# Estimation of starting times of quasinormal modes in ringdown gravitational waves with the Hilbert-Huang transform

## TL;DR

This paper introduces a new method to accurately estimate the start time, frequency, and amplitude of quasinormal modes in gravitational wave signals from black hole mergers, validated on simulations and real data.

## Contribution

It presents a novel technique for identifying the QNM start time and parameters, improving analysis of gravitational wave signals from black hole mergers.

## Key findings

- QNM frequencies match theoretical values within 1% for simulated data.
- The method reveals a correlation between QNM start time and black hole spin.
- Parameters estimated from GW150914 are consistent with LIGO's results.

## Abstract

It is known that a quasinormal mode (QNM) of a remnant black hole dominates a ringdown gravitational wave (GW) in a binary black hole (BBH) merger. To study properties of the QNMs, it is important to determine the time when the QNMs appear in a GW signal as well as to calculate its frequency and amplitude. In this paper, we propose a new method of estimating the starting time of the QNM and calculating the QNM frequency and amplitude of BBH GWs. We apply it to simulated merger waveforms by numerical relativity and the observed data of GW150914. The results show that the obtained QNM frequencies and time evolutions of amplitudes are consistent with the theoretical values within 1% accuracy for pure waveforms free from detector noise. In addition, it is revealed that there is a correlation between the starting time of the QNM and the spin of the remnant black hole. In the analysis of GW150914, we show that the parameters of the remnant black hole estimated through our method are consistent with those given by LIGO and a reasonable starting time of the QNM is determined.