A kinematically constrained kick distribution for isolated neutron stars

¹ Department of Astrophysics/IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, The Netherlands
² School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
³ The ARC Center of Excellence for Gravitational Wave Discovery – OzGrav, Australia
⁴ Department of Physics, University of Warwick, Coventry CV4 7AL, UK

^★ Corresponding author: paul.disberg@monash.edu

Received: 3 March 2025
Accepted: 1 July 2025

Abstract

Context. The magnitudes of the velocity kicks that neutron stars (NSs) obtain at their formation have long been a topic of discussion, with the latest studies analysing the velocities of young pulsars and favouring a bimodal kick distribution.

Aims. In previous work, a novel method was proposed to determine kicks based on the eccentricity of Galactic trajectories, which is also applicable to older objects. We applied this method to the isolated pulsars with a known parallax – both young and old – in order to kinematically constrain the NS natal kick distribution and investigate its proposed bimodality. Since this method is applicable to older pulsars, we effectively increase the sample size with ~50% compared to the pulsars younger than 10 Myr.

Methods. We assumed the velocity vectors of the pulsars to be distributed isotropically in the local standard of rest frame, and for each pulsar we sampled 100 velocities taking into account this assumption. These velocity vectors were used to trace back the trajectories of the NSs through the Galaxy and estimate their eccentricity. Then, we simulated kicked objects in order to evaluate the relationship between kick magnitude and Galactic eccentricity, which was used to infer the kicks corresponding to the estimated eccentricities.

Results. The resulting kick distributions indeed show a bimodal structure for young pulsars and our fits resemble the ones from literature well. However, for older pulsars the bimodality vanishes and instead we find a log-normal kick distribution peaking at ~200 km/s and a median of ~400 km/s (for velocities below 1000 km/s). We also compare our methods to literature that suggests natal kicks are significantly higher and follow a Maxwellian with σ = 265 km/s. We cannot reproduce these results using their sample and distance estimates, and instead find kicks that are consistent with our proposed distribution.

Conclusions. We conclude that our kinematically constrained kick distribution is well described by a log-normal distribution with μ = 6.38 and σ = 1.01, normalised between 0 and 1000 km/s. This analysis reveals no evidence for bimodality in the larger sample, and we suggest that the bimodality found by existing literature may be caused by their relatively small sample size.