Dark matter substructure on small scales is currently weakly constrained, and its study may shed light on the nature of the dark matter. In this work we study the gravitational effects of dark matter substructure on measured pulsar phases in pulsar timing arrays (PTAs). Due to the stability of pulse phases observed over several years, dark matter substructure around the Earth-pulsar system can imprint discernible signatures in gravitational Doppler and Shapiro delays. We compute pulsar phase correlations induced by general dark matter substructure, and project constraints for a few models such as monochromatic primordial black holes (PBHs), and Cold Dark Matter (CDM)-like NFW subhalos. This work extends our previous analysis, which focused on static or single transiting events, to a stochastic analysis of multiple transiting events. We find that stochastic correlations, in a PTA similar to the Square Kilometer Array (SKA), are uniquely powerful to constrain subhalos as light as ∼10⁻¹³ M⊙, with concentrations as low as that predicted by standard CDM.

中文翻译：

---

暗物质子结构的可观测性与脉冲星时间相关性

小尺度暗物质亚结构目前受到弱约束，其研究可能有助于揭示暗物质的本质。在这项工作中，我们研究了暗物质子结构对脉冲星定时阵列 (PTA) 中测量的脉冲星相位的引力影响。由于多年来观察到的脉冲相位的稳定性，地球-脉冲星系统周围的暗物质子结构可以在引力多普勒和夏皮罗延迟中留下可辨别的特征。我们计算由一般暗物质子结构引起的脉冲星相位相关性，并为一些模型预测约束，例如单色原始黑洞 (PBH) 和类似冷暗物质 (CDM) 的 NFW 亚晕。这项工作将我们之前专注于静态或单个过渡事件的分析扩展到对多个过渡事件的随机分析。