Extinction Laws toward Stellar Sources within a Dusty Circimstellar Medium and Implications for Type Ia Supernovae

Many astronomical objects are surrounded by dusty environments. In such dusty objects, multiple scattering processes of photons by circumstellar (CS) dust grains can effectively alter extinction properties. In this paper, we systematically investigate effects of multiple scattering on extinction laws for steady-emission sources surrounded by the dusty CS medium, using a radiation transfer simulation based on the Monte Carlo technique. In particular, we focus on whether and how the extinction properties are affected by properties of CS dust grains, adopting various dust grain models. We {\bf confirm} that behaviors of the (effective) extinction laws are highly dependent on the properties of CS grains. Especially, the total-to-selective extinction ratio $R_{V}$, which characterizes the extinction law, can be either increased or decreased, compared to the case without multiple scattering. We find that the criterion for this behavior is given by a ratio of albedos in the $B$ and $V$ bands. We also find that either small silicate grains or polycyclic aromatic hydrocarbons (PAHs) are necessary for realizing a low value of $R_{V}$ as often measured toward Type Ia supernovae, if the multiple scattering by CS dust is responsible for their non-standard extinction laws. Using the derived relations between the properties of dust grains and the resulting effective extinction laws, we propose that the extinction laws toward dusty objects could be used to constrain the properties of dust grains in CS environments.