A New Estimation of Mass Accumulation Efficiency in Helium Shell Flashestoward Type Ia Supernova Explosions

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(logṀ+5.35)2+1.05 for -7.3<logṀ < -5.9 and ηHe=1 for -5.9 ≤ logṀ ≲ -5, where the mass accretion rate Ṁ 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 logṀ=-6.3 and ηHe=0.57 for logṀ=-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.