Evolution of Close White Dwarf Binaries

We describe the evolution of double degenerate binary systems, consisting of components obeying the zero temperature mass radius relationship for white dwarf stars, from the onset of mass transfer to one of several possible outcomes including merger, tidal disruption of the donor, or survival as a semi-detached AM CVn system. We use a combination of analytic solutions and numerical integrations of the standard orbit-averaged first-order evolution equations, including direct impact accretion and the evolution of the components due to mass exchange. We include also the effects of mass-loss during super-critical (super-Eddington) mass transfer and the tidal and advective exchanges of angular momentum between the binary components. We cover much the same ground as Marsh et al.(2004) with the additional effects of the advective or consequential angular momentum from the donor and its tidal coupling to the orbit which is expected to be stronger than that of the accretor. With the caveat that our formalism does not include an explicit treatment of common envelope phases, our results suggest that a larger fraction of detached double white dwarfs than what has been hitherto assumed, survive the onset of mass transfer, even if this mass transfer is initially unstable and rises to super-Eddington levels. In addition, as a consequence of the tidal coupling, systems that come into contact near the mass transfer instability boundary undergo a phase of oscillation cycles in their orbital period (and other system parameters). Much of the formalism developed here would also apply to other mass-transferring binaries, and in particular to cataclysmic variables and Algol systems.