The single degenerate model is the most widely accepted progenitor model of type Ia supernovae (SNe Ia), in which a carbon-oxygen white dwarf (CO WD) accretes hydrogen-rich material from a main sequence or a slightly evolved star (WD+MS) to increase its mass, and explodes when its mass approaches the Chandrasekhar mass limit. During the mass transfer phase between the two components, an optically thick wind may occur and the material lost as wind may exist as circumstellar material (CSM). Searching for the CSM around a progenitor star is helpful for discriminating different progenitor models of SNe Ia. In addition, the CSM is a source of color excess. The purpose of this paper is to study the color excess produced from the single-degenerate progenitor model with an optically thick wind, and reproduce the distribution of color excesses of SNe Ia. Meng et al. systemically carried out binary evolution calculations of the WD +MS systems for various metallicities and showed the parameters of the systems before Roche lobe over flow and at the moment of supernova explosion in Meng & Yang. With the results of Meng et al., we calculate the color excesses of SNe Ia at maximum light via a simple analytic method. We reproduce the distribution of color excesses of SNe Ia by our binary population synthesis approach if the velocity of the optically thick wind is taken to be an order of magnitude of 10 km s-1. However, if the wind velocity is larger than 100 km s-1, the reproduction is bad.
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