On the local dark matter density

Context. In 2012, we applied a three-dimensional formulation to kinematic measurements of the Galactic thick disk and derived a surprisingly low dark matter density at the solar position. This result was challenged by Bovy & Tremaine (2012, ApJ, 756, 89), who claimed that the observational data are consistent with the expected local dark matter density if a one-dimensional approach is adopted.
Aims: We aim at clarifying whether their work definitively explains our result by analyzing the assumption at the base of their formulation and their claim that this returns a lower limit for the local dark matter density, which is accurate within 20%.
Methods: We find that the validity of their formulation depends on the underlying mass distribution. We therefore analyze the predictions that their hypothesis casts on the radial gradient of the azimuthal velocity ∂_Rv̅ and compare it with observational data as a testbed for the validity of their formulation.
Results: We find that their hypothesis requires too steep a profile of ∂_Rv̅(Z), which is inconsistent with the observational data both in the Milky Way and in external galaxies. As a consequence, their results are biased and largely overestimate the mass density. Dynamical simulations also show that, contrary to their claims, low values of ∂_Rv̅ are compatible with a Milky Way-like potential with radially constant circular velocity. We nevertheless confirm that, according to their criticism, our assumption ∂_Rv̅ = 0 is only an approximation. If this hypothesis is released, and the available information about ∂_Rv̅ in the thick disk is used, the resulting local dark matter density increases by a tiny amount, from 0 ± 1 to 2 ± 3 mM_⊙ pc^-3, with an upper limit of ~3.5 mM_⊙ pc^-3. Hence, this approximation has negligible influence on our results.
Conclusions: Our analysis shows that their criticism is not a viable explanation for the inferred lack of dark matter at the solar position detected by us. More studies are required to understand these unexpected results.