We apply the vertical Jeans equation to the kinematics of Milky Way stars in the solar neighbourhood to measure the local dark matter density .
More than 90,000 G- and K-type dwarf stars are selected from the cross-matched sample of LAMOST DR5 and Gaia DR2 for our analyses .
The mass models applied consist of a single exponential stellar disc , a razor thin gas disc and a constant dark matter density .
We first consider the simplified vertical Jeans equation which ignores the tilt term and assumes a flat rotation curve .
Under a Gaussian prior on the total stellar surface density , the local dark matter density inferred from Markov Chain Monte Carlo simulations is 0.0133 _ { -0.0022 } ^ { +0.0024 } { M } _ { \odot } { pc } ^ { -3 } .
The local dark matter densities for subsamples in an azimuthal angle range of -10 ^ { \circ } < \phi < 5 ^ { \circ } are consistent within their 1 \sigma errors .
However , the northern and southern subsamples show a large discrepancy due to plateaux in the northern and southern vertical velocity dispersion profiles .
These plateaux may be the cause of the different estimates of the dark matter density between the north and south .
Taking the tilt term into account has little effect on the parameter estimations and does not explain the north and south asymmetry .
Taking half of the difference of \sigma _ { z } profiles as unknown systematic errors , we then obtain consistent measurements for the northern and southern subsamples .
We discuss the influence of the vertical data range , the scale height of the tracer population , the vertical distribution of stars and the sample size on the uncertainty of the determination of the local dark matter density .