Rates of Strongly Lensed Tidal Disruption Events

TL;DR

This work develops a Monte Carlo framework to predict both unlensed and strongly lensed tidal disruption event (TDE) rates for current and future surveys (e.g., ZTF and LSST) across multiple bands. It couples three black hole mass functions (BHMFs) with two TDE luminosity models and temperature prescriptions to compute observable rates via a rate integral, while incorporating band-specific magnitude bounds through AB magnitudes. A key finding is that the assumed TDE temperature largely dominates the rate scatter, with the g-band consistently offering the highest detectability; BHMF redshift evolution has a comparatively small impact for LSST depths. The study extends to lensing, using a lensing code to generate mock catalogs and derive lensed-TDE rates, lensed fractions, and lens-system parameters, predicting that LSST will observe a few lensed TDEs in its 10-year lifetime, most with lens redshifts below unity and image separations of order a few arcseconds. Overall, the results provide practical forecasts for unlensed and lensed TDE yields, highlighting the critical role of TDE temperature and offering a framework for interpreting future observations and their cosmological utility.

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 employ Monte Carlo integration to calculate the unlensed and lensed TDE rate as a function of limiting magnitude in $u$, $g$, $r$, and $i$-bands. We investigate 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 black hole (BH) mass. We predict the highest unlensed TDE rate to be in $g$-band. It ranges from $16$ to $5,440\;\mathrm{yr}^{-1}\;(20,000\;\mathrm{deg}^2)^{-1}$ for the Zwicky Transient Facility, being more consistent with the observed rate at the low end. For LSST, we expect a rate in $g$-band between $3,580$ and $82,060\;\mathrm{yr}^{-1}\;(20,000\;\mathrm{deg}^2)^{-1}$. A higher theoretical prediction is understandable, 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 $g$-band. Its predicted rates range from $0.43$ to $15\;\mathrm{yr}^{-1}\;(20,000\;\mathrm{deg}^2)^{-1}$ for LSST. The scatter of predicted rates reduces when we consider the fraction of lensed TDEs; that is, 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.

Figures (17)

• Figure 1: Three different bhmf we consider showing significantly different redshift evolutions. Left panel: Redshift independent bhmf from derivation_of_the_BHMF_Gallo_2019. Middle panel: bhmf derived by the TRINITY model z_dep_BHMF_TRINITY_1. Right panel: bhmf calculated by combining a gsmf GSMF and a bh-to-bulge mass relation bh_bulge_mass_relation. The $z$-independent bhmf has a different normalization than the other two. Up to redshift of 2, TRINITY and COSMOS2015 agree closely.
• Figure 1: Schematic view of a gravitational lens. The light travels along the blue path, meaning we observe the image at a different angular position $\vec{\theta}$ compared to the true angular source position $\vec{\beta}$ indicated with the green line.
• Figure 2: Three different tde luminosity functions dependent on bh mass. For low bh masses, $L_{1}$ is Eddington limited. The two $L_{2}$ models do not yet differ through their treatment of temperature, as temperature is not involved yet. However, they differ because of a correction factor that accounts for the spread of specific energy in the resulting debris. The $T$-independent model assumes this factor to be constant.
• Figure 2: Differential rate of unlensed tde for five representative models. The first row shows the tde redshift, and the second row shows the bh mass. These figures are calculated for lsst magnitude limits.
• Figure 3: tde temperature dependent on bh mass using the $L_{2}$ model. We assumed a solar-like star, that is, $M_\star = 1 \; \mathrm{M}_\odot$ and $R_\star = 1 \; \mathrm{R}_\odot$.