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A model for the formation and evolution of binary millisecond radio pulsarsin systems with low mass companions (< 0.1 Msun) is investigated using a binarypopulation synthesis technique. Taking into account the non conservativeevolution of the system due to mass loss from an accretion disk as a result ofpropeller action and from the companion via ablation by the pulsar, thetransition from the accretion powered to rotation powered phase isinvestigated. It is shown that the operation of the propeller and ablationmechanisms can be responsible for the formation and evolution of black widowmillisecond pulsar systems from the low mass X-ray binary phase at an orbitalperiod of ~0.1 day. For a range of population synthesis input parameters, theresults reveal that a population of black widow millisecond pulsarscharacterized by orbital periods as long as ~0.4 days and companion masses aslow as ~0.005 Msun can be produced. The orbital periods and minimum companionmass of this radio millisecond pulsar population critically depend on thethermal bloating of the semi-degenerate hydrogen mass losing component, withlonger orbital periods for a greater degree of bloating. Provided that theradius of the companion is increased by about a factor of 2 relative to a fullydegenerate, zero temperature configuration, an approximate agreement betweenobserved long orbital periods and theoretical modeling of hydrogen rich donorscan be achieved. We find no discrepancy between the estimated birth rates forLMXBs and black widow systems, which on average are $\sim~1.3\times10^{-5} {\rmyr}^{-1}$ and $1.3\times10^{-7} {\rm yr}^{-1}$ respectively.

Accretion, Ablation and Propeller Evolution in Close Millisecond Pulsar Binary Systems