Jeans analysis of the Galactic thick disk and the local dark matter
  density
  Dynamical estimates of the mass surface density at the solar radius can be
made up to a height of 4 kpc using thick disk stars as tracers of the
potential. We investigate why different Jeans estimators of the local surface
density lead to puzzling and conflicting results. Using the Jeans equations, we
compute the vertical (F_z) and radial (F_R) components of the gravitational
force, as well as Gamma(z), defined as the radial derivative of V_c^2, with
V_c^{2}= -RF_R. If we assume that the thick disk does not flare and that all
the components of the velocity dispersion tensor of the thick disk have a
uniform radial scalelength of 3.5 kpc, Gamma takes implausibly large negative
values, when using the currently available kinematical data of the thick disk.
This implies that the input parameters or the model assumptions must be
revised. We have explored, using a simulated thick disk, the impact of the
assumption that the scale lengths of the density and velocity dispersions do
not depend on the vertical height z above the midplane. In the lack of any
information about how these scale radii depend on z, we define a different
strategy. By using a parameterized Galactic potential, we find that acceptable
fits to F_z, F_R and Gamma are obtained for a flaring thick disk and a
spherical dark matter halo with a local density larger than 0.0064 M_sun
pc^{-3}. Disk-like dark matter distributions might be also compatible with the
current data of the thick disk. A precise measurement of Gamma at the midplane
could be very useful to discriminate between models.
