Rapid identification of lensed type Ia supernovae with color-magnitude selection

Strongly lensed type Ia supernovae (SNe Ia) provide a unique cosmological probe to address the Hubble tension problem in cosmology. In addition to the sensitivity of the time delays to the value of the Hubble constant, the transient and standard candle nature of SNe Ia also enable valuable joint constraints on the model of the lens and the cosmological parameters. The upcoming Legacy Survey of Space and Time (LSST) with the Vera C. Rubin Observatory is expected to increase the number of observed SNe Ia by an order of magnitude in ten years of its lifetime. However, finding such systems in the LSST data is a challenge. In this work, we revisit the color-magnitude (CM) diagram used previously as a means to identify lensed SNe Ia and extend the work further as follows. We simulate LSST-like photometric data ($rizy$ bands) of lensed SNe Ia and analyze it in the CM parameter space. We find that a subset of lensed SNe Ia are redder compared to unlensed SNe Ia at a given magnitude, both in the rising and falling phases of their light curves and for SNe up to $z=3$. We propose a modified selection criterion based on these new results. We show that the contamination coming from unlensed core-collapse (CC) SNe is negligible, whereas a small fraction of lensed CC SNe types Ib and Ic may get selected by this criterion as potential lensed SNe. Finally, we demonstrate that our criterion works well on a wide sample of observed unlensed SNe Ia, a handful of known multiply-imaged lensed SNe systems, and a representative sample of observed CC SNe as well as super-luminous supernovae.