Constraints on dark matter in the solar system

Abstract

We have searched for and estimated the possible gravitational influence of dark matter in the Solar system based on the EPM2011 planetary ephemerides using about 677 thousand positional observations of planets and spacecraft. Most of the observations belong to present-day ranging measurements. Our estimates of the dark matter density and mass at various distances from the Sun are generally overridden by their errors ($\sigma$). This suggests that the density of dark matter ${\rho}_{dm}$, if present, is very low and is much less than the currently achieved error of these parameters. We have found that ${\rho}_{dm}$ is less than $1.1\cdot10^{-20}$ g cm$^{-3}$ at the orbital distance of Saturn, ${\rho}_{dm}<1.4\cdot10^{-20}$ g cm$^{-3}$ at the orbital distance of Mars, and ${\rho}_{dm}<1.4\cdot10^{-19}$ g cm$^{-3}$ at the orbital distance of the Earth. We also have considered the case of a possible concentration of dark matter to the Solar system center. The dark matter mass in the sphere within Saturn's orbit should be less than $1.7\cdot10^{-10} M_{\odot}$ even if its possible concentration is taken into account.