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In the single degenerate (SD) scenario for Type Ia supernova (SN Ia)progenitors, an accreting white dwarf (WD) is expected to undergo a supersoftX-ray source (SSS) phase. Recently, Gilfanov & Bogdan (2010, hereafter GB10)claimed that observed X-ray fluxes of early type galaxies would be too low tobe consistent with the prediction of the SD scenario based on rather simpleassumptions. We present realistic evolutionary models of SD systems andcalculate durations of SSS phases. In most cases, accreting WDs spend a largefraction of time in the optically thick wind phase and the recurrent nova phaserather than the SSS phase. Thus the SSS phase lasts only for a few hundredthousand years. This is by a factor of ~10 shorter than those adopted by GB10where the SN~Ia progenitor WD was assumed to spend most of its life as a SSS.The theoretical X-ray luminosity of the SSS has a large uncertainty because ofthe uncertain atmospheric model of mass-accreting WDs and absorption of softX-rays by the companion star's cool wind material. We thus adopt an average ofthe observed fluxes of existing symbiotic SSSs, i.e., ~0.4 x 10^{36} erg s^{-1}for 0.3--0.7 keV. Using these SSS duration and soft X-ray luminosity, we showthat the observed X-ray flux obtained by GB10 is rather consistent with ourestimated flux in early type galaxies based on the SD scenario. This is astrong support for the SD scenario as a main-contributor of SNe Ia in earlytype galaxies.

Supersoft X-ray Phase of Single Degenerate Type Ia Supernova Progenitors in Early Type Galaxies