On local dark matter density

Abstract: 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 dark matter density if a one-dimensional approach is adopted. We analyze the assumption at the bases of their formulation and their claim that this returns a lower limit for the local dark matter density, which is accurate within 20%. 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 dV/dR and compare it with observational data as a testbed for the validity of their formulation. We find that their hypothesis requires too steep a profile of dV(Z)/dR, 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 dV/dR are compatible with a Milky Way like potential with radially constant circular velocity. We nevertheless confirm that, according to their criticism, our assumption dV/dR=0 is only an approximation. If this hypothesis is released, and the available information about dV/dR in the thick disk is used, the resulting local dark matter density increases by a tiny amount, from 0+-1 to 2+-3 mM_sun pc^-3, with an upper limit of ~3.5 mM_sun pc^-3. Hence, this approximation has negligible influence on our results. 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.