Testing general relativity with amplitudes of subdominant gravitational-wave modes

TL;DR

This paper introduces an improved amplitude test for general relativity using gravitational-wave signals, focusing on higher-order modes, and demonstrates its robustness and sensitivity with numerical simulations and real data.

Contribution

The paper develops a refined subdominant-mode amplitude test for GR, systematically benchmarking its performance and robustness against various physical and modeling effects.

Findings

Reliable for aligned-spin and mildly precessing systems

Detects strongest constraints on the (4,4) mode deviation

Responds to phase perturbations, indicating potential false positives

Abstract

We present an improved subdominant-mode amplitude (SMA) test of general relativity (GR), which probes amplitude-level deviations in the higher-order modes of gravitational-wave (GW) signals from binary black hole mergers while keeping the dominant quadrupole mode fixed. Using a comprehensive parameter-estimation campaign, we benchmark the test against Gaussian noise fluctuations, waveform modeling systematics, and physical effects such as spin precession and orbital eccentricity. When applied to numerical-relativity simulations, the SMA test performs reliably for aligned-spin and mildly precessing systems but exhibits measurable biases for strongly precessing or eccentric binaries. Although designed to detect amplitude deviations, the test also responds coherently to phase perturbations, yielding apparent GR violations when applied to phase-modified waveforms. Applied to recent GW detections, we report the strongest constraint on the hexadecapolar (4,4) mode amplitude deviation, $\delta A_{44} = -0.30^{+1.16}_{-3.45}$, consistent with GR. With these results, this work establishes the SMA test as a robust and broadly sensitive framework for probing strong-field gravity and demonstrates a systematic approach for assessing the robustness of GW tests of GR.