Formation of millisecond pulsars I. Evolution of low-mass X-ray binaries with Porb > 2 days

We have performed detailed numerical calculations of the non-conservative evolution of close binary systems with low-mass (1.0 − 2.0M⊙) donor stars and a 1.3M⊙ accreting neutron star. Rather than using analytical expressions for simple polytropes, we calculated the thermal response of the donor star to mass loss, in order to determine the stability and follow the evolution of the mass transfer. Tidal spin-orbit interactions and Reimers wind mass-loss were also taken into account. We have re-calculated the correlation between orbital period and white dwarf mass in wide binary radio pulsar systems. Furthermore, we find an anti-correlation between orbital period and neutron star mass under the assumption of the ”isotropic re-emission” model and compare this result with observations. We conclude that the accretion efficiency of neutron stars is rather low and that they eject a substantial fraction of the transferred material even when accreting at a sub-Eddington level. The mass-transfer rate is a strongly increasing function of initial orbital period and donor star mass. For relatively close systems with light donors (Porb < 10 days and M2 < 1.3M⊙) the mass-transfer rate is sub-Eddington, whereas it can be highly super-Eddington by a factor of ∼ 10 for wide systems with relatively heavy donor stars (1.6 ∼ 2.0M⊙) as a result of their deep convective envelopes. We briefly discuss the evolution of X-ray binaries with donor stars in excess of 2M⊙. Based on our calculations we present evidence that PSR J1603–7202 evolved through a phase with unstable mass transfer from a relatively heavy donor star and therefore is likely to host a CO white dwarf companion.