Statistical validation of the detection of a multimode quasi-normal spectrum from a perturbed black hole

When two black holes merge, the late stage of gravitational wave emission is a superposition of exponentially damped sinusoids. According to the black hole no-hair theorem, this ringdown spectrum depends only on the mass and angular momentum of the final black hole. An observation of more than one ringdown mode can test this fundamental prediction of general relativity. Here we provide strong observational evidence for a multimode black hole ringdown spectrum using the gravitational wave event GW190521, with a Bayes factor of 56 preferring two fundamental modes over one. The dominant mode is the l=m=2 harmonic, and the sub-dominant mode corresponds to the l=m=3 harmonic. We present an extensive study of simulated signal injections that confidently supports the statistical evidence. Two methods are employed to search for quasi-normal modes in the data, using signal models that are agnostic or assuming the Kerr solution for the black hole. Analysing the statistical properties of these methods in detail for signals similar to GW190521, we find they perform robustly and effectively in distinguishing the presence of multiple quasi-normal modes from noise. We also find that simulated GW190521-like signals with a (3, 3, 0) mode present yield tight  constraints on deviations of that mode from Kerr, whereas constraints on the (2, 2, 1) overtone of the dominant mode yield wide constraints that are not consistent with Kerr. These results on simulated signals are similar to what we find for GW190521. Applying our methods to GW190521, we estimate the redshifted mass and dimensionless spin of the final black hole as ~328 solar masses and ~0.86, respectively. The detection of the two modes disfavours an equal-mass binary; the mass ratio is constrained to 0.4 (+0.2−0.3). We find that the final black hole is consistent with the no-hair theorem and constrain the fractional deviation from general relativity of the sub-dominant mode’s frequency to be −0.008 (+0.08−0.09).