We determine the Galactic potential in the solar neigbourhood from RAVE observations. We select red clump stars for which accurate distances, radial velocities, and metallicities have been measured. Combined with data from the 2MASS and UCAC catalogues, we build a sample of ~4600 red clump stars within a cylinder of 500?pc radius oriented in the direction of the South Galactic Pole, in the range of 200?pc to 2000?pc distances. We deduce the vertical force and the total mass density distribution up to 2 kpc away from the Galactic plane by fitting a distribution function depending explicitly on three isolating integrals of the motion in a separable potential locally representing the Galactic one with four free parameters. Because of the deep extension of our sample, we can determine nearly independently the dark matter mass density and the baryonic disc surface mass density. We find (i) at 1?kpc Kz/ (2πG) = 68.5 ± 1.0 M⊙?pc-2; and (ii) at 2?kpc Kz/ (2πG) = 96.9 ± 2.2 M⊙?pc-2. Assuming the solar Galactic radius at R0 = 8.5 kpc, we deduce the local dark matter density ρDM(z = 0) = 0.0143 ± 0.0011 M⊙pc-3 = 0.542 ± 0.042 Gev cm-3 and the baryonic surface mass density Σbar = 44.4 ± 4.1 M⊙pc-2. Our results are in agreement with previously published Kz determinations up to 1?kpc, while the extension to 2?kpc shows some evidence for an unexpectedly large amount of dark matter. A flattening of the dark halo of order 0.8 can produce such a high local density in combination with a circular velocity of 240?km?s-1. It could also be consistent with a spherical cored dark matter profile whose density does not drop sharply with radius. Another explanation, allowing for a lower circular velocity, could be the presence of a secondary dark component, a very thick disc resulting either from the deposit of dark matter from the accretion of multiple small dwarf galaxies, or from the presence of an effective “phantom” thick disc in the context of effective galactic-scale modifications of gravity.
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