Spin and orbital evolution in low-mass binary pulsars

We consider the spin and orbital evolution of low-mass binary radio pulsars which are not members of globular clusters. We show that their current spin periods can be understood in terms of their likely mass-transfer history. Systems with orbital periods greater than or similar to 50 days are the endpoints of low-mass X-ray binaries whose orbital evolution is driven by the nuclear expansion of the secondary. For shorter periods, orbital angular momentum losses are significant, and the mass-transferring progenitor undergoes a phase of Eddington or super-Eddington mass transfer which spins up the neutron star to an Eddington-limited equilibrium period. These systems subsequently enter a propeller phase and are probably undetectable as low-mass X-ray binaries, largely resolving the inferred discrepancy between the current number of binary pulsars and their likely progenitors. Spin-down of the neutron stars in this propeller phase is evidently ineffective. The observed relation between spin period, magnetic field, and orbital period is in apparent agreement with simple ideas of the equilibrium spin period but requires much lower fastness parameters than predicted by current theory.