We carried out the first multi-wavelength (optical/UV and X-ray) photometric reverberation mapping of a tidal disruption flare (TDF) ASASSN-14li. We find that its X-ray variations are correlated with and lag the optical/UV fluctuations by 32$pm$4 days. Based on the direction and the magnitude of the X-ray time lag, we rule out X-ray reprocessing and direct emission from a standard circular thin disk as the dominant source of its optical/UV emission. The lag magnitude also rules out an AGN disk-driven instability as the origin of ASASSN-14li and thus strongly supports the tidal disruption picture for this event and similar objects. We suggest that the majority of the optical/UV emission likely originates from debris stream self-interactions. Perturbations at the self-interaction sites produce optical/UV variability and travel down to the black hole where they modulate the X-rays. The time lag between the optical/UV and the X-rays variations thus correspond to the time taken by these fluctuations to travel from the self-interaction site to close to the black hole. We further discuss these time lags within the context of the three variants of the self-interaction model. High-cadence monitoring observations of future TDFs will be sensitive enough to detect these echoes and would allow us to establish the origin of optical/UV emission in TDFs in general.
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