Although several dozen double white dwarfs ( DWDs ) have been observed , for many the exact nature of the evolutionary channel ( s ) 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 ) .
However , it has been shown that if both CE events obey the standard \alpha _ { \mathrm { CE } } -prescription ( parametrizing energy loss ) , it is not possible to reproduce all of the observed systems .
The \gamma -prescription was proposed as an alternative to this description , instead parametrizing the fraction of angular momentum carried away in dynamical-timescale mass loss .
In this paper , we analyze simultaneous energy and angular-momentum conservation , and show that the \gamma -prescription can not adequately describe a CE event for an arbitrary binary , nor can the first phase of mass loss always be understood in general as a dynamical-timescale event .
We consider in detail the first episode of mass transfer in binary systems with initially low companion masses , with a primary mass in the range 1.0–1.3 M _ { \odot } and an initial mass ratio between the secondary and primary stars of 0.83–0.92 .
In these systems , the first episode of dramatic mass loss may be stable , non-conservative mass transfer .
This strips the donor ’ s envelope and dramatically raises the mass ratio ; the considered progenitor binary systems can then evolve into DWDs after passing through a single CE during the second episode of mass loss .
We find that such a mechanism reproduces the properties of the observed DWD systems which have an older component with M \lesssim 0.46 M _ { \odot } and mass ratios between the younger and older WDs of q \geq 1 .