2002ApJ...564..930L

Binary and millisecond pulsars (BMSPs) with He white dwarf companions are generally thought to be recycled in low-mass X-ray binaries (LMXBs). Here we investigate the formation of three recently discovered binary pulsars: PSRs J1232-6501, J1810-2005, and J1904+0412. These pulsars are in circular orbits with low-mass white dwarf companions, but their spin periods and period derivatives are considerably larger than that of most BMSPs. It has been suggested that these mildly recycled pulsars are descendants of intermediate-mass X-ray binaries (IMXBs), in which, due to higher mass transfer rates and shorter evolutionary timescales, smaller amounts of mass may be accreted by the neutron stars than in LMXBs. As a demonstration, we calculate the evolution of the possible IMXB progenitor system: a binary consisting of a 1.3 M_☉ neutron star and a 3.0 M_☉ main-sequence star. The results show that after a short, rapid mass transfer phase, the binary evolves into an LMXB, with nearly all of the transferred mass accreted by the neutron star. Thus, low-mass binary pulsars born in this way should have masses (and hence spin periods and magnetic fields) comparable to those from LMXBs. To account for the discrepancy between the mildly recycled pulsars and BMSPs, we suggest that the accretion disks in some IMXBs may suffer thermal-viscous instability when they evolve to low-mass systems and the mass transfer rate declines. This may greatly reduce the active X-ray time and the amount of mass transferred onto the neutron stars and help alleviate the LMXB-BMSP birthrate problem.