Disk-corona modeling for spectral index and luminosity correlation of tidal disruption events

We present a relativistic disk-corona model for a steady state advective accretion disk to explain the UV to X-ray spectral index \(\alpha_{\text{OX}}\) evolution of \textbf{four} tidal disruption event (TDE) sources XMMSL2J1446, XMMSL1J1404, XMMSL1J0740, \textbf{and AT2018fyk}. The viscous stress in our model depends on gas (\(P_g\)) and total (\(P_t\)) pressures as \(\tau_{r\phi} \propto P_g^{\mu} P_t^{1-\mu}\), where \(\mu\) is a constant. We compare various steady and time-dependent sub-Eddington TDE accretion models along with our disk-corona model to the observed \(\alpha_{\text{OX}}\) of TDE sources and find that the disk-corona model agrees with the observations better than the other models. We find that \(\mu\) is much smaller than unity for TDE sources XMMSL2J1446, XMMSL1J1404, and XMMSL1J0740. We also compare the relativistic model with a non-relativistic disk-corona model. The relativistic accretion dynamics reduce the spectral index relative to the non-relativistic accretion by increasing the energy transport to the corona. We estimate the mass accretion rate for all the sources and find that the observed luminosity follows a nearly linear relation with the mass accretion rate. The ratio of X-ray luminosity from the disk to the corona increases with the mass accretion rate. The observed \(\alpha_{\text{OX}}\) shows positive and negative correlations with luminosity. The disk-corona model explains the negative correlation seen in the TDE sources XMMSL1J0740, XMMSL2J1446, and XMMSL1J1404. However, TDE AT2018fyk shows a positive correlation at higher luminosity and shows a better fit when a simple spherical adiabatic outflow model is added to the relativistic disk-corona model. Even though the disk luminosity dominates at a higher mass accretion rate, we show that the accretion models without a corona are unable to explain the observations, and the presence of a corona is essential.