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Binary population synthesis study on supersoft X-ray phase of single degenerate type Ia supernova progenitors

In the single degenerate (SD) scenario for type Ia supernovae (SNe Ia), a mass-accreting white dwarf is expected to experience a supersoft X-ray source (SSS) phase. However, some recent observations showed that the expected number of the mass-accreting WD is much lower than that predicted from theory, whatever in spiral or elliptical galaxies. In this paper, we did a binary population synthesis study on the relative duration of the SSS phase to their whole mass-increasing phase of WDs leading to SNe Ia. We found that for about 40% progenitor systems, the relative duration is shorter than 2% and the evolution of the mean relative duration shows that it is always smaller than 5%, whatever for young or old SNe Ia. In addition, before SNe Ia explosion, more than 55% progenitor systems are experiencing a dwarf novae phase, and only no more than 10% is staying SSS phase. These results are consistent with the recent observations, and imply that both in early- and late-type galaxies, only a small fraction of mass-accreting WD resulting in SNe Ia contribute to the supersoft X-ray flux. So, although our results are not directly related to the X-ray output of SN Ia progenitor, the low supersoft X-ray luminosity observed in early type galaxies may have no ability to exclude the validity of SD model. On the contrary, it is evidence to support the SD scenario.