Growing White Dwarfs to the Chandrasekhar Limit: The Parameter Space of the Single Degenerate SNIa Channel

Can a white dwarf, accreting hydrogen-rich matter from a non-degenerate companion star, ever exceed the Chandrasekhar mass and explode as a type Ia supernova? We explore the range of accretion rates that allow a white dwarf (WD) to secularly grow in mass, and derive limits on the accretion rate and on the initial mass that will allow it to reach $1.4M_\odot$ --- the Chandrasekhar mass. We follow the evolution through a long series of hydrogen flashes, during which a thick helium shell accumulates. This determines the effective helium mass accretion rate for long-term, self-consistent evolutionary runs with helium flashes. We find that net mass accumulation always occurs despite helium flashes. Although the amount of mass lost during the first few helium shell flashes is a significant fraction of that accumulated prior to the flash, that fraction decreases with repeated helium shell flashes. Eventually no mass is ejected at all during subsequent flashes. This unexpected result occurs because of continual heating of the WD interior by the helium shell flashes near its surface. The effect of heating is to lower the electron degeneracy throughout the WD, and especially in the outer layers. This key result yields helium burning that is quasi-steady state, instead of explosive. We thus find a remarkably large parameter space within which long-term, self-consistent simulations show that a WD can grow in mass and reach the Chandrasekhar limit, despite its helium flashes.