Rates of strongly lensed tidal disruption events

A comprehensive investigation of black hole, luminosity, and temperature dependencies

¹ Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Straße 1, 85748 Garching, Germany
² Max Planck Institute for Astrophysics, Karl-Schwarzschild Str. 1, 85748 Garching, Germany
³ JILA, University of Colorado and National Institute of Standards and Technology, 440 UCB, Boulder, 80308 CO, USA
⁴ Department of Astrophysical and Planetary Sciences, 391 UCB, Boulder, 80309 CO, USA
⁵ Department of Astronomy and Astrophysics, and Institute for Gravitation and the Cosmos, Pennsylvania State University, 525 Davey Lab, 251 Pollock Road, University Park, PA 16802, USA
⁶ Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong, PR, China
⁷ Center for Frontier Science, Chiba University, 1-33 Yayoicho, Inage, Chiba 263-8522, Japan
⁸ Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoicho, Inage, Chiba 263-8522, Japan

^⋆ Corresponding author: elias.mamuzic@tum.de; emamuzic@MPA-Garching.MPG.DE

Received: 4 March 2025
Accepted: 9 July 2025

Abstract

In the coming years, surveys such as the Rubin Observatory’s Legacy Survey of Space and Time (LSST) are expected to increase the number of observed Tidal Disruption Events (TDEs) substantially. We employed Monte Carlo integration to calculate the unlensed and lensed TDE rate as a function of limiting magnitude in the u, g, r, and i bands. We investigated the impact of multiple luminosity models, black hole mass functions (BHMFs), and flare temperatures on the TDE rate. Notably, this includes a semi-analytical model, which enables the determination of the TDE temperature in terms of (BH) mass. We predict the highest unlensed TDE rate to be in the g band. It ranges from 16 to 5440 yr⁻¹ (20 000 deg²)⁻¹ for the (ZTF), and it is more consistent with the observed rate at the low end. For LSST, we expect a rate in the g band between 3580 and 82 060 yr⁻¹ (20 000 deg²)⁻¹. A higher theoretical prediction is within reason, as we do not consider observational effects such as completeness. The unlensed and lensed TDE rates are insensitive to the redshift evolution of the BHMF, even for LSST limiting magnitudes. The best band for detecting lensed TDEs is also the g band. Its predicted rates range from 0.43 to 15 yr⁻¹ (20 000 deg²)⁻¹ for LSST. The scatter of predicted rates reduces when we consider the fraction of lensed TDEs; that is, only a few in ten thousand TDEs will be lensed. Despite the large scatter in the rates of lensed TDEs, our comprehensive considerations of multiple models suggest that lensed TDEs will occur in the 10-year LSST lifetime, providing an exciting prospect for detecting such events. We expect the median redshift of a lensed TDE to be between 1.5 and 2. In this paper, we additionally report on lensed TDE properties, such as the BH mass and time delays.