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.