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Accurate distance determination to astrophysical objects is essential for the understanding of their intrinsic brightness and size. The distance to SN 1987A has been previously measured by the expanding photosphere method and by using the angular size of the circumstellar rings with absolute sizes derived from light curves of narrow UV emission lines, with reported distances ranging from 46.77 to 55 kpc. In this study, we independently determined the distance to SN 1987A using photometry and imaging polarimetry observations of AT 2019xis, a light echo of SN 1987A, by adopting a radiative transfer model of the light echo developed in Ding et al. We obtained distances to SN 1987A in the range from 49.09 ± 2.16 kpc to 59.39 ± 3.27 kpc, depending on the interstellar polarization and extinction corrections, which are consistent with the literature values. This study demonstrates the potential of using light echoes as a tool for distance determination to astrophysical objects in the Milky Way, up to kiloparsec level scales.

Spectropolarimetry enables us to measure the geometry and chemical structure of the ejecta in supernova explosions, which is fundamental for the understanding of their explosion mechanism(s) and progenitor systems. We collected archival data of 35 Type Ia supernovae (SNe Ia), observed with Focal Reducer and Low-Dispersion Spectrograph (FORS) on the Very Large Telescope at 127 epochs in total. We examined the polarization of the Si ii λ6355 Å line ($p_{\rm Si\, \small {II}}$) as a function of time, which is seen to peak at a range of various polarization degrees and epochs relative to maximum brightness. We reproduced the $\Delta m_{15}\!-\!p_{\rm Si\, \small {II}}$ relationship identified in a previous study, and show that subluminous and transitional objects display polarization values below the $\Delta m_{15}\!-\!p_{\rm Si\, \small {II}}$ relationship for normal SNe Ia. We found a statistically significant linear relationship between the polarization of the Si ii λ6355 Å line before maximum brightness and the Si ii line velocity and suggest that this, along with the $\Delta m_{15}\!-\!p_{\rm Si\, \small {II}}$ relationship, may be explained in the context of a delayed-detonation model. In contrast, we compared our observations to numerical predictions in the $\Delta m_{15}\!-\!v_{\rm Si\, \small {II}}$ plane and found a dichotomy in the polarization properties between Chandrasekhar and sub-Chandrasekhar mass explosions, which supports the possibility of two distinct explosion mechanisms. A subsample of SNe displays evolution of loops in the q–u plane that suggests a more complex Si structure with depth. This insight, which could not be gleaned from total flux spectra, presents a new constraint on explosion models. Finally, we compared our statistical sample of the Si ii polarization to quantitative predictions of the polarization levels for the double-detonation, delayed-detonation, and violent-merger models.