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

Abstract

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, $L_X \sim \exp(-m^{7/6})$, 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 $M_{\rm lim} \simeq 3 \times 10^7 M_\odot$, 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 $M \sim 10^7M_\odot$, consistent with our analysis.