Constraining dark matter sub-structure with the dynamics of   astrophysical systems
  The accuracy of the measurements of some astrophysical dynamical systems allows to constrain the existence of incredibly small gravitational perturbations. In particular, the internal Solar System dynamics (planets, Earth-Moon) opens up the possibility, for the first time, to prove the abundance, mass and size, of dark sub-structures at the Earth vicinity. We find that adopting the standard dark matter density, its local distribution can be composed by sub-solar mass halos with no currently measurable dynamical consequences, regardless of the mini-halo fraction. On the other hand, it is possible to exclude the presence of dark streams with linear mass densities higher than $\lambda_{\rm st}> 10^{-10} \Msun/\AU$ (about the Earth mass spread along the diameter of the SS up to the Kuiper belt). In addition, we review the dynamics of wide binaries inside the dwarf spheroidal galaxies in the MW. The dynamics of such kind of binaries seem to be compatible with the presence of a huge fraction of dark sub-structure, thus their existence is not a sharp discriminant of the dark matter hypothesis as been claimed before. However, there are regimes where the constraints from different astrophysical systems may reveal the sub-structure mass function cut-off scale. 
Alma X. Gonzalez-Morales, Octavio Valenzuela and Luis A. Aguilar
astro-ph.CO