The Kick Velocity Distribution of Isolated Neutron Stars

Abstract: Neutron stars (NSs) are thought to receive natal kicks at their formation in supernovae. In order to investigate the magnitude of these kicks, we analyze the proper motions and distance estimates -- either through parallax or dispersion measures -- of young isolated pulsars and infer their three-dimensional velocities relative to their local standard of rest. We find that the velocities based on parallax distances of pulsars younger than $10$ Myr follow a log-normal distribution with a mean of $\ln\left(v/\text{km}/\text{s}^{-1}\right)=5.60\pm0.12$ and a standard deviation of $0.68\pm0.10$, peaking at ${\sim}150$--$200$ km s$^{-1}$, which we adopt as our fiducial kick distribution. Using a previously established method that infers kick magnitudes through the eccentricity of Galactic trajectories, we also estimate the kick velocities of older pulsars, which we find to be consistent with our fiducial kick distribution. A log-normal fit to all pulsars with ages below $40$ Myr yields a more constraining (but possibly more prone to systematic errors) fit with mean and standard deviation of $5.67\pm0.10$ and $0.59\pm0.08$, respectively. Moreover, we (1) resolve the tension between our results and the Maxwellian distribution found by Hobbs et al. (2005), which has a ${\sim}50\%$ higher median velocity, by showing that their analysis is missing a Jacobian needed to correct for its logarithmic histogram bin sizes, and (2) argue that the bimodality found by others is not statistically significant and that previous results are consistent with our inferred kick distribution, effectively reconciling the literature on observed NS kicks.