Context. Supersoft X-ray sources (SSSs) have been proposed as one of the progenitors for Type Ia supernovae. However, the exact origin of the quasi-periodic variability in the optical light curve remains a mystery. Aims. In this work, our goal is to investigate the effect of the feedback of an evolved main-sequence companion star on X-ray irradiation and find whether periodic X-ray irradiation of the companion star could reproduce periodic mass transfer. Methods. Using the Modules for Experiments in Stellar Astrophysics (MESA) code, we modeled the evolutionary track of the companion star under the influence of supersoft X-ray irradiation, and we calculated the resulting mass transfer rate. Results. We find that the supersoft X-ray heating of the companion star can result in the expansion of the companion, causing it to greatly overflow its Roche lobe and thereby increasing the mass transfer rate. The periodic X-ray irradiation on the companion stars leads to periodic changes in the mass transfer rate. For a given companion star, higher irradiation efficiencies result in a higher mass transfer rate. Additionally, the mass transfer rate increases as the mass of the companion star decreases for a given irradiation efficiency. Conclusions. The companion star undergoing thermal timescale mass transfer is periodically irradiated by the X-rays from the WD, which can lead to periodic enhancement of the mass transfer rate. The mechanism could be the origin of the quasi-periodic optical light curve in supersoft X-ray sources.
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