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We estimated the dynamical surface mass density Sigma at the solar positionbetween Z=1.5 and 4 kpc from the Galactic plane, as inferred from thekinematics of thick disk stars. The formulation is exact within the limit ofvalidity of a few basic assumptions. The resulting trend of Sigma(Z) matchesthe expectations of visible mass alone, and no dark component is required toaccount for the observations. We extrapolate a dark matter (DM) density in thesolar neighborhood of 0+-1 mM_sun pc^-3, and all the current models of aspherical DM halo are excluded at a confidence level higher than 4sigma. Adetailed analysis reveals that a small amount of DM is allowed in the volumeunder study by the change of some input parameter or hypothesis, but not enoughto match the expectations of the models, except under an exotic combination ofnon-standard assumptions. Identical results are obtained when repeating thecalculation with kinematical measurements available in the literature. Wedemonstrate that a DM halo would be detected by our method, and therefore theresults have no straightforward interpretation. Only the presence of a highlyprolate (flattening q>2) DM halo can be reconciled with the observations, butthis is highly unlikely in LambdaCDM models. The results challenge the currentunderstanding of the spatial distribution and nature of the Galactic DM. Inparticular, our results may indicate that any direct DM detection experiment isdoomed to fail, if the local density of the target particles is negligible.

Kinematical and chemical vertical structure of the Galactic thick disk II. A lack of dark matter in the solar neighborhood