Simulations of Shapiro, Gravitational, and Doppler time delays in pulsar networks for ultralight dark matter

The study of ultralight dark matter helps to constrain the lower bound of the mass in minimally coupled dark matter models. The granular structure of ultralight dark matter density fields produces metric perturbations which have been identified as a potentially interesting probe of this model. For dark matter masses $m\ensuremath{\gtrsim}{10}^{\ensuremath{-}17}\text{ }\text{ }\mathrm{eV}$, these perturbations would fluctuate on timescales comparable to observational timescales. In this paper, we estimate the expected time delay these fluctuations would generate in simulated pulsar signals. We simulate arrays of mock pulsars in a fluctuating granular density field. We calculate the expected Shapiro time delay, gravitational redshift, and Doppler shift and compare analytical estimates with the results of simulations. Finally, we provide a comparison with existing pulsar observation sensitivities.