  We perform a comprehensive analysis of a population of 19 X-ray bright tidal
disruption events (TDEs), fitting their X-ray spectra with a new, physically
self consistent, relativistic accretion disc model. Not all of the TDEs inhabit
regions of parameter space where the model is valid, or have sufficient data
for a detailed analysis, and physically interpretable parameters for a
sub-sample of 11 TDEs are determined. These sources have thermal (power-law
free) X-ray spectra. The radial sizes measured from these spectra lie at values
consistent with the inner-most stable circular orbit of black holes with masses
given by the $M_{\rm BH}-\sigma$ relationship, and can be used as an
independent measurement of $M_{\rm BH}$. The bolometric disc luminosity can
also be inferred from X-ray data. All of the TDEs have luminosities which are
sub-Eddington ($L_{\rm bol, disc} \lesssim L_{\rm edd}$), and larger than the
typical hard-state transitional luminosity of X-ray binary discs ($L_{\rm bol,
disc} \gtrsim 0.01 L_{\rm edd}$). The {\it peak} bolometric luminosity is found
to be linearly correlated with the $M_{\rm BH}-\sigma$ mass. The TDE
X-ray-to-bolometric correction can reach values up to $\sim 100$, and grows
exponentially at late times, resolving the missing energy problem. We show that
the peak disc luminosities of some TDEs are smaller than their observed optical
luminosities, implying that not all of the early time optical emission can be
sourced from reprocessed disc emission. Our results are supportive of the
hypothesis that thermal X-ray bright TDEs are in accretion states analogous to
the ``soft'' accretion state of X-ray binaries, and that black hole accretion
processes are scale (mass) invariant.
