Analyzing black-hole ringdowns with orthonormal modes

TL;DR

This paper introduces an efficient Bayesian method using Gram-Schmidt orthonormalization to analyze multiple quasinormal modes in black hole ringdowns, improving parameter estimation and computational efficiency for testing general relativity.

Contribution

It presents a novel Bayesian analysis technique that reduces mode correlations and simplifies amplitude marginalization in black hole spectroscopy.

Findings

Reduces parameter correlations between modes

Enables analytic marginalization over mode amplitudes

Validated with both synthetic and numerical waveforms

Abstract

The ringdown signal following a black hole (BH) merger can be modeled as a superposition of BH quasinormal modes (QNMs), offering a clean setup for testing gravitational theories. In particular, detecting multiple QNMs enables consistency checks of their frequencies and damping times, serving as a test of general relativity -- a technique known as black hole spectroscopy. However, incorporating additional QNMs introduces challenges such as increased parameter correlations and higher computational costs in data analysis. To address this, we propose an efficient Bayesian analysis method that applies the Gram-Schmidt algorithm to the QNMs. This reduces the correlation between the modes and enables analytic marginalization over the mode amplitudes. We validate our approach using damped sinusoids and numerical waveforms from the Simulating eXtreme Spacetimes catalog.