The observed velocity distribution of young pulsars

TL;DR

This paper develops a formalism to compare pulsar velocity models directly with observations, finding a two-maxwellian distribution best explains the observed velocities, with implications for pulsar birth velocities.

Contribution

It introduces a formalism for direct comparison of pulsar velocity models with observed parallax and proper motion data, and demonstrates that a two-maxwellian model fits the data better than a single one.

Findings

A two-maxwellian velocity distribution significantly improves fit over a single Maxwellian.

Approximately 42% of pulsars have velocities around 120 km/s, and 58% around 540 km/s.

A small fraction (~5%) of pulsars have very low birth velocities (<60 km/s).

Abstract

We argue that comparison with observations of theoretical models for the velocity distribution of pulsars must be done directly with the observed quantities, i.e. parallax and the two components of proper motion. We develop a formalism to do so, and apply it to pulsars with accurate VLBI measurements. 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 sigma sqrt{8/pi}=120 km/s, and 58% in a maxwellian with average velocity 540 km/s. About 5% of the pulsars has a velocity at birth less than 60\,km/s. For the youngest pulsars (tau_c<10 Myr), these numbers are 32% with 130 km/s, 68% with 520 km/s, and 3%, with appreciable uncertainties.