The impact of spin-kick alignment on the inferred velocity distribution of isolated pulsars

The speeds of young isolated pulsars are generally inferred from their observed 2-d velocities on the plane of the sky under the assumption that the unobserved radial velocity is not special, i.e., that the measured 2-d velocity is an isotropic projection of the full 3-d velocity. However, if pulsar spins are preferentially aligned with kicks, then the observer's viewing angle relative to the pulsar velocity vector is in fact special because the direction of the spin impacts the detectability of the pulsar. This means that the measured 2-d velocity of observable pulsars is not an isotropic projection, which affects inference on 3-d velocities. We estimate this effect and conclude that it could lead to a ~15% systematic over-estimate of neutron star natal kicks if young pulsars have high obliquity angles and narrow beams, but the exact correction factor depends on the distribution of beam-spin and spin-kick misalignment angles and beam widths.