A novel ringdown amplitude-phase consistency test

TL;DR

This paper introduces a new null test based on amplitude and phase consistency of ringdown modes in black hole mergers, providing a novel way to test General Relativity and explore alternative theories or objects.

Contribution

The paper develops the amplitude-phase consistency test for ringdown signals, offering a new method to verify GR predictions and analyze gravitational wave data beyond traditional spectroscopy.

Findings

GW190521 is consistent with the test despite large measurement errors.

The test can accommodate multiple loud ringdown detections in the future.

It complements standard black-hole spectroscopy for testing gravity.

Abstract

The ringdown signal emitted during a binary black hole coalescence can be modeled as a linear superposition of the characteristic damped modes of the remnant black hole that get excited during the merger phase. While checking the consistency of the measured frequencies and damping times against the Kerr BH spectrum predicted by General Relativity (GR) is a cornerstone of strong-field tests of gravity, the consistency of measured excitation amplitudes and phases have been largely left unexplored. For a nonprecessing, quasi-circular binary black hole merger, we find that GR predicts a narrow region in the space of mode amplitude ratio and phase difference, independently of the spin of the binary components. % Using this unexpected result, we develop a new null test of strong-field gravity which demands that the measured amplitudes and phases of different ringdown modes should lie within this narrow region predicted by GR. We call this the \emph{amplitude-phase consistency test} and introduce a procedure for performing it using information from the ringdown signal. Lastly, we apply this test to the GW190521 event, using the multimodal ringdown parameters inferred by Capano et al. (2021) \cite{Capano:2021etf}. While ringdown measurements errors for this event are large, we show that GW190521 is consistent with the amplitude-phase consistency test. Our test is particularly well suited for accommodating multiple loud ringdown detections as those expected in the near future, and can be used complementarily to standard black-hole spectroscopy as a proxy for modified gravity, compact objects other than black holes, binary precession and eccentricity.