The origin of the near-infrared excess in SN Ia 2012dn: Circumstellar dust around the super-Chandrasekhar supernova candidate

The nature of progenitors of the so-called super-Chandrasekhar candidate Type Ia supernovae (SC-SNe Ia) has been actively debated. Recently, Yamanaka et al. (2016) reported a near-infrared (NIR) excess for SN 2012dn, and proposed that the excess originates from an echo by circumstellar (CS) dust. In this paper, we examine a detailed distribution of the CS dust around SN 2012dn, and investigate implications of the CS dust echo scenario for general cases of SC-SNe Ia. We find that a disk/bipolar CS medium configuration reproduces the NIR excess fairly well, where the radial density distribution is given by a stationary mass loss. The inner radius of the CS dust is $0.04$ pc. The mass-loss rate of the progenitor system is estimated to be $1.2 \times 10^{-5}$ and $3.2 \times 10^{-6}$ M$_{\odot}$ yr$^{-1}$ for the disk and bipolar CS medium configurations, respectively, which adds another support for the single degenerate scenario. Our models limit SN 2009dc, another SC-SN Ia, to have a dust mass less than $0.16$ times that of SN 2012dn. While this may merely indicate some variation on the CS environment among SC-SNe Ia, this could raise another interesting possibility. There could be two classes among SC-SNe Ia; the brighter SC-SNe Ia in a clean environment (SN 2009dc) and the fainter SC-SNe Ia in a dusty environment (SN 2012dn).