Determining Type Ia Supernovae Host galaxy extinction probabilities and a statistical approach to estimating the absorption-to-reddening ratio $R_V$

We investigate limits on the extinction values of Type Ia supernovae to statistically determine the most probable color excess, E(B-V), with galactocentric distance, and use these statistics to determine the absorption-to-reddening ratio, $R_V$, for dust in the host galaxies. We determined pixel-based dust mass surface density maps for 59 galaxies from the Key Insight on Nearby Galaxies: a Far-Infrared Survey with \textit{Herschel} (KINGFISH, Kennicutt et al. (2011)). We use Type Ia supernova spectral templates (Hsiao et al. 2007) to develop a Monte Carlo simulation of color excess E(B-V) with $R_V$ = 3.1 and investigate the color excess probabilities E(B-V) with projected radial galaxy center distance. Additionally, we tested our model using observed spectra of SN 1989B, SN 2002bo and SN 2006X, which occurred in three KINGFISH galaxies. Finally, we determined the most probable reddening for Sa-Sap, Sab-Sbp, Sbc-Scp, Scd-Sdm, S0 and Irregular galaxy classes as a function of $R/R_{25}$. We find that the largest expected reddening probability are in Sab-Sb and Sbc-Sc galaxies, while S0 and Irregulars are very dust poor. We present a new approach for determining the absorption-to-reddening ratio $R_V$ using color excess probability functions, and find for a sample of 21 SNe Ia observed in Sab-Sbp galaxies, and 34 SNe in Sbc-Scp, an $R_V$ of 2.71 $\pm$ 1.58 and $R_V$ = 1.70 $\pm$ 0.38 respectively.

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