Constraining the Deviation of Kerr Metric via Bumpy Parameterization and Particle Swarm Optimization in Extreme Mass-Ratio Inspirals

TL;DR

This paper enhances the analysis of deviations from Kerr black holes in EMRI gravitational wave signals by integrating particle swarm optimization with matched filtering, revealing degeneracies that impact parameter estimation and proposing methods to mitigate systematic errors.

Contribution

It introduces a novel combination of PSO and matched filtering to better explore parameter degeneracies in EMRI GW data analysis, improving upon previous Fisher matrix approaches.

Findings

Identified significant degeneracies in likelihood peaks due to bumpy parameters.

Demonstrated systematic errors in parameter estimation caused by degeneracies.

Showed that ensemble information can mitigate these systematic errors.

Abstract

Measurement of deviations in the Kerr metric using gravitational wave (GW) observations will provide a clear signal of new Physics. Previous studies have developed multiple parameterizations (e.g. ``bumpy" spacetime) to characterize such deviations in extreme mass ratio inspirals (EMRI) and employed analyses based on the Fisher information matrix (FIM) formalism to quantify the constraining power of space-borne GW detectors like LISA and Tianqin, e.g., achieving a constraint sensitivity levels of $10^{-4} \sim 10^{-2}$ on the dimensionless bumpy parameter $\delta \tilde{Q}$ under varying source configurations in analytical kluge waveform for LISA. In this paper, we advance prior analyses by integrating particle swarm optimization (PSO) with matched filtering under a restricted parameter search range to enforce a high probability of convergence for PSO. Our results reveal a significant number of degenerate peaks in the likelihood function over the signal parameter space with values that exceed the injected one. This extreme level of degeneracy arises from the involvement of the additional bumpy parameter $\delta \tilde{Q}$ in the parameter space and introduces systematic errors in parameter estimation. We show that these systematic errors can be mitigated using information contained in the ensemble of degenerate peaks, thereby restoring the reliability of astrophysical inferences about EMRI systems from GW observations. This study highlights the critical importance of accounting for such degeneracies, which are absent in FIM-based analyses, and points out future directions for improving EMRI data analysis.