Birth Kick Distributions and the Spin-Kick Correlation of Young Pulsars
Evidence from pulsar wind nebula symmetry axes and radio polarization observations suggests that pulsar motions correlate with the spin directions. We assemble this evidence for young isolated pulsars and show how it can be used to quantitatively constrain birth kick scenarios. We illustrate by computing several plausible, but idealized, models where the momentum thrust is proportional to the neutrino cooling luminosity of the proto-neutron star. Our kick simulations include the effects of pulsar acceleration and spin-up and our maximum likelihood comparison with the data constrains the model parameters. The fit to the pulsar spin and velocity measurements suggests that: i) the anisotropic momentum required amounts to ~10% of the neutrino flux, ii) while a pre-kick spin of the star is required, the preferred magnitude is small 10-20rad/s, so that for the best-fit models iii) the bulk of the spin is kick-induced with $\bar Ω$ ~120rad/s and iv) the models suggest that the anisotropy emerges on a timescale $τ$ ~1-3s.