Ultralight Dark Matter Statistics for Pulsar Timing Detection

TL;DR

This paper develops a statistical framework for detecting ultralight dark matter via pulsar timing, emphasizing the importance of dark matter field coherence and its impact on metric fluctuation correlations.

Contribution

It introduces a consistent statistical method for ultralight dark matter detection, deriving the two-point function of metric fluctuations relevant for pulsar timing arrays.

Findings

Derived the two-point function of metric fluctuations due to ultralight dark matter.

Highlighted the importance of dark matter coherence length in pulsar timing analysis.

Provided a framework for incorporating dark matter statistics into future detection efforts.

Abstract

Fluctuations in ultralight dark matter produce significant metric perturbations, which may be detected by monitoring the arrival times of light from millisecond pulsars. While searches using this technique are already underway, they do not consistently account for the statistical properties of the dark matter field. The statistics of this field depend on the velocity dispersion of dark matter and, consequently, its coherence length. In the mass range relevant for pulsar timing arrays, the coherence length is comparable to separations between pulsars, making it crucial to incorporate its effects into the analysis. This work presents a consistent statistical method for gravitational direct detection of ultralight dark matter. Our key result is the derivation of the two-point function of the metric fluctuations, which we apply to pulsar timing and discuss its implementation in future searches.