We estimated the dynamical surface mass density \Sigma at the solar position between Z =1.5 and 4 kpc from the Galactic plane , as inferred from the kinematics of thick disk stars .
The formulation is exact within the limit of validity of a few basic assumptions .
The resulting trend of \Sigma ( Z ) matches the expectations of visible mass alone , and no dark component is required to account for the observations .
We extrapolate a dark matter ( DM ) density in the solar neighborhood of 0 \pm 1 mM _ { \odot } pc ^ { -3 } , and all the current models of a spherical DM halo are excluded at a confidence level higher than 4 \sigma .
A detailed analysis reveals that a small amount of DM is allowed in the volume under study by the change of some input parameter or hypothesis , but not enough to match the expectations of the models , except under an exotic combination of non-standard assumptions .
Identical results are obtained when repeating the calculation with kinematical measurements available in the literature .
We demonstrate that a DM halo would be detected by our method , and therefore the results have no straightforward interpretation .
Only the presence of a highly prolate ( flattening q > 2 ) DM halo can be reconciled with the observations , but this is highly unlikely in \Lambda CDM models .
The results challenge the current understanding of the spatial distribution and nature of the Galactic DM .
In particular , our results may indicate that any direct DM detection experiment is doomed to fail , if the local density of the target particles is negligible .