Reconstructing the evolution of white dwarf binaries: further evidence for an alternative algorithm for the outcome of the common-envelope phase in close binaries

Abstract

We determine the possible masses and radii of the progenitors of white dwarfs in binaries from fits to detailed stellar evolution models and use these to reconstruct the mass-transfer phase in which the white dwarf was formed. We confirm the earlier finding that in the first phase of mass transfer in the binary evolution leading to a close pair of white dwarfs, the standard common-envelope formalism equating the energy balance in the system, does not work. An algorithm equating the angular momentum balance can explain the observations. This conclusion is now based on ten observed systems rather than three. With the latter algorithm the separation does not change much for approximately equal mass binaries. Assuming constant efficiency in the standard α-formalism and a constant value of γ, we investigate the effect of both methods on the change in separation in general and conclude that when there is observational evidence for strong shrinkage of the orbit, the γ-algorithm also leads to this. We then extend our analysis to all close binaries with at least one white dwarf component and reconstruct the mass transfer phases that lead to these binaries. We find that all observations can be explained with a single value of γ, making the γ-algorithm a useful tool to predict the outcome of common-envelope evolution. We discuss the consequences of our findings for different binary populations in the Galaxy, including massive binaries, for which the reconstruction method cannot be used (abbriged).