Strong lensing of tidal disruption events: Detection rates in imaging surveys

Tidal disruption events (TDEs) are multi-messenger transients in which a star is tidally destroyed by a supermassive black hole at the center of galaxies. The Rubin Observatory Legacy Survey of Space and Time (LSST) is anticipated to annually detect hundreds to thousands of TDEs, such that the first gravitationally lensed TDE may be observed in the coming years. Using Monte-Carlo simulations, we quantify the rate of both unlensed and lensed TDEs as a function of limiting magnitudes in four different optical bands ($u$, $g$, $r$, and $i$) for a range of TDE temperatures that match observations. Dependent on the temperature and luminosity model, we find that $g$ and $r$ bands are the most promising bands with unlensed TDE detections that can be as high as ${\sim}10^{4}$ annually. By populating a cosmic volume with realistic distributions of TDEs and galaxies that can act as gravitational lenses, we estimate that a few lensed TDEs (depending on the TDE luminosity model) can be detected annually in $g$ or $r$ bands in the LSST survey, with TDE redshifts in the range of ${\sim}0.5$ to ${\sim}2$. The ratio of lensed to unlensed detections indicates that we may detect ${\sim}1$ lensed event for every $10^{4}$ unlensed events, which is independent of the luminosity model. The number of lensed TDEs decreases as a function of the image separations and time delays, and most of the lensed TDE systems are expected to have image separations below ${\sim}3"$ and time delays within ${\sim}30$ days. At fainter limiting magnitudes, the $i$ band becomes notably more successful. These results suggest that strongly lensed TDEs are likely to be observed within the coming years and such detections will enable us to study the demographics of black holes at higher redshifts through the lensing magnifications.