Geometry of the Milky Way's dark matter from dynamical models of the tilted stellar halo

TL;DR

This work constrains the Milky Way's dark matter halo geometry by modelling the Gaia Sausage-Enceladus (GSE) stellar debris as a near-equilibrium, tilted triaxial system. Using Schwarzschild orbit-superposition modelling in a fixed Galactic potential that couples a tilted dark matter halo to the disc, the authors fit to the GSE density and anisotropy data, enforcing a coplanar arrangement of halo major axes with the disc. They find a near-prolate DM halo with a long-axis tilt of $\beta_{dm}=43_{-8}^{+22}^\circ$ and a short-to-long axis density ratio $q_{dm}=0.87_{-0.09}^{+0.05}$, with the tilt increasing with radius from $\sim10^\circ$ at 6 kpc to $\sim35^\circ$ at 60 kpc, and the halo remaining more spherical than the stellar halo. Spherical haloes are ruled out, and oblate haloes struggle to reproduce the GSE’s triaxial structure, especially under the anisotropy constraint. The best-fitting model provides realistic initial conditions for halo perturbation studies and satellite interactions, and the fiducial potential along with an $N$-body snapshot of the GSE is made publicly available for community use.

Abstract

The shape and orientation of the Milky Way's dark matter halo remain poorly constrained. Observations of the accreted stellar halo show that it is triaxial and tilted with respect to the disc. If this configuration is long-lived, it can be used to place constraints on the shape and orientation of the dark matter halo that can support it close to steady state. We fit equilibrium orbit-superposition (Schwarzschild) models to the stellar halo in a realistic Milky Way potential with a tilted dark matter halo, assuming that the long axes of each halo and the disc normal are coplanar. These models are matched to parametric density fits and velocity anisotropy measurements of Gaia Sausage-Enceladus (GSE) stars at radii $r\in[6,60]$ kpc. The observations are consistent with a (near-)prolate dark matter halo whose density has a short-to-long axis ratio of $q_\mathrm{dm}=0.87_{-0.09}^{+0.05}$. The long axis is inclined at an angle of $β_\mathrm{dm}=43_{-8}^{+22}\,^\circ$ to the disc plane, which exceeds the stellar halo tilt by $\approx18^\circ$. Spherical haloes cannot support the observed structure of the GSE in equilibrium. The best-fitting dynamical GSE model has a radius-dependent shape and orientation; between radii of 6 and 60 kpc the tilt increases from $β_*(r)\approx10^\circ$ to $\approx35^\circ$. Our model provides a good fit to the observed triaxial structure and dynamics of the GSE. It is therefore an excellent source of realistic initial conditions for simulations of the halo, such as for investigating perturbations from satellites or the Galactic bar.

Figures (15)

• Figure 1: Coordinate systems used in this paper. Left-hand panel: Top-down projection (from the North Galactic Pole) showing the $(x,y,z)$ and $(x',y',z)$ coordinates. The $\odot$ symbol marks the position of the Sun, and the ellipse illustrates the orientation of the stellar halo's major axis. Middle panel: Edge-on projection to the Galactic disc (viewed down the $y'$-axis). The orange axes indicate the stellar halo coordinate system $(X_*,Y_*,Z_*)$. Right-hand panel: as above, but showing the dark matter halo coordinate system $(X_\mathrm{dm}, Y_\mathrm{dm}, Z_\mathrm{dm})$ in green. The black dashed ellipse illustrates the orientation of the dark matter halo.
• Figure 2: Constraints on the anisotropy profile of GSE stars. The coloured points indicate measurements from RR Lyrae iorio2021, K giants and BHBs bird2021, and BHBs from lancaster2019 (red squares). The black unfilled triangles indicate the constraint chosen for our fit.
• Figure 3: Results of the Schwarzschild fits in a prolate dark matter halo. The $x$ and $y$-axes correspond to the tilt $\beta_\mathrm{dm}$ of the dark matter major axis with respect to the Galactic plane, and the short-to-long axis ratio $q_\mathrm{dm}$ respectively. The blue pixels indicate the log-likelihood of the model. The black contours are calculated from a smoothed log-likelihood and placed at the $\mathrm{log}\,\mathcal{L}/\mathcal{L}_\mathrm{max}=-n^2/2$ levels, where $n\in\{0.5, 1.0, 1.5, 2.0\}$. The black histograms in the bottom and left-hand panels show the marginalized posteriors of $\beta_\mathrm{dm}$ and $q_\mathrm{dm}$, assuming uniform priors. Their medians and 16th/84th percentiles are marked with black dashed lines and printed in their respective panels. For comparison the red dashed lines and bands indicate the analogous quantities of the stellar halo fit by han2022.
• Figure 4: Like Fig. \ref{['fig:logL_grid_prolate']}, but with a fixed axis ratio $p_\mathrm{dm}=0.88$. The dotted line marks where $q_\mathrm{dm}=p_\mathrm{dm}$ (i.e. where the halo is prolate). The results are very similar to those for the prolate halo, except that slightly lower values of $q_\mathrm{dm}$ are permitted ($q_\mathrm{dm}\sim0.7$).
• Figure 5: 3D shape of the fiducial prolate dark matter halo compared to the han2022 stellar halo in the standard $(x,y,z)$ Galactocentric coordinate system. These are evaluated at ellipsoidal radii $r_\mathrm{dm}=30$ kpc and $r_*=20$ kpc respectively. Their major axes are shown as solid lines. The red $\odot$ symbol and circle mark the position of the Sun and the disc respectively.