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

TL;DR

This work constrains the local dark matter density in the solar neighbourhood by performing a vertical Jeans analysis on Gaia DR3 K-dwarf tracers, augmented with SoS radial velocities. It advances the methodology by representing the velocity moments and the tilt term as Gaussian processes and inferring the posterior with geometric variational inference (geoVI), enabling uncertainty propagation in a high-dimensional parameter space. The study finds ρ_{\mathrm{dm}} = 0.0117 ± 0.0035 M_sun pc^{-3} (0.44 ± 0.13 GeV cm^{-3}) at the Sun’s position, with the tilt term contributing subdominantly but non-negligibly; modelling choices for the tilt term significantly impact the inferred density. The approach demonstrates a flexible, data-driven framework that can incorporate complex covariances and measurement uncertainties, while also highlighting the need to account for non-axisymmetries and time-dependent disequilibria in future work.

Abstract

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 ${ρ_\mathrm{dm} = 0.0117 \pm 0.0035\, \mathrm{M}_\odot\,\mathrm{pc}^{-3} = 0.44 \pm 0.13\, \mathrm{GeV}\,\mathrm{cm}^{-3}}$ 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.

Figures (9)

• Figure 1: Left panel: Colour-magnitude diagram of the initially selected stars in the Gaia DR3 catalogue within our cylindrical volume. Centre panel: Zoom-in on the considered region within the main sequence. The lines indicate the edges of our equal-number bins. Every bin, except for the rightmost one, contains $50\,000$ stars. After applying our cuts, only stars in-between the solid lines were kept. Right panel: The vertical density profile of the stars in the selected bins. The dashed lines indicate discarded bins. All lines are normalised so that the area under the curve is equal to $1$.
• Figure 2: Star counts $n_*$ as a function of height $z$ above the Galactic disk. The blue crosses assume the mean parallax of each star, while the black and grey points show the mean and standard deviation (in log-space) of $1\,000$ realisations sampled from the parallax errors. The bin width is $40\,\mathrm{pc}$.
• Figure 3: Vertical velocity dispersion $\overline{\varv_z^2}$ as a function of height $z$ above the Galactic disk. All samples are shown. The shaded region indicates the availability of stellar velocity data.
• Figure 4: Like Fig. \ref{['fig:resvz2']}, but for the radial velocity dispersion $\overline{\varv_R^2}$.
• Figure 5: Like Fig. \ref{['fig:resvz2']}, but for the velocity covariance $\overline{\varv_z \varv_R}$.