Measuring gravitational-wave higher-order modes

TL;DR

This paper analyzes the detectability of higher-order gravitational wave modes from binary black hole mergers, highlighting their significance, how to measure them, and their limited observability in current detectors.

Contribution

It introduces a method to decompose higher modes and proposes a simple SNR threshold for their observation, providing new insights into their detectability.

Findings

The $ ext{l}=3$, $m=3$ mode is most significant across the detector's sensitive band.

Higher modes are mainly observable in systems with unequal masses and edge-on orientations.

A simple SNR threshold can effectively determine the observability of higher harmonics.

Abstract

We investigate the observability of higher harmonics in gravitational wave signals emitted during the coalescence of binary black holes. We decompose each mode into an overall amplitude, dependent upon the masses and spins of the system, and an orientation-dependent term, dependent upon the inclination and polarization of the source. Using this decomposition, we investigate the significance of higher modes over the parameter space and show that the $\ell = 3$, $m = 3$ mode is most significant across much of the sensitive band of ground-based interferometric detectors, with the $\ell = 4$, $m = 4$ having a significant contribution at high masses. We introduce the higher mode signal-to-noise ratio (SNR), and show that a simple threshold on this SNR can be used as a criterion for observation of higher harmonics. Finally, we investigate observability in a population of binaries and observe that higher harmonics will only be observable in a few percent of binaries, typically those with unequal masses and viewed close to edge-on.