The origin of thermal optical and UV emission from stellar tidal disruption flares (TDFs) remains an open question. We present Hubble Space Telescope far-UV (FUV) observations of eight optical/UV selected TDFs 5-10 years post-peak. Six sources are cleanly detected, showing point-like FUV emission from the centers of their host galaxies. We discover that the light curves of TDFs from low-mass black holes ($<10^{6.5} M_odot$) show significant late-time flattening. Conversely, FUV light curves from high-mass black hole TDFs are generally consistent with an extrapolation from the early-time light curve. The observed late-time emission cannot be explained by existing models for early-time TDF light curves (i.e. reprocessing or circularization shocks), but is instead consistent with a viscously spreading, unobscured accretion disk. These disk models can only reproduce the observed FUV luminosities, however, if they are assumed to be thermally and viscously stable, in contrast to the simplest predictions of alpha-disk theory. For one TDF in our sample, we measure an upper limit to the UV luminosity that is significantly lower than expectations from theoretical modeling and an extrapolation of the early-time light curve. This dearth of late-time emission could be due to a disk instability/state change absent in the rest of the sample. The disk models that explain the late-time UV detections solve the TDF missing energy problem by radiating a rest-mass energy of ~0.1 solar mass over a period of decades, primarily in extreme UV wavelengths.
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