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Can a white dwarf, accreting hydrogen-rich matter from a non-degeneratecompanion star, ever exceed the Chandrasekhar mass and explode as a type Iasupernova? 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 onthe initial mass that will allow it to reach $1.4M_\odot$ --- the Chandrasekharmass. We follow the evolution through a long series of hydrogen flashes, duringwhich a thick helium shell accumulates. This determines the effective heliummass accretion rate for long-term, self-consistent evolutionary runs withhelium flashes. We find that net mass accumulation always occurs despite heliumflashes. Although the amount of mass lost during the first few helium shellflashes is a significant fraction of that accumulated prior to the flash, thatfraction decreases with repeated helium shell flashes. Eventually no mass isejected at all during subsequent flashes. This unexpected result occurs becauseof continual heating of the WD interior by the helium shell flashes near itssurface. The effect of heating is to lower the electron degeneracy throughoutthe WD, and especially in the outer layers. This key result yields heliumburning that is quasi-steady state, instead of explosive. We thus find aremarkably large parameter space within which long-term, self-consistentsimulations show that a WD can grow in mass and reach the Chandrasekhar limit,despite its helium flashes.

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