Detectability of Strongly Gravitationally Lensed Tidal Disruption Events

More than 100 tidal disruption events (TDEs) have been detected at multi-bands, which can be viewed as extreme laboratories to investigate the accretion physics and gravity in the immediate vicinity of massive black holes. Future transient surveys are expected to detect several tens of thousands of TDEs, among which a small fraction may be strongly gravitationally lensed by intervening galaxies. In this paper, we statistically etsimate the detection rate of lensed TDEs, with dependence on the limiting magnitude of the transient all-sky surveys searching for them. We find that the requisite limiting magnitude for an all-sky transient survey to observe at least $1$ yr$^{-1}$ is $\gtrsim 21.3$, $21.2$, and $21.5$ mag in the $u$, $g$, and $z$ bands, respectively. If the limiting magnitude of the all-sky survey can reach $\sim 25-26$ mag in the $u$, $g$, and $z$ bands, the detection rate can be upto about several tens to hundreds per year. The discovery and identification of the first image of the lensed TDE can be taken as an early warning of the second and other subsequent images, which may enable detailed monitoring of the pre-peak photometry and spectroscopy evolution of the TDE. The additional early-stage information may help to constrain the dynamical and radiation processes involving in the TDEs.