Aspects of mass transfer in X-ray binaries: a model for three classes of binary millisecond pulsars.

The possibility that some close binary systems in their X-ray phase evolve into a second common envelope and spiral-in phase is very important for the formation of short orbital period binary millisecond pulsars. We demonstrate how simple "bifurcation mechanisms" may lead to the existence of three classes of binary millisecond pulsars and a possible gap in the orbital period distribution. Recent discoveries indicate such a gap could exist. Furthermore, we demonstrate that the expected theoretical correlation between orbital periods and white dwarf companion masses does not seem to fit recent observations of wide-orbit (P_orb_>100days) low-mass binary pulsars....