tokens: circles mark the mass coordinate . The last few profiles show the envelope oscillating due to mass transfer rates falling below the steady He-burning regime. On the low mass donor end, however, carbon may not ignite at all. The model with initial donor mass stays at lower accretion rates and falls far enough below the steady helum burning range that the mild helium oscillations become powerful enough to blow off mass. The blue dashed line shows how the maximum temperature in the shell will oscillate between the flashing helium burning shell and the hot, compressed C/O ashes below the burning layer. At these accretion rates, however, the accretion efficiency stays above 70%, allowing the WD to gain enough mass to trigger carbon ignition in the core. We compare our accreted mass retention efficiency calculated in the final stages of this model using super-Eddington winds to the analytical estimates of Kato Hachisu ( 2004 ) and Wang et al. ( 2015 ) in Figure 7 . Wang et al. ( 2015 ) used MESA (r3661) for their study, but used the default super-Eddington wind settings, whereas we triggered super-Eddington winds while the WD is still in a compact configuration in order to speed the computation. Systems with donor mass , therefore, will fall to lower accretion rates and efficiencies, and ultimately lose contact before a core ignition occurs. The components, now both C/O WDs, will spiral in due to GWR and contribute to the double-degenerate channel for SNe Ia, as discussed in Section 6 . Figure 7. The top panel shows the accreted mass retention efficiency during the last stages of the system with the donor stars. The black line shows what we calculated by taking the ratio of the growth rate of the accretor and the mass loss rate of the donor. The red short-dashed lines show the retention efficiency given analytically by Kato Hachisu ( 2004 ) for 1.3 and cores. The blue long-dashed lines show the retention efficiency given analytically by Wang et al. ( 2015 ) for 1.3 and cores. The bottom panel shows the mass transfer rate being donated to the WD. Between the high and low mass donor limits is the region where core carbon ignitions occur. This is where the donor mass is high enough that the accretion rates do not fall too far below the stability boundary before is reached, but also low enough that it avoids a carbon shell ignition from long sustained high accretion rates. A clear example of this is shown in Figure 8 , with the trajectories of the core and envelope shown with profiles in space for a system with . In Figure 9 we show the composition and temperature profile when this model has grown to , the same profile as that in Figure 8 . As the C/O envelope is , this shows that the base is at a temperature minimum, and the temperature maximum in the envelope is only deep. The core ignition in these models indicates that they are likely SN Ia progenitors. Figure 8. Profiles of of the WD in the binary system with . Markings have the same meaning as
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