Enlighten the dark in the Milky Way with dynamical models

Since the first studies of galactic rotation curves we have seen evidence of a dark mass component in the halos of galaxies we can not observe directly. As the motion of astronomical objects are sensitive to the underlying gravitational potential, we can use dynamical models to infer the distribution of dark matter in galaxies including the Milky Way. An accurate determination of the dark matter density in the solar neighbourhood is therefore important for understanding the nature and distribution of dark matter in the universe. We begin by analysing the coupled motion of G-type dwarf stars in the solar neighbourhood using data from the Sloan Extension for Galactic Understanding and Exploration survey. The coupling is illustrated by the tilt of velocity ellipsoid, which we find to be close to the alignment with the spherical coordinate system and hence pointing to the Galactic centre. We proceed then by introducing a novel axisymmetric Jeans model that accounts for the tilt of the velocity ellipsoid. We apply it to the sample of G-type dwarf stars and make use of a discrete likelihood method to measure the local dark matter density to be 0.013 +- 0.0015 M_sun / pc³ and the baryonic surface density to be 52 +- 3 M_sun pc². If we ignore the coupled motion in the axisymmetric Jeans model, we will underestimate the local dark matter density by at least 33%. We next measure the dark matter distribution in the Galactic halo by applying our axisymmetric Jeans model to K-giants out to a heliocentric distance of 100 kpc. As the halo contains many substructures affecting the velocity distribution of our K-giants, we develop a model that accounts for the variable velocity distribution of the largest of them, the Sagittarius stream. In this way, we are able to robustly estimate the mass profile of the galaxy of M(r