  The analysis of the vertical velocity dispersion of disc stars is the most
direct astronomical means of estimating the local dark matter density,
$\rho_{DM}$. Current estimates based on the mid-plane dynamic density use a
local baryonic correction that ignores the non-local effects of spiral
structure and significantly underestimates the amount of dynamically relevant
gas; the additional gas plus the remaining uncertainties make it practically
impossible to measure $\rho_{DM}$ from mid-plane kinematics alone. The sampling
of inhomogeneous tracer populations with different scale-heights and
scale-lengths results in a systematic increase in the observed dispersion
gradients and changes in the nominal density distributions that, if not
properly considered, can be misinterpreted as a sign of more dark matter. If
the disc gravity is modelled using an infinite disc, the local variation in the
vertical gravity due to the globally exponential disc components results in an
underestimation of the baryonic contribution by as much as ~40% Given only the
assumptions of stationarity, an axially and vertically symmetric disc, doubly
exponential tracer and mass-component density profiles, a phenomenologically
justified model for the cross-dispersion component $\sigma_{Rz}$, and a
realistic model for $g_z$, it is possible to solve the full vertical Jeans
equation analytically for the vertical dispersion $\sigma_{z}(z)$ and hence
test the robustness of previous attempts at measuring $\rho_{DM}$. When the
model parameters are estimated from SEGUE G dwarf star data, it is still not
possible to explain the difference in behaviour seen in the simple thick- and
thin-disc datasets reported by Buedenbender et al.. Rather than being a
fundamental problem with the kinematical model, this effect appears to be a
further sign of the difficulty of defining and handling kinematically
homogeneous tracer populations.
