The observed velocity distribution of young pulsars

Institute of Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
e-mail: F.Verbunt@astro.ru.nl; A.Igoshev@astro.ru.nl; E.Cator@science.ru.nl

Received: 6 July 2017
Accepted: 29 September 2017

Abstract

We argue that comparison with observations of theoretical models for the velocity distribution of pulsars must be done directly with the observed quantities, that is parallax and the two components of proper motion. We have developed a formalism to do so, and applied it to pulsars with accurate VLBI measurements. For computational convenience, we model the data with Maxwellians. We find that a distribution with two Maxwellians improves significantly on a single Maxwellian. The “mixed” model takes into account that pulsars move away from their place of birth, a narrow region around the Galactic plane. The best model has 42% of the pulsars in a Maxwellian with average velocity $\mathit{\sigma }\sqrt{\mathrm{8}\mathit{/}\mathit{\pi }}\mathrm{=}\mathrm{120}$ km s^-1, and 58% in a Maxwellian with average velocity 540 km s^-1. About 5% of the pulsars has a velocity at birth less than 60 km s^-1. For the youngest pulsars (τ_c < 10 Myr), these numbers are 32% with 130 km s^-1, 68% with 520 km s^-1, and 3%, with appreciable uncertainties. Our analysis shows that the velocity distribution is wider than can be described with a single Maxwellian; it does not prove that two Maxwellians provide a better description than other wide models.