An Efficient Signal to Noise Approximation for Eccentric Inspiraling Binaries

TL;DR

This paper presents a computationally efficient approximation method for estimating the signal-to-noise ratio of eccentric inspiraling binaries, aiding in population analysis and parameter estimation for gravitational wave detectors like LISA and DECIGO.

Contribution

The authors develop a new approximation technique that accurately estimates the SNR for eccentric inspirals across a broad frequency range, reducing computational costs compared to traditional methods.

Findings

Approximation estimates SNR within a factor of two over most frequencies.

Method remains accurate despite noise power-law dependence.

Useful for discriminating between different black hole merger populations.

Abstract

Eccentricity has emerged as a potentially useful tool for helping to identify the origin of black hole mergers. However, owing to the large number of harmonics required to compute the amplitude of an eccentric signal, eccentric templates can be computationally very expensive, making statistical analyses to distinguish distributions from different formation channels very challenging. In this paper, we outline a method for estimating the signal-to-noise ratio for inspiraling binaries at lower frequencies such as those proposed for LISA and DECIGO. Our approximation can be useful more generally for any quasi-periodic sources. We argue that surprisingly, the signal-to-noise ratio evaluated at or near the peak frequency (of the power) is well approximated by using a constant noise curve, even if in reality the noise strain has power law dependence. We furthermore improve this initial estimate over our previous calculation to allow for frequency-dependence in the noise to expand the range of eccentricity and frequency over which our approximation applies. We show how to apply this method to get an answer accurate to within a factor of two over almost the entire projected observable frequency range. We emphasize this method is not a replacement for detailed signal processing. The utility lies chiefly in identifying theoretically useful discriminators among different populations and providing fairly accurate estimates for how well they should work. This approximation can furthermore be useful for narrowing down parameter ranges in a computationally economical way when events are observed. We furthermore show a distinctive way to identify events with extremely high eccentricity where the signal is enhanced relative to na\"ive expectations on the high frequency end.