In the single degenerate ( SD ) scenario for Type Ia supernova ( SN Ia ) progenitors , an accreting white dwarf ( WD ) is expected to undergo a supersoft X-ray source ( SSS ) phase .
Recently , Gilfanov & Bogdán ( 2 ) , hereafter GB10 claimed that observed X-ray fluxes of early type galaxies would be too low to be consistent with the prediction of the SD scenario based on rather simple assumptions .
We present realistic evolutionary models of SD systems and calculate durations of SSS phases .
In most cases , accreting WDs spend a large fraction of time in the optically thick wind phase and the recurrent nova phase rather than the SSS phase .
Thus the SSS phase lasts only for a few hundred thousand years .
This is by a factor of \sim 10 shorter than those adopted by GB10 where 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 of the uncertain atmospheric model of mass-accreting WDs and absorption of soft X-rays by the companion star ’ s cool wind material .
We thus adopt an average of the observed fluxes of existing symbiotic SSSs , i.e. , \sim 0.4 \times 10 ^ { 36 } erg s ^ { -1 } for 0.3–0.7 keV .
Using these SSS duration and soft X-ray luminosity , we show that the observed X-ray flux obtained by GB10 is rather consistent with our estimated flux in early type galaxies based on the SD scenario .
This is a strong support for the SD scenario as a main-contributor of SNe Ia in early type galaxies .