The origin of single radio pulsars

By comparing relative rates of supernovae versus formation rates of single radio pulsars, recycled pulsars, binary pulsars and X-ray binaries we put strong limits on the progenitors of radio pulsars and on the requirement of an asymmetry in the supernova. The assumption that radio pulsars are only formed in type Ib and type Ic supernovae from interacting binaries (Iben & Tutukov, 1998) breaks down on the implication that in that case either the formation rate of binary pulsars (double neutron stars) should be of the order of 20% of the single pulsar birth rate or, alternatively, almost all single pulsars (85% to 98%) should originate from Thorne-Żytkow stars. In the latter case the pulsar velocity distribution is inconsistent with observations. Also, in that case the difference between the supernova rate and the pulsar formation rate would be about one order of magnitude, i.e. much larger than observed. Allowing type II supernovae from single stars and non-interacting binaries to form radio pulsars solves this conundrum, but then a kick is required in order to explain the high velocities of single radio pulsars. A kick is also required to understand the small birth rate, relative to the supernova rate, of binary pulsars consisting of two neutron stars.