Quantifying Systematic Biases in Black Hole Spectroscopy

TL;DR

This paper introduces a linear-signal analysis method to efficiently quantify systematic biases in black hole ringdown spectroscopy, improving the understanding of uncertainties and aiding in the development of more accurate models.

Contribution

It demonstrates the effectiveness of linear-signal analysis for bias quantification in black hole spectroscopy, offering a computationally efficient alternative to traditional Bayesian methods.

Findings

Linear analysis predicts biases at intermediate SNRs (~50) for small unmodeled effects.

The Fisher information matrix and bias formula are validated against Bayesian sampling.

The approach helps explain high-SNR issues in quasinormal mode extraction.

Abstract

How long after the merger of two black holes can one rely on linear perturbation theory, and how many quasinormal modes are in the ringdown? Such questions suggest that black hole spectroscopy suffers from systematic uncertainties that potentially spoil ringdown analyses, both from high-accuracy simulations and in data from gravitational wave detectors. In this work, we demonstrate that linear-signal analysis is a powerful tool for quantifying biases, allowing for detailed explorations that are computationally too expensive for traditional Bayesian injection and recovery approaches. We quantify the validity of the Fisher information matrix and bias formula by comparing it to robust but slow Bayesian sampling. Working with flat noise in the time domain, statistical errors and systematic biases can mostly be detected analytically. Due to its efficiency, we provide detailed parameter space analyses for potentially unmodeled small contributions from overtones, quadratic modes, and tails. We find linear signal analysis well suited for predicting biases in simple ringdown models at intermediate signal-to-noise ratios (SNRs) of order 50 when unmodeled effects are small. It is also valuable in explaining ongoing issues in extracting quasinormal modes from high-precision simulations, as one can understand them as high-SNR signals. Therefore, this approach offers promising prospects for improving ringdown models by efficiently identifying and incorporating systematic uncertainties, ultimately enhancing the accuracy and robustness of black hole spectroscopy.