Mass accumulation efficiency in helium shell flashes for various white dwarf masses

Abstract

We have calculated the mass accumulation efficiency during helium shell flashes on white dwarfs (WDs) of mass 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, and $1.35 M_{\odot}$ for the helium accretion rates $\log\dot M_{\rm He} \ (M_{\odot}$ yr$^{-1}) = -7.4$ to -5.8. This efficiency is a crucial factor for binary evolutions of Type Ia supernovae. For less massive WDs ($< 0.8 \ M_{\odot}$) no wind mass loss occurs and all the accreted mass accumulates on the WD if the Roche lobe size is large enough. The efficiency takes the minimum values in between 1.1 and 1.2 $M_{\odot}$ WD for a given mass accretion rate and increases in both less and more massive WDs. The mass accumulation efficiency is larger than 0.5 for $\log\dot M_{\rm He} \geq -6.72$ in all the WD masses.