Young single pulsars are observed to move in the sky at speeds of many hundreds of kilometres per second.  These high speeds are imparted by asymmetries in the supernova explosions that give birth to the neutron stars.  Measuring the distribution of these birth kicks is important for understanding supernova explosions.  It is also necessary to explain how neutron stars are retained in clusters with escape velocities of only a few tens of kilometres per second, and for predicting how often neutron star birth kicks will disrupt binaries, flinging out a newly born neutron star.  The latter is particularly relevant for the formation of neutron star binaries that can be observed in radio waves, X-rays, or, if merging with another neutron star or black hole, as gravitational waves.

We can generally measure only two components of a pulsar’s motion: the projection onto the plane of the sky.  This is done by multiplying the proper motion by the distance to the pulsar.  The third component of the motion, along the radial direction connecting the Earth and the pulsar, cannot be measured directly.

The total speed is generally inferred by assuming that the radial component is not special: that, on average, its magnitude samples the same distribution as the two observed velocity components.  However, in a paper published in the Astrophysical Journal in 2023 (ApJ 944, 153), OzGrav CI Ilya Mandel (Monash) and collaborator Andrei Igoshev (Leeds) argued that this is not the case, and the radial motion direction can indeed be special.

This paper, entitled “The impact of spin-kick alignment on the inferred velocity distribution of isolated pulsars”, points out that if pulsar kick direction is preferentially aligned with the pulsar rotational (spin) axis, then the very detectability of the pulsar — which requires that the beam of the pulsar sometimes, but not always, sweeps past our radio telescopes on Earth — creates a special direction.

Consider, for example, a pulsar that is emitting two narrow beams of radiation at 90 degrees to its spin axis.  This pulsar could only be detected by an observer located in the pulsar’s equatorial plane.  Suppose that the pulsar’s rotation axis is perfectly aligned with the spin axis.  In that case, the pulsar has no radial velocity component: the projected 2-dimensional velocity on the plane of the sky represents the full pulsar speed.  Alternatively, if we imagined that the 2-dimensional velocity we see was a random projection of the full velocity, we would systematically over-estimate the pulsar’s speed by a factor of sqrt(3/2).

The exact level of such a bias depends on the degree of misalignment between the pulsar spin and its radio beams, the size of these beams, and the level of kick-spin alignment.  While some of these quantities are uncertain, Mandel & Igoshev conclude that pulsar velocities may be over-estimated by up to ~15% by methods that don’t account for this systematic bias.

Written by OzGrav Chief Investigator Ilya Mandel and Andrei P. Igoshev, University of Leeds.