On The Formation of Double White Dwarfs: Reevaluating How We Parametrize the Common Envelope Phase

One class of compact binaries of special interest is that of double white dwarfs (DWDs). For many of these systems, the exact nature of the evolutionary channels by which they form remains uncertain. The canonical explanation calls for the progenitor binary system to undergo two subsequent mass-transfer events, both of which are unstable and lead to a common envelope (CE) phase. However, it has been shown that if both CE events obey the standard αCE prescription, it is not possible to reproduce all of the observed systems. As an alternative prescription, the γ-formalism was proposed, which parametrizes the fraction of angular momentum carried away with mass loss, in contrast to the αCE prescription, which parametrizes energy loss. We demonstrate that the γ-prescription is also inadequate in describing the evolution of an arbitrary DWD binary; clearly we require a deeper understanding of the physical mechanisms underlying their formation. We then present a detailed model for the evolution of Red Giant – Main Sequence binaries during the first episode of mass transfer, and demonstrate that their evolution into DWDs need not arise through two phases of dynamical mass loss. Instead, the first episode of dramatic mass loss may be stable, non-conservative mass transfer. The second phase is then well described by the αCE prescription. We find that the considered progenitors can reproduce the properties of the observed helium DWDs in which the younger component is the more massive. 1. Problems with Parametrizing CE Evolution In order to explain the dramatic loss of mass and angular momentum needed to form the majority of observed close binaries with at least one degenerate component, Paczynski (1976) and Ostriker (1976) first suggested such systems undergo a common envelope (CE) phase during their evolution. In this event one component expands on the giant branch to engulf the other leading to spiral-in and the removal of the envelope. In the standard picture, the consequent orbital shrinkage is parametrized in a simple manner in terms of the mass lost and an efficiency factor αCE (though see Ivanova, this volume):