Evidence for the spin-kick alignment of pulsars from the statistics of their magnetic inclinations

It is thought that isolated neutron stars receive a natal kick velocity at birth nearly aligned with their spin axis. Direct observational confirmation of this alignment is currently limited to a single source in a supernova remnant (PSR J0538+2817), for which the three-dimensional velocity has been well constrained. Meanwhile, pulsar polarisation statistics suggest the existence of a spin-kick correlation, though both aligned and orthogonal cases remain possible. However, if the velocities of radiopulsars are predominantly aligned with their spin axes, a systematic difference in the observed transverse velocities of pulsars with small and large magnetic obliquities would be expected. In particular, due to projection effects, weakly oblique rotators should exhibit smaller, less scattered transverse velocities. Conversely, the transverse velocities of pulsars with large magnetic inclination should reflect their actual three-dimensional velocities. This study uses this idea to analyse samples of 13 weakly and 25 strongly oblique pulsars with known distances and proper motions. We find that their peculiar velocities are distributed differently, with statistical confidence levels of 0.007 and 0.016 according to the Anderson-Darling and Kolmogorov-Smirnov tests, respectively. We performed a detailed population synthesis of isolated pulsars, considering the evolution of their viewing geometry in isotropic and spin-aligned kick scenarios. The observed split in the transverse velocity distributions and its amplitude are consistent with the spin-aligned kick model, but not with the isotropic case. At the same time, an orthogonal kick would predict a similar effect, but with the opposite sign. This provides robust support for pulsar spin kick alignment based on statistics, independently of polarisation.