An upper observable black hole mass scale for tidal disruption events with thermal X-ray spectra

We comprehensively model the X-ray luminosity emergent from time dependent relativistic accretion discs, developing analytical models of the X-ray luminosity of thermal disc systems as a function of black hole mass $M$, disc mass $M_d$, and disc $\alpha$-parameter. The X-ray properties of these solutions will be directly relevant for understanding TDE observations. We demonstrate an extremely strong suppression of thermal X-ray luminosity from large mass black holes, $L_X\sim \exp (-m^{7\mathrm{/}6})$, where $m$ is a dimensionless mass, roughly the the black hole mass in unity of ${10}^6$M${}_{\odot }$. This strong suppression results in upper-observable black hole mass limits, which we demonstrate to be of order $M_{\mathrm{l}\mathrm{i}\mathrm{m}}\simeq 3\times {10}^7{M}_{\odot }$, above which thermal X-ray emission will not be observable. This upper observable black hole mass limit is a function of the remaining disc parameters, and the full dependence can be described analytically (eq. 82). We demonstrate that the current population of observed X-ray TDEs is indeed consistent with an upper black hole mass limit of order $M\sim {10}^7{M}_{\odot }$, consistent with our analysis.