Detection of Unresolved Strongly Lensed Supernovae with 7-Dimensional Telescope

Gravitationally lensed supernovae (glSNe) are a powerful tool for exploring the realms of astronomy and cosmology. Time-delay measurements and lens modeling of glSNe can provide a robust and independent method for constraining the expansion rate of the universe. The study of unresolved glSNe light curves presents a unique opportunity for utilizing small telescopes to investigate these systems. In this work, we investigate diverse observational strategies for the initial detection of glSNe using the 7-Dimensional Telescope (7DT), a multitelescope system composed of twenty 50-cm telescopes. We implement different observing strategies on a subset of 5807 strong lensing systems and candidates identified within the Dark Energy Camera Legacy Survey (DECaLS), as reported in various publications. Our simulations under ideal observing conditions indicate the maximum expected annual detection rates for various glSNe types (Type Ia and core-collapse (CC)) using the 7DT target observing mode in the $r$-band at a depth of 22.04 mag, as follows: 7.46 events for type Ia, 2.49 for type Ic, 0.8 for type IIb, 0.52 for type IIL, 0.78 for type IIn, 3.75 for type IIP, and 1.15 for type Ib. Furthermore, in the case of medium-band filter observations (m6000) at a depth of 20.61 in the Wide-field Time-domain Survey (WTS)program, the predicted detection rate for glSNe Ia is 2.53 $yr^{-1}$. Given targeted follow-up observations of these initially detected systems with more powerful telescopes, we can apply a model-independent approach to forecast the ability to measure $H_{0}$ using a Gaussian process from Type Ia Supernovae (SNe Ia) data and time-delay distance information derived from glSNe systems, which include both Ia and CC types. We forecast that the expected detection rate of glSNe systems can achieve a $2.7\%$ precision in estimating the $H_{0}$.