Theoretical Considerations on the Properties of Accreting Millisecond Pulsars

We examine a number of evolutionary scenarios for the recently discovered class of accretion-powered millisecond X-ray pulsars in ultracompact binaries, including XTE JO929-314 and XTE J1751-305. These systems have very short orbital periods of Porb = 43.6 and 42.4 minutes, respectively, and extremely small mass functions. We focus on a particular scenario that can naturally explain the present-day properties of these systems. This model invokes a donor star that was either very close to the main-sequence turnoff at the onset of mass transfer or had sufficient time to evolve during the mass-transfer phase. We have run a systematic set of binary evolution calculations with a wide range of initial conditions.