Potential-density pairs and vertical tilt of the stellar velocity ellipsoid

We define new potential-density pairs and examine the impact of the potential flattening on the vertical velocity ellipsoid tilt, $\delta$. By means of numerical integrations and analytical calculations, we estimate $\delta$ in a variety of galactic potentials. We show that at 1 kpc above the Galactic plane at the solar radius, $\delta$ can differ by 5 degrees, depending on whether the dark matter halo is flat or spherical. This result excludes the possibility of an extremely flattened Galactic dark halo.