ABSTRACT
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 (Large Sky Area Multi-Object Fibre Spectroscopic Telescope) fifth data release and Gaia second data release 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 that 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 $0.0133_{-0.0022}^{+0.0024}\ {\rm M}_{\odot }\, {\rm pc}^{-3}$. The local dark matter densities for subsamples in an azimuthal angle range of −10° < ϕ < 5° are consistent within their 1σ 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 σz 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.
Bound on the dark matter density in the Solar System from planetary motions
