The effect of magnetic fields in common-envelope evolution on the formation of cataclysmic variables

A common-envelope phase of evolution is the most probable route by which cataclysmic variables can form from their much wider progenitors. Inside the common envelope, the white dwarf core of the former giant and the newly swallowed, unevolved main-sequence star spiral together until they are close enough that magnetic braking will subsequently drive the pair into the semidetached state that is a cataclysmic variable. At the same time, the energy released from their orbit must drive away the envelope so that the spiralling-in stops at just the right moment. The presence of this more and more rapidly orbiting pair inside the more slowly rotating common envelope will inevitably lead to growing differential rotation within the envelope. This will in turn, via an α-Ω dynamo, lead to strong magnetic fields. These magnetic fields, by their tendency to reduce differential rotation and to drive stellar winds, can achieve both the reduction in orbital period of the two cores and the expulsion of the envelope. We construct a simple self-consistent model of the dynamo and its associated effects, and find that common-envelope systems with small envelope mass can eject the envelope without much reduction in orbital separation, while those with large envelope mass undergo coalescence of the two cores without much loss of the envelope. In between there is a regime in which the final separation is such that pre-cataclysmic variables can be formed. The remnant magnetic fields provide a simple explanation for the considerable range in white dwarf fields from polars to non-magnetic cataclysmic variables.