A New Class of High-Mass X-ray Binaries: Implications for Core Collapse and Neutron-Star Recoil

We investigate an interesting new class of high-mass X-ray binaries (HMXBs) with long orbital periods (P_orb > 30 days) and low eccentricities (e <~ 0.2). The orbital parameters suggest that the neutron stars in these systems did not receive a large impulse, or ``kick,'' at the time of formation. We develop a self-consistent phenomenological picture wherein the neutron stars born in the observed wide HMXBs receive only a small kick (<~ 50 km/s), while neutron stars born in isolation, in the majority of low-mass X-ray binaries, or in many of the well-known HMXBs with P_orb <~ 30 days receive the conventional large kicks, with a mean speed of ~ 300 km/s. We propose that the magnitude of the natal kick to a neutron star born in a binary system depends on the rotation rate of the pre-collapse core. We further suggest that the rotation rate of the core is a strong, well-defined function of the evolutionary path of the progenitor star.