Journal title:

Monthly Notices of the Royal Astronomical Society

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 masstransfer 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 commonenvelope formalism (the alphaformalism) equating the energy balance in the system (implicitly assuming angular momentum conservation) does not work. An algorithm equating the angular momentum balance (implicitly assuming energy conservation) can explain the observations. This conclusion is now based on 10 observed systems rather than three. With the latter algorithm (the gammaalgorithm) the separation does not change much for approximately equalmass binaries. Assuming constant efficiency in the standard alphaformalism and a constant value of gamma, 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 gammaalgorithm also leads to this. We then extend our analysis to all close binaries with at least one white dwarf component and reconstruct the masstransfer phases that lead to these binaries. In this way we find all possible values of the efficiency of the standard alphaformalism and of gamma that can explain the observed binaries for different progenitor and companion masses. We find that all observations can be explained with a single value of gamma, making the gammaalgorithm a useful tool to predict the outcome of commonenvelope 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.
