Polarization Analysis of Ringdown Signals

TL;DR

This paper investigates the polarization characteristics of black hole merger ringdown signals, demonstrating how polarization measurements can infer source inclination and highlighting limitations for precessing systems.

Contribution

It introduces a constrained polarization model for ringdown signals, enabling inclination inference from polarization data and analyzing its limitations for precessing black hole mergers.

Findings

Polarization measurements can infer source inclination from ringdown signals.

The constrained model accurately fits non-precessing systems like GW150914.

The model shows biases when applied to precessing systems like GW190521.

Abstract

Merging binary black holes exhibit a ringdown phase in which they primarily emit gravitational waves in the shape of damped sinusoids corresponding to quasi-normal modes of the Kerr remnant. In general, each mode carries four degrees of freedom encoding amplitude and phase information. When the modes are excited with equatorial reflection symmetry, as is the case for black hole mergers with spins (anti)aligned to the orbital angular momentum, the symmetry constrains two degrees of freedom. As a result, the relationship between polarization amplitudes and phases in each mode is fixed by the viewing (inclination) angle to the equatorial plane. We use such a constrained model to fit the ringdown signals of both non-precessing and precessing systems such as GW150914 and GW190521, respectively. We show that we can measure the degree of circular polarization and handedness of ringdown signals like those of GW150914, even if only the two LIGO detectors are available; such a polarization measurement can be translated into an inferred source inclination assuming the reflection symmetry above, again using the ringdown signal alone. On the other hand, the constrained polarization model is insufficient to capture the polarization structure of signals from precessing systems, leading to biases in the inferred mode frequencies and amplitudes. We explore the magnitude of this effect by fitting GW190521-like injections with the restricted model, finding weaker predictive accuracy relative to the arbitrary-polarization model and potentially significant systematic biases. As our detectors continue to improve, using the correct polarization model is increasingly important to avoid biased ringdown measurements.