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Abstract

One of the major aims of gravitational wave astronomy is to observationally
test the Kerr nature of black holes. The strongest such test, with minimal
additional assumptions, is provided by observations of multiple ringdown modes,
also known as black hole spectroscopy. For the gravitational wave merger event
GW190521, we have previously claimed the detection of two ringdown modes
emitted by the remnant black hole. In this paper we provide further evidence
for the detection of multiple ringdown modes from this event. We analyze the
recovery of simulated gravitational wave signals designed to replicate the
ringdown properties of GW190521. We quantify how often our detection statistic
reports strong evidence for a sub-dominant $(\ell,m,n)=(3,3,0)$ ringdown mode,
even when no such mode is present in the simulated signal. We find this only
occurs with a probability $\sim 0.02$, which is consistent with a Bayes factor
of $56 \pm 1$ (1$\sigma$ uncertainty) found for GW190521. We also quantify our
agnostic analysis of GW190521, in which no relationship is assumed between
ringdown modes, and find that less than 1 in 500 simulated signals without a
$(3,3,0)$ mode yield a result as significant as GW190521. Conversely, we verify
that when simulated signals do have an observable $(3,3,0)$ mode they
consistently yield a strong evidence and significant agnostic results. 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. Our results strongly support our previous conclusion that
the gravitational wave signal from GW190521 contains an observable sub-dominant
$(\ell,m,n)=(3,3,0)$ mode.