# Testing the no-hair theorem with GW150914

## TL;DR

This paper analyzes GW150914 gravitational-wave data to detect black hole ringdown modes, confirming the no-hair theorem with high confidence and measuring the black hole's properties solely from postinspiral data.

## Contribution

It provides the first evidence of overtones in the black hole ringdown, enabling measurement of black hole parameters independently from the full waveform.

## Key findings

- Detection of fundamental quasinormal mode and overtones with 3.6σ confidence.
- Measurement of black hole mass and spin from postinspiral data consistent with full waveform estimates.
- Supports the no-hair theorem at approximately 10% confidence level.

## Abstract

We analyze gravitational-wave data from the first LIGO detection of a binary black-hole merger (GW150914) in search of the ringdown of the remnant black hole. Using observations beginning at the peak of the signal, we find evidence of the fundamental quasinormal mode and at least one overtone, both associated with the dominant angular mode ($\ell=m=2$), with $3.6\sigma$ confidence. A ringdown model including overtones allows us to measure the final mass and spin magnitude of the remnant exclusively from postinspiral data, obtaining an estimate in agreement with the values inferred from the full signal. The mass and spin values we measure from the ringdown agree with those obtained using solely the fundamental mode at a later time, but have smaller uncertainties. Agreement between the postinspiral measurements of mass and spin and those using the full waveform supports the hypothesis that the GW150914 merger produced a Kerr black hole, as predicted by general relativity, and provides a test of the no-hair theorem at the ${\sim}10\%$ level. An independent measurement of the frequency of the first overtone yields agreement with the no-hair hypothesis at the ${\sim 20}\%$ level. As the detector sensitivity improves and the detected population of black hole mergers grows, we can expect that using overtones will provide even stronger tests.