We present a theoretical light curve model of the recurrent nova M31N 2008-12a, the current record holder for the shortest recurrence period (1 yr). We combined interior structures calculated using a Henyey-type evolution code with optically thick wind solutions of hydrogen-rich envelopes, which give the proper mass-loss rates, photospheric temperatures, and luminosities. The light curve model is calculated for a 1.38 M_sun white dwarf (WD) with an accretion rate of 1.6 times 10^{-7} M_sun yr^{-1}. This model shows a very high effective temperature (log T_ph (K) geq 4.97) and a very small wind mass-loss rate (dot M_wind leq 9.3 times 10^{-6} M_sun yr^{-1}) even at the maximum expansion of the photosphere. These properties are consistent with the faint optical peak of M31N 2008-12a because the brightness of the free-free emission is proportional to the square of the mass-loss rate. The model well reproduces the short supersoft X-ray turn-on time of 6 days and turnoff time of 18 days after the outburst. The ejecta mass of our model is calculated to be 6.3 times 10^{-8} M_sun, corresponding to 37% of the accreted mass. The growth rate of the WD is 0.63 times the mass accretion rate, making it a progenitor for a Type Ia supernova. Our light curve model predicts a bright supersoft X-ray phase one or two days before the optical peak. We encourage detection of this X-ray flash in future outbursts.
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