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

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We define new potential-density pairs and examine the impact of the potential flattening on the vertical velocity ellipsoid tilt, δ. By means of numerical integrations and analytical calculations, we estimate δ in a variety of galactic potentials. We show that at 1 kpc above the Galactic plane at the solar radius, δ 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.