Relativistic X-ray reverberation from super-Eddington accretion flow

X-ray reverberation is a powerful technique which maps out the structure of the inner regions of accretion disks around black holes using the echoes of the coronal emission reflected by the disk. While the theory of X-ray reverberation has been developed almost exclusively for standard thin disks, recently reverberation lags have been observed from likely super-Eddington accretion sources such as the jetted tidal disruption event Swift J1644+57. In this paper, we extend X-ray reverberation studies into the super-Eddington accretion regime, focusing on investigating the lags in the Fe K{\alpha} line region. We find that the coronal photons are mostly reflected by the fast and optically thick winds launched from super-Eddington accretion flow, and this funnel-like reflection geometry produces lag-frequency and lag-energy spectra with unique characteristics. The lag-frequency spectra exhibits a step-function like decline near the first zero-crossing point. As a result, the shape of the lag-energy spectra remains almost independent of the choice of frequency bands and linearly scales with the black hole mass for a large range of parameter spaces. Not only can these morphological differences be used to distinguish super-Eddington accretion systems from sub-Eddington systems, they are also key for constraining the reflection geometry and extracting parameters from the observed lags. When explaining the X-ray reverberation lags of Swift J1644+57, we find that the super-Eddington disk geometry is preferred over the thin disk, for which we obtain a black hole mass of 5-6 million solar masses and a coronal height around 10 gravitational radii by fitting the lag spectra to our modeling.