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

We present Chandra X-ray observations of four optically selected tidal disruption events (TDEs) obtained 4-9 yr after discovery. Three sources were detected with luminosities between 9 x 10(40) and 3 x 10(42) erg s(-1). The spectrum of PTF09axc is consistent with a power law of index 2.5 +/- 0.1, whereas the spectrum of PTF09ge is very soft. The power-law spectrum of PTF09axc and prior literature findings provide evidence that TDEs transition from an early-time soft state to a late-time hard state many years after disruption. We propose that the time to peak luminosity for optical and X-ray emission may differ substantially in TDEs, with X-rays being produced or becoming observable later. This delay helps explain the differences in observed properties such as L-opt/L-X of optically and X-ray-selected TDEs. We update TDE rate predictions for the eROSITA instrument: it ranges from 3 to 990 yr(-1), depending sensitively on the distribution of black hole spins and the time delay between disruption and peak X-ray brightness. We further predict an asymmetry in the number of retrograde and prograde disks in samples of optically and X-ray-selected TDEs. The details of the observational biases can contribute to observed differences between optically and X-ray-selected TDEs (with optically selected TDEs being fainter in X-rays for retrograde TDE disks).