Boltzmann Meets Lorentz: A Surrogate Model for Black Hole Echoes
  The existence of black hole horizons has not been strictly proven
observationally, and indeed it may not be possible to do so. However,
alternatives may be established by the observation of gravitational wave echoes
that probe possible near-horizon structure. These echoes are proposed to be
generated in exotic compact objects that are horizonless and feature a
partially reflecting "wall" inside their light rings, creating a cavity in
which gravitational perturbations may echo, while leaking out through the
angular momentum barrier with each pass. The characteristic signature of echoes
is a comb of nearly evenly spaced spectral resonances. While approximately
true, deviations from this simple picture can lead to severe observational
signal losses. In this paper, we explore such subtleties with the latest
results for echo sourcing and geometry. A physically motivated echo model is
then developed as a sum over Lorentzian spectral lines, parametrized by
functions of the horizon frame frequency and the size of the cavity. Our final
spectrum is a function of only the mass and spin of the black hole, as well as
the UV scale of the near-horizon physics. We then apply this model in a search
for echoes in the gravitational wave event with the loudest ringdown signal in
LIGO/Virgo, i.e. GW190521. We interpret our findings as a measurement of the
fractional energy in post-merger echoes equal to $E_{echoes} / E_{GR} = 8.9 \pm
4.5\%$, where the uncertainty range represents the 90% credible region. The
robustness of this result is tested against noise backgrounds and simulated
injections, and we find that a signal persists through modifications to the
model and changes in the data search.
