Prospects for detecting dark matter halo substructure with pulsar timing

One of the open questions of modern cosmology is the nature and properties of the dark matter halo and its substructures. In this work we study the gravitational effect of dark matter substructures on pulsar timing observations. Since millisecond pulsars are stable and accurate emitters, they have been proposed as plausible astrophysical tools to probe the gravitational effects of dark matter structures. We study this effect on pulsar timing through Shapiro time delay (or integrated Sachs-Wolfe (ISW) effect) and Doppler effects statistically, showing that the latter dominates the signal. For this task, we relate the power spectrum of pulsar frequency change to the matter power spectrum on small scales, which we compute using the stable clustering hypothesis, as well as other models of nonlinear structure formation. We compare this power spectrum with the reach of current and future observations of pulsar timing designed for gravitational wave detection. Our results show that while current observations are unable to detect these signals, the sensitivity of the upcoming square kilometer array is only a factor of few weaker than our optimistic predictions.