Supernova kicks, magnetic braking, and neutron star binaries

We consider the formation of low-mass X-ray binaries (LMXBs) containing accreting neutron stars via the helium star supernova channel. The predicted relative number of short-period transients provides a sensitive test of the input physics in this process. We investigate the effect of varying mean kick velocities, orbital angular momentum loss efficiencies, and common-envelope ejection efficiencies on the subpopulation of short-period systems, both transient and persistent. Guided by the thermal-viscous disk instability model in irradiation-dominated disks, we posit that short-period transients have donors close to the end of core hydrogen burning. We find that with increasing mean kick velocity the overall short-period fraction, s, grows, while the fraction r of systems with evolved donors among short-period systems drops. This effect, acting in opposite directions on these two fractions, allows us to constrain models of LMXB formation through comparison with observational estimates of s and r. Without fine tuning or extreme assumptions about evolutionary parameters, consistency between models and current observations is achieved for a regime of intermediate average kick magnitudes of about 100-200 km s^-1, provided that (1) orbital braking for systems with donor masses in the range 1-1.5 M_⊙ is weak, i.e., much less effective than a simple extrapolation of standard magnetic braking beyond 1.0 M_⊙ would suggest, and (2) the efficiency of common-envelope ejection is low.