A new estimation of mass accumulation efficiency in helium shell flashes toward Type Ia supernova explosions

We have calculated the mass accumulation efficiency during helium shell fla shes to examine whether or not a carbon-oxygen white dwarf(C+O WD) grows up to the Chandrasekhar mass limit to ignite a Type Ia supernova (SN Ia) expl osion. It has been frequently argued that luminous supersoft X-ray sources (SSSs) and symbiotic stars are progenitors of SNe Ia. In such systems, a CO WD accretes hydrogen-rich matter from a companion and burns hydrogen stea dily on its surface. The WD develops a helium layer underneath the hydrogen -rich envelope and undergoes periodic helium shell flashes. Using the OPAL opacity, we have reanalyzed a full cycle of helium shell flashes on a 1.3 M ., C+O WD and confirmed that the helium envelope of the WD expands to blow a strong wind. A part of the accumulated matter is lost by the wind. The ma ss accumulation efficiency in helium shell flashes is estimated as eta(He) = -0.175(log M + 5.35)(2) + 1.05 for -7.3 < log M < -5.9 and eta(He) 1 for -5.9 less than or equal to log M less than or similar to -5, where the mass accretion rate hi is in units of M., yr(-1). In relatively high mass accre tion rates, as expected in recent SN Ia progenitor models, the mass accumul ation efficiency is large enough for C+O WDs to grow to the Chandrasekhar m ass, i.e., eta(He) = 0.9 for log M = -6.3 and eta(He) = 0.57 for log M = -7 .0. The wind velocity (similar to 1000 km s(-1)) is much faster than the or bital velocity of the binary (less than or similar to 300 km s(-1)), and th erefore the wind cannot be accelerated further by the companion's motion. W e suggest observational counterparts of helium shell flashes in relation to long-term variations in supersoft X-ray fluxes of SSSs and symbiotic stars .