Spectroscopic analysis of the strongly lensed SN~Encore: Constraints on cosmic evolution of Type Ia supernovae

Strong gravitational lensing magnifies the light from a background source, allowing us to study these sources in detail. Here, we study the spectra of a $z = 1.95$ lensed Type Ia supernova SN~Encore for its brightest Image A, taken 39 days apart. We infer the spectral age with template matching using the supernova identification (SNID) software and find the spectra to be at 29.0 $\pm 5.0$ and 37.4 $\pm 2.8$ rest-frame days post maximum respectively, consistent with separation in the observer frame after accounting for time-dilation. Since SNe~Ia measure dark energy properties by providing relative distances between low- and high-$z$ SNe, it is important to test for evolution of spectroscopic properties. Comparing the spectra to composite low-$z$ SN~Ia spectra, we find strong evidence for similarity between the local sample of SN~Encore. The line velocities of common SN~Ia spectral lines, Si II 6355 and Ca II NIR triplet are consistent with the distribution for the low-$z$ sample as well as other lensed SNe~Ia, e.g. iPTF16geu ($z = 0.409$) and SN~H0pe ($z = 1.78$). The consistency in SN~Ia spectra across cosmic time demonstrates the utility of using SNe~Ia in the very high-$z$ universe for dark energy inference. We also find that the spectra of SN~Encore match the predictions for explosion models very well. With future large samples of lensed SNe~Ia, spectra at such late phases will be important to distinguish between different explosion scenarios.