizing parameters, enabling faster inference without sacrificing accuracy.

Findings

FIREFLY reduces analysis time from hours to minutes.

The method maintains consistent posterior and evidence results.

Acceleration increases with more QNMs considered.

Abstract

Gravitational-wave (GW) ringdown signals from black holes (BHs) encode crucial information about the gravitational dynamics in the strong-field regime, which offers unique insights into BH properties. In the future, the improving sensitivity of GW detectors is to enable the extraction of multiple quasi-normal modes (QNMs) from ringdown signals. However, incorporating multiple modes drastically enlarges the parameter space, posing computational challenges to data analysis. Inspired by the $F$-statistic method in the continuous GW searches, we develope an algorithm, dubbed as FIREFLY, for accelerating the ringdown signal analysis. FIREFLY analytically marginalizes the amplitude and phase parameters of QNMs to reduce the computational cost and speed up the full-parameter inference from hours to minutes, while achieving consistent posterior and evidence. The acceleration becomes more significant when more QNMs are considered. Rigorously based on the principle of Bayesian inference and importance sampling, our method is statistically interpretable, flexible in prior choice, and compatible with various advanced sampling techniques, providing a new perspective for accelerating future GW data analysis.