Origin and Binary Evolution of Millisecond Pulsars

We review the channels of formation, the orbital and the spin evolution of neutron stars (NSs) in binary systems that lead to the formation of millisecond pulsars (MSP), in the context of the recycling scenario. The basics of binary evolution and the key concepts of angular momentum losses are given. After discussing the case of Cataclysmic Variables and long-period MSP binaries with a compact companion, we focus on the evolution of systems with a short orbital period and a low companion mass, in which the recycling phase can be caught ‘in the act’. IrradiationIrradiation of the companion by the NS (either in the accretion or in the radio MSP stage) plays a central role in the evolution of these systems, possibly causing cyclic LMXB stages which would help to explain the high positive $${{\dot {P}}_{\mathrm {orb}}}$$ ’s of some LMXB systems, and account for the (apparently) different birthrates Birthrate of LMXB and MSP. Irradiation Irradiation by the MSP may also be able to drive the donor to a stage in which either radio-ejection Radio-ejection (in the redbacks) or mass loss due to the companion expansion, may govern the evolution to the black widow stage and to the final disruption of the companion.