Gravitational wave ringdown analysis using the $\mathcal{F}$-statistic

TL;DR

This paper introduces a novel time-domain method based on the $ ext{F}$-statistic for analyzing black hole ringdown signals, significantly improving computational efficiency and handling multiple modes effectively.

Contribution

The paper presents a new time-domain approach for ringdown analysis that maintains a constant parameter space and analytically maximizes over extrinsic parameters, enabling faster and more robust multi-mode analysis.

Findings

Parameter estimation is up to five orders of magnitude faster.

The method effectively handles multiple overtone modes.

It offers broad applicability for current and future gravitational wave detectors.

Abstract

After the final stage of the merger of two black holes, the ringdown signal takes an important role on providing information about the gravitational dynamics in strong field. We introduce a novel time-domain (TD) approach, predicated on the $\mathcal{F}$-statistic, for ringdown analysis. This method diverges from traditional TD techniques in that its parameter space remains constant irrespective of the number of modes incorporated. This feature is achieved by reconfiguring the likelihood and analytically maximizing over the extrinsic parameters that encompass the amplitudes and reference phases of all modes. Consequently, when performing the ringdown analysis under the assumption that the ringdown signal is detected by the Einstein Telescope, parameter estimation computation time is shortened by at most five orders of magnitude compared to the traditional TD method. We further establish that traditional TD methods become difficult when including multiple overtone modes due to close oscillation frequencies and damping times across different overtone modes. Encouragingly, this issue is effectively addressed by our new TD technique. The accessibility of this new TD method extends to a broad spectrum of research and offers flexibility for various topics within black hole spectroscopy applicable to both current and future gravitational wave detectors.