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We present a systematic analysis of the X-ray emission of a sample of 17optically selected, X-ray-detected tidal disruption events (TDEs) discoveredbetween 2014 and 2021. The X-ray light curves show a diverse range of temporalbehaviors, with most sources not following the expected power-law decline. TheX-ray spectra are mostly extremely soft and consistent with thermal emissionfrom the inner region of an accretion disk that cools as the accretion ratedecreases. Three sources show the formation of a hard X-ray corona around 200days after the UV/optical peak. The shape of the spectral energy distribution,traced by the ratio ($L_{\rm BB}/L_{\rm X}$) between the UV/optical and X-rayluminosities, shows a wide range $L_{\rm BB}/L_{\rm X} \in (0.5, 3000)$ atearly-times, and converges to disk-like values $L_{\rm BB}/L_{\rm X} \in (0.5,10)$ at late-times. The evolution of the derived physical parameters favors adecrease in the optical depth of a reprocessing layer instead of delayed diskformation to explain the late-time X-ray brightening found in several sources.We estimate the fraction of optically discovered TDEs with $L_{\rm X}\geq10^{42}$ erg s$^{-1}$ to be at least $40\%$, and find that the X-ray loudnessis independent of black hole mass. We combine our sample with those from X-raysurveys to construct an X-ray luminosity function, best fitted by a brokenpower-law with a brake at $\sim 10^{44}$ erg s$^{-1}$. We show that there is nodichotomy between optically and X-ray selected TDEs; instead, there is acontinuum of early time $L_{\rm BB}/L_{\rm X}$, at least as wide as $L_{\rmBB}/L_{\rm X} \in (0.1, 3000)$, with optical/X-ray surveys selectingpreferentially, but not exclusively, from the higher/lower end of thedistribution. Our findings are consistent with an orientation-dependent andtime-evolving reprocessing layer, and support viewing-angle unification models.

A systematic analysis of the X-ray emission in optically selected tidal  disruption events: observational evidence for the unification of the  optically and X-ray selected populations