Implications from Late-time X-Ray Detections of Optically Selected Tidal Disruption Events: State Changes, Unification, and Detection Rates

Using Chandra X-ray observations we detect three out of four optically-selected tidal disruption events (TDEs) 4-9 years after their discovery. The spectrum of PTF09axc is consistent with a power law with index of 2.5$\pm$0.1, whereas the spectrum of PTF09ge is consistent with a power law of index 3.9$\pm$0.5. The power law spectrum of PTF09axc may signal that TDEs transition from a soft state to a low-hard state many years after disruption. The mismatch in Eddington fractions of these sources (~5% for PTF09axc; ~0.2% for PTF09ge) could indicate that, as is the case for X-ray binaries, mass accretion rate is not the sole parameter responsible for TDE state changes. We propose that the time to peak luminosity for optical and X-ray emission may differ substantially in an individual TDE, with X-rays being produced or becoming observable later. This delay can serve to explain the differences in observed properties such as L_opt/L_X of optically and X-ray selected TDEs. We update predictions for the soon-to-be-launched eROSITA instrument, finding an eROSITA TDE detection rate of 3 yr$^{-1}$ to 990 yr$^{-1}$, a range that depends sensitively on (i) the distribution of black hole spins and (ii) the typical time delay between disruption and peak X-ray brightness. We further predict that X-ray selected TDE samples will have a strong bias towards prograde disks (up to 1-2 orders of magnitude if most supermassive black holes spin rapidly, and less so if most spin slowly). On the other hand, in flux-limited samples of optically-selected TDEs, there seems to exist a more modest (~factor of a few) bias for either retrograde or prograde disks, depending on the underlying optical emission mechanism and regime of loss cone repopulation. These observational biases can contribute to observed differences between optically and X-ray selected TDEs.