Local dark matter density from Gaia DR3 K-dwarfs using Gaussian processes

The local dark matter density provides constraints on dark matter models and is of importance for experiments hoping to detect dark matter particles in the laboratory. The advent of extensive survey data calls for more complex physical modelling and more sophisticated statistical analysis, particularly to account for correlated uncertainties. In this paper, 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 ${\rho_\mathrm{dm} = 0.0117 \pm 0.0035\, \mathrm{M}_\odot\,\mathrm{pc}^{-3} = 0.44 \pm 0.13\, \mathrm{GeV}\,\mathrm{cm}^{-3}}$ 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.