Challenges in Binary Pulsar Timing Detection of Dark Matter Subhalos

Abstract

Recently, binary pulsar timing has been proposed as a viable probe of dark matter subhalos with masses of $\sim 10^7\,M_{\odot}$ in the solar neighborhood. We present a comprehensive analytical framework that incorporates the subhalo mass function, projection effects of line-of-sight acceleration, and the spatiotemporal geometric requirements for joint detection by binary systems, enabling a quantitative evaluation of the detectability of nearby subhalos. Applying this framework to the current binary pulsar sample, we find a probability $\leq 1.6 \times 10^{-4}$ of detecting at least one subhalo within the effective volume. An independent timing residual analysis shows no statistically significant excess in line-of-sight accelerations beyond predictions from data-driven Galactic gravitational potential models. These results place stringent constraints on detecting $<10^8~M_{\odot}$ dark matter subhalos with existing pulsar timing data, aligning with the theoretical expectation that such subhalos have a low survival probability in the solar neighborhood. A low detection prospect still holds even for future Square Kilometre Array observations.

Figures (2)

• Figure 1: Geometric configuration and effective detection volumes for joint subhalo detection by binary pulsars. (a) Detection method. Light blue regions show the effective detection range of an individual pulsar, shaped by the LOS acceleration projection factor $r_{\rm det} \propto \sqrt{|\cos\theta|}$, forming an axisymmetric bi-lobed volume. The dark blue marks the intersection of two such volumes; a subhalo can be jointly detected only within this overlap, enabling positional constraints. (b) Detection geometry for the six neighboring binary pulsar pairs in this study. Dotted circles indicate the reference detection limit for an ideal acceleration sensitivity of $1.0 \times 10^{-9}\,\mathrm{m\,s^{-2}}$. Each panel shows the projected positions of a binary pair relative to the Sun (yellow dot). Red and blue regions represent the sensitivity lobes of each pulsar to a $10^7\,M_\odot$ subhalo under current precision; purple shading marks their joint volume. At least one subhalo must lie in this overlap to yield a joint detection, with theoretical probability $\mathcal{P}_{\rm det}$.
• Figure 2: Comparison of distance and residual distributions for high-precision (J1713+0747) and low-precision (J1640+2224) pulsars. Upper panel: Violin plots of $\dot{P}_{\rm res}$ using Gala2022. MC propagation of asymmetric distance errors revises significance downward ($2.59\sigma \rightarrow 1.93\sigma$), showing that Gaussian assumptions can inflate significance in low-precision systems. We note that $\dot{P}_{\rm GW}$ is negligible and omitted. Lower panel: Distance PDFs. For J1640+2224, MC sampling (grey dashed) reveals the non-Gaussian long tail from $d=1/\varpi$, while GEP (green) underestimates the uncertainty.