On the progenitors of millisecond pulsars by the recycling evolutionary channel

The recycling model suggested that low-mass X-ray binaries (LMXBs) could evolve into binary millisecond pulsars (BMSPs). In this work, we attempt to investigate the progenitor properties of BMSPs formed by the recycling evolutionary channel, and if sub-millisecond pulsars can be produced by this channel. Using Eggleton's stellar evolution code, considering that the dead pulsars can be spun up to a short spin period by the accreting material and angular momentum from the donor star, we have calculated the evolution of close binaries consisting of a neutron star and a low-mass main-sequence donor star, and the spin evolution of NSs. In calculation, some physical process such as the thermal and viscous instability of a accretion disk, propeller effect, and magnetic braking are included. Our calculated results indicate that, all LMXBs with a low-mass donor star of 1.0 - 2.0 $M_\odot$ and a short orbital period ($\la 3-4 \rm d$) can form millisecond pulsars with a spin period less than 10 ms. However, it is difficult to produce sub-millisecond pulsars by this evolutionary channel. In addition, our evolutionary scenario cannot account for the existence of BMSPs with a long orbital period ($P_{\rm orb}\ga 70-80\rm d$).