Dark matter in the Milky Way. I. The isothermal disk approximation

We solve the combined Poisson-Boltzmann equation for the gravitational potential of the Milky Way for an isothermal distribution of stars and gas perpendicular to the Galactic disk. In contrast to the standard assumption that the dark matter is distributed in a spheroidal way, we focus our analysis on the question of whether a fraction of the Galactic dark matter might be distributed in a disklike way. Using gaseous tracers for the gravitational potential and taking all relevant observational constraints into account, we find that a disklike dark matter distribution with a local scale height of 4 kpc provides a self-consistent and stable solution of the Poisson-Boltzmann equation. This implies that both the mass distribution and the dynamics of the Milky Way for Rless than or similar to35 kpc are dominated by a massive dark matter disk. For larger galactocentric radii the gravitational potential approaches spherical symmetry, implying an approximately spherical dark matter distribution on such scales.