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

TL;DR

This paper develops a Bayesian inference framework to detect dark matter substructures like primordial black holes using pulsar timing data, providing realistic forecasts and constraints for future observations.

Contribution

It introduces a Bayesian method for analyzing pulsar timing data to search for dark matter-induced phase shifts, improving detection prospects and constraints compared to previous analyses.

Findings

Constraints on PBH abundance align with previous results for most masses.

Future PTAs could detect PBHs as small as 10^{-11} M_sun with optimistic timing.

Background sources like SMBH mergers can affect detection and need to be distinguished.

Abstract

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