Long-term evolution of double white dwarf binaries accreting through direct impact

Abstract: We calculate the long-term evolution of angular momentum in double white dwarf binaries undergoing direct impact accretion over a broad range of parameter space. We allow the rotation rate of both components to vary, and account for the exchange of angular momentum between the spins of the white dwarfs and the orbit, while conserving the total angular momentum. We include gravitational, tidal, and mass transfer effects in the orbital evolution, and allow the Roche radius of the donor star to vary with both the stellar mass and the rotation rate. We examine the long-term stability of these systems, focusing in particular on those systems that may be progenitors of AM CVn or Type Ia Supernovae. We find that our analysis yields an increase in the predicted number of stable systems compared to that in previous studies. Additionally, we find that by properly accounting for the effects of asynchronism between the donor and the orbit on the Roche-lobe size, we eliminate oscillations in the orbital parameters which are found in previous studies. Removing these oscillations can reduce the peak mass transfer rate in some systems, keeping them from entering an unstable mass transfer phase.