Observational signatures of the circumstellar material (CSM) around Type Ia supernovae (SNe Ia) provide a unique perspective to the progenitor systems. The pre-supernova evolution of the SN progenitors may naturally eject CSM in most of the popular scenarios of SN Ia explosions. In this study, we investigate the influence of dust scattering on the light curves and polarizations of SNe Ia. A Monte Carlo method is constructed to numerically solve the radiative transfer process through the CSM. Three types of geometric distributions of the CSM are considered: spherical shell, axisymmetric disk, and axisymmetric shell. We show that both the distance of the dust to the SNe and the geometric distribution of the dust affect the light curve and color evolutions of SNe. Contrary to previous studies, we found that the geometric location of the hypothetical CS dust cannot be reliably constrained based on photometric data alone even for the best observed cases such as SN 2006X and SN~2014J, and time dependent polarimetry is an inimitable way to establish the geometric location of any dusty CSM. Our model results show that time sequence of broad-band polarimetry with appropriate time coverage from a months to about one year after explosion can provide unambiguous limits on the presence of CS dust around SNe Ia.
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