Laurin Söding, Ruben Bartel, Philipp Mertsch

Modern astrophysical surveys have produced a wealth of data on the positions and velocities of stars in the Milky Way with varying accuracies. An ever-increasing detail in observational data calls for more complex physical models and in turn more sophisticated statistical methods to extract information. We perform a vertical Jeans analysis, including a local approximation of the tilt term, using a sample of $200\,000$ K-dwarf stars from the Gaia DR3 catalogue. After combination with the Survey-of-Surveys (SoS) catalogue, $160\,888$ of those have radial velocity measurements. We use Gaussian processes as priors for the covariance matrix of radial and vertical velocities. Joint inference of the posterior distribution of the local dark matter density and the velocity moments is performed using geometric variational inference. We find a local dark matter density of ${\rho_\mathrm{dm} = 0.0131 \pm 0.0041\, \mathrm{M}_\odot\,\mathrm{pc}^{-3} = 0.50 \pm 0.15\, \mathrm{GeV}\,\mathrm{cm}^{-3}}$ at the Sun's position, which is in agreement with most other recent analyses. By comparing a ($z$-dependent) Gaussian process prior with a ($z$-independent) scalar prior for the tilt term, we quantify its impact on estimates of the local dark matter density and argue that careful modelling is required to mitigate systematic biases.