We present numerical waveforms of gravitational-wave echoes from spinning exotic compact objects (ECOs) that result from binary black hole coalescence. We obtain these echoes by solving the Teukolsky equation for the $psi_4$ associated with gravitati
onal waves that propagate toward the horizon of a Kerr spacetime, and process the subsequent reflections of the horizon-going wave by the surface of the ECO, which lies right above the Kerr horizon. The trajectories of the infalling objects are modified from Kerr geodesics, such that the gravitational waves propagating toward future null infinity match those from merging black holes with comparable masses. In this way, the corresponding echoes approximate to those from comparable-mass mergers. For boundary conditions at the ECO surface, we adopt recent work using the membrane paradigm, which relates $psi_0$ associated with the horizon-going wave and $psi_4$ of the wave that leaves the ECO surface. We obtain $psi_0$ of the horizon-going wave from $psi_4$ using the Teukolsky-Starobinsky relation. The echoes we obtain turn out to be significantly weaker than those from previous studies that generate echo waveforms by modeling the ringdown part of binary black hole coalescence waveforms as originating from the past horizon.
We analyze extensive spectroscopic and photometric data of the hypervariable quasar SDSS J131424+530527 (RMID 017) at z=0.456, an optical changing look quasar from the Sloan Digital Sky Survey Reverberation Mapping project that increased in optical l
uminosity by a factor of 10 between 2014 and 2017. The observed broad emission lines all respond in luminosity and width to the changing optical continuum, as expected for photoionization in a stratified, virialized broad emission line region. The luminosity changes therefore result from intrinsic changes in accretion power rather than variable obscuration. The variability is continuous and apparently stochastic, disfavoring an origin as a discrete event such as a tidal disruption flare or microlensing event. It is coordinated on day timescales with blue leading red, consistent with reprocessing powering the entire optical SED. We show that this process cannot work in a standard thin disk geometry on energetic grounds, and would instead require a large covering factor reprocessor. Disk instability models could potentially also explain the data, provided that the instability sets in near the inner radius of a geometrically thick accretion disk.
