Bolometric correction factor and radiative efficiency for the super-Eddington accretion flow in tidal disruption events

The estimate of the bolometric luminosity and the radiative efficiency are two key aspects for understanding the properties of the accretion flow around a supermassive black hole (BH). In this paper, we focus on the estimate of the bolometric luminosity and the radiative efficiency of the early super-Eddington accretion flow in tidal disruption events (TDEs). Specifically, we first perform radiation hydrodynamic simulations of super-Eddington accretion flow in TDE environment, and then calculate the corresponding emergent spectra with the method of post processing for the simulation data. Based on the emergent spectra, we calculate the isotropic-equivalent X-ray bolometric correction factor $k_\mathrm{bol}$ and the radiative efficiency $\eta$ of the super-Eddington accretion flow. We find that both $k_\mathrm{bol}$ and $\eta$ are BH mass and viewing-angle dependent. $k_\mathrm{bol}$ is in the range of about a few tens to a few thousands, and $\eta$ is in the range of $\sim 10^{-3}-10^{-1}$ for BH mass in the range of $10^{6-7}M_\odot$ and the viewing angle in the range of $0^{\rm o}-90^{\rm o}$. Finally, we apply the derived $k_\mathrm{bol}$ and $\eta$ to some specific TDEs to estimate the accreted mass during an event, which can significantly alleviate the so-called missing energy problem in TDEs.