Angular emission patterns of remnant black holes

TL;DR

This paper investigates the angular emission patterns of remnant black holes during ringdown, proposing a comprehensive method to test General Relativity by analyzing spatial distributions and mode excitations in gravitational wave signals.

Contribution

It introduces a global fitting procedure for temporal and spatial dependences of ringdown emissions, demonstrating the superiority of spheroidal harmonics and exploring mode excitation correlations.

Findings

Spheroidal harmonics better represent ringdown angular patterns.

Differences in emission patterns are distinguishable in numerical relativity waveforms.

Retrograde mode excitation is dominant when remnant spin is anti-aligned with orbital angular momentum.

Abstract

The gravitational radiation from the ringdown of a binary black hole merger is described by the solution of the Teukolsky equation, which predicts both the temporal dependence and the angular distribution of the emission. Many studies have explored the temporal feature of the ringdown wave through black hole spectroscopy. In this work, we further study the spatial distribution, by introducing a global fitting procedure over both temporal and spatial dependences, to propose a more complete test of General Relativity. We show that spin-weighted spheroidal harmonics are the better representation of the ringdown angular emission patterns compared to spin-weighted spherical harmonics. The differences are distinguishable in numerical relativity waveforms. We also study the correlation between progenitor binary properties and the excitation of quasinormal modes, including higher-order angular modes, overtones, prograde and retrograde modes. Specifically, we show that the excitation of retrograde modes is dominant when the remnant spin is anti-aligned with the binary orbital angular momentum. This study seeks to provide an analytical strategy and inspire the future development of ringdown test using real gravitational wave events.