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Dark matter substructure, such as primordial black holes (PBHs) and axionminiclusters, can induce phase shifts in pulsar timing arrays (PTAs)measurements due to gravitational effects. In order to gain a more realisticforecast for the detectability of such models of dark matter with PTAs, wepropose a Bayesian inference framework to search for phase shifts generated byPBHs and perform the analysis on mock PTA data. For most PBH masses theconstraints on the dark matter abundance agree with previous (frequentist)analyses (without mock data) to $\mathcal{O}(1)$ factors. This furthermotivates a dedicated search for PBHs (and dense small scale structures) in themass range from $10^{-8}\,M_{\odot}$ to well above $10^2\,M_{\odot}$ with theSquare Kilometer Array. Moreover, with a more optimistic set of timingparameters, future PTAs are predicted to constrain PBHs down to$10^{-11}\,M_{\odot}$. Lastly, we discuss the impact of backgrounds, such asSupermassive Black Hole Mergers, on detection prospects, suggesting a futureprogram to separate a dark matter signal from other astrophysical sources.

Bayesian Forecasts for Dark Matter Substructure Searches with Mock Pulsar Timing Data