Formation of binary millisecond pulsars by accretion-induced collapse of white dwarfs

It has generally been assumed that neutron stars (NSs) that become millisecond pulsars (MSPs) originated in a core-collapse supernova. The possibility of formation by accretion-induced collapse (AIC) of an oxygen/neon white dwarf (WD) has largely been ignored or considered negligible. Here, we demonstrate that population synthesis calculations with generic assumptions yield birthrates of binary MSPs via AIC that are comparable to and can exceed those for core collapse. Allowing both modes for NS formation, we estimate birthrates and orbital period distributions and compare these with observations of binary MSPs and low-mass X-ray binaries. Our calculations show that both the core-collapse and AIC routes lead to populations of binary systems that can be identified with X-ray binaries while transferring matter and binary MSPs at the end of an accretion phase. The estimated birthrates indicate that the often-neglected AIC route cannot be ignored. It also appears that this route can provide a better match to the period distributions of some types of binary MSPs. In particular, it appears to be the major route to the orbital period distribution of long-period (a few days or greater) systems with helium WD companions under certain model assumptions. The birthrate problem confronting the low- and intermediate-mass X-ray binaries remains but can still be resolved by invocation of irradiation-driven limit cycles.