We have calculated the mass accumulation efficiency during helium shell flashes 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) explosion. It has been frequently argued that luminous supersoft X-ray sources (SSSs) and symbiotic stars are progenitors of SNe Ia. In such systems, a C+O WD accretes hydrogen-rich matter from a companion and burns hydrogen steadily 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 mass accumulation efficiency in helium shell flashes is estimated as ηHe = -0.175(log M + 5.35)2 + 1.05 for -7.3 < log M < -5.9 and ηHe = 1 for -5.9 ≤ log Ṁ ≲ -5, where the mass accretion rate M is in units of M⊙ yr 1. In relatively high mass accretion rates, as expected in recent SN Ia progenitor models, the mass accumulation efficiency is large enough for C+O WDs to grow to the Chandrasekhar mass, i.e., ηHe = 0.9 for log Ṁ = -6.3 and ηHe = 0.57 for log Ṁ = -7.0. The wind velocity (∼1000 km s-1) is much faster than the orbital velocity of the binary (≲300 km s-1), and therefore the wind cannot be accelerated further by the companion's motion. We suggest observational counterparts of helium shell flashes in relation to long-term variations in supersoft X-ray fluxes of SSSs and symbiotic stars.
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