Dimensionally Reduced Waveforms for Spin-Induced Quadrupole Searches

TL;DR

This paper introduces simplified, highly accurate gravitational waveforms for binary systems with large spin-induced quadrupoles, enabling more effective searches for exotic compact objects in gravitational wave data.

Contribution

The authors develop two dimensionally-reduced waveform models from six-dimensional post-Newtonian waveforms, tailored for systems with large quadrupolar deviations, improving computational efficiency and search effectiveness.

Findings

Over 80% of injections achieved effectualness > 0.999

Waveforms effectively detect systems with spins |χ_i| ≤ 0.6 and quadrupoles κ_i ≤ 10^3

Provided analytic estimates for frequency cutoffs related to minimum binding energy

Abstract

We present highly accurate, dimensionally-reduced gravitational waveforms for binary inspirals whose components have large spin-induced quadrupole moments. The spin-induced quadrupole of a body first appears in the phase of a waveform at the early inspiral stage of the binary coalescence, making it a relatively clean probe of the internal structure of the body. However, for objects with large quadrupolar deviations from Kerr, searches using binary black hole (BBH) models would be ineffective. In order to perform a computationally-feasible search, we present two dimensionally-reduced models which are derived from the original six-dimensional post-Newtonian waveform for such systems. Our dimensional reduction method is guided by power counting in the post-Newtonian expansion, suitable reparameterizations of the source physics, and truncating terms in the phase that are small in most physically well-motivated regions of parameter space. In addition, we note that large quadrupolar deviations cause the frequency at which a binary system reaches its minimum binding energy to be reduced substantially. This minimum signals the end of the inspiral regime and provides a natural cutoff for the PN waveform. We provide accurate analytic estimates for these frequency cutoffs. Finally, we perform injection studies to test the effectualness of the dimensionally reduced waveforms. We find that over $80\%$ of the injections have an effectualness of $\varepsilon > 0.999$, significantly higher than is typically required for standard BBH banks, for systems with component spins of $|\chi_i| \lesssim 0.6$ and dimensionless quadrupole of $\kappa_i \lesssim 10^3$. Importantly, these waveforms represent an essential first step towards enabling an effective search for astrophysical objects with large quadrupoles.