Reduced Basis representations of multi-mode black hole ringdown gravitational waves

TL;DR

This paper develops a highly efficient Reduced Basis method for representing multi-mode black hole ringdown gravitational waves, enabling compact, accurate, and computationally feasible template banks for detection and analysis.

Contribution

The authors introduce a novel RB approach that achieves exponential convergence, significantly reducing the number of templates needed for multi-mode ringdown searches compared to traditional methods.

Findings

RB waveforms can represent any QNM with accuracy less than 10^{-13}

Fewer RB waveforms are needed for two-mode ringdowns than metric-based templates

RB method scales linearly with the number of modes, unlike exponential growth in standard approaches

Abstract

We construct compact and high accuracy Reduced Basis (RB) representations of single and multiple quasinormal modes (QNMs). The RB method determines a hierarchical and relatively small set of the most relevant waveforms. We find that the exponential convergence of the method allows for a dramatic compression of template banks used for ringdown searches. Compressing a catalog with a minimal match $\MMm=0.99$, we find that the selected RB waveforms are able to represent {\em any} QNM, including those not in the original bank, with extremely high accuracy, typically less than $10^{-13}$. We then extend our studies to two-mode QNMs. Inclusion of a second mode is expected to help with detection, and might make it possible to infer details of the progenitor of the final black hole. We find that the number of RB waveforms needed to represent any two-mode ringdown waveform with the above high accuracy is {\em smaller} than the number of metric-based, one-mode templates with $\MMm=0.99$. For unconstrained two-modes, which would allow for consistency tests of General Relativity, our high accuracy RB has around $10^4$ {\em fewer} waveforms than the number of metric-based templates for $\MMm=0.99$. The number of RB elements grows only linearly with the number of multipole modes versus exponentially with the standard approach, resulting in very compact representations even for many multiple modes. The results of this paper open the possibility of searches of multi-mode ringdown gravitational waves.