Detection of a dark matter sub-halo near the Sun from pulsar timing

Using pulsar accelerations, we identify and constrain the properties of a dark matter sub-halo in the Galaxy for the first time from analyzing the acceleration field of binary and solitary pulsars. The sub-halo is characterized by analyzing a local deviation from a smooth potential. We are able to constrain both the mass and location of the sub-halo. The Bayes factors for the models are in the range of $\sim$ 20-40, which indicate strong evidence (though not yet decisive) for the sub-halo. We examine \textit{Gaia} data and the atomic and molecular hydrogen data of our Galaxy and show that the measured deviation from a smooth potential cannot arise from the gas or the stars in our Galaxy. Additionally, by analyzing the full sample of binary pulsars with available acceleration measurements that span 3.4 kpc in Galactocentric radius from the Sun and 3.6 kpc in vertical height, we find that massive (with mass $>10^{8}~M_{\odot}~$) sub-halos are disfavored for the Milky Way within several kiloparsec of the Sun. While smaller sub-halos may be present, they are beyond the reach of current direct acceleration measurements. The presence of a $\sim 10^{7}~M_{\odot}$ sub-halo within a few kpc of the Sun is potentially consistent with the expected number counts of sub-halos in the prevailing $\Lambda$CDM paradigm, for a substantial sub-halo mass fraction. As the number and precision of direct acceleration measurements continues to grow, we will obtain tighter constraints on dark matter sub-structure in our Galaxy. These measurements now open a new avenue for studying dark matter and have implications across many fields of astrophysics - from understanding the nature of dark matter to galaxy formation.