On the Initial Spin Period Distribution of Neutron Stars

We derive the initial spin period distribution of neutron stars by studying the population of young pulsars associated with supernova remnants. Our hierarchical Bayesian approach accounts for the measurement uncertainties of individual observations and selection effects. Without correcting for selection effects, as done in previous studies, we find that pulsar initial spin periods follow a Weibull distribution, peaking at 40 ms, which is favored against a lognormal distribution with a Bayes factor of 200. The known selection effects in radio pulsar surveys, including pulse broadening and period-dependent beaming fraction, have been quantitatively investigated. We show that, based on measurements of pulsar luminosity and spin period from the ATNF Pulsar Catalogue, the impact of pulse broadening on the inference of the pulsar period distribution is likely to be insignificant. Correcting for the beaming selection effect, the Weibull distribution remains the preferred model, while its peak slightly shifts to longer periods at 50 ms. Our method will prove useful in constraining the birth properties of neutron stars in the Square Kilometre Array era.