Investigating dark matter substructure with pulsar timing – I. Constraints on ultracompact minihaloes

Abstract

Small-scale dark matter structure within the Milky Way is expected to affect pulsar timing. The change in gravitational potential induced by a dark matter halo passing near the line of sight to a pulsar would produce a varying delay in the light travel time of photons from the pulsar. Individual transits produce an effect that would either be too rare or too weak to be detected in 30-year pulsar observations. However, a population of dark matter subhalos would be expected to produce a detectable effect on the measured properties of pulsars if the subhalos constitute a significant fraction of the total halo mass. The effect is to increase the dispersion of measured period derivatives across the pulsar population. By statistical analysis of the ATNF pulsar catalogue, we place an upper limit on this dispersion of $\log \sigma_{\dot{P}} \leq -17.05$. We use this to place strong upper limits on the number density of ultracompact minihalos within the Milky Way. These limits are completely independent of the particle nature of dark matter.