Mass and shape of the Milky Way’s dark matter halo with globular clusters from Gaia and Hubble

Aims. We estimate the mass of the inner (< 20 kpc) Milky Way and the axis ratio of its inner dark matter halo using globular clusters as tracers. At the same time, we constrain the distribution in phase-space of the globular cluster system around the Galaxy. Methods. We use the Gaia Data Release 2 catalogue of 75 globular clusters’ proper motions and recent measurements of the proper motions of another 20 distant clusters obtained with the Hubble Space Telescope. We describe the globular cluster system with a distribution function (DF) with two components: a flat, rotating disc-like one and a rounder, more extended halo-like one. While fixing the Milky Way’s disc and bulge, we let the mass and shape of the dark matter halo and we fit these two parameters, together with six others describing the DF, with a Bayesian method. Results. We find the mass of the Galaxy within 20 kpc to be M(<20 kpc) = 1.91−0.17+0.18×1011 M⊙, of which MDM(<20 kpc) = 1.37−0.17+0.18×1011 M⊙ is in dark matter, and the density axis ratio of the dark matter halo to be q = 1.30 ± 0.25. Assuming a concentration-mass relation, this implies a virial mass Mvir = 1.3±0.3×1012 M⊙. Our analysis rules out oblate (q < 0.8) and strongly prolate halos (q > 1.9) with 99% probability. Our preferred model reproduces well the observed phase-space distribution of globular clusters and has a disc component that closely resembles that of the Galactic thick disc. The halo component follows a power-law density profile ρ ∝ r−3.3, has a mean rotational velocity of Vrot ≃ −14km s−1 at 20 kpc, and has a mildly radially biased velocity distribution (β ≃ 0.2 ± 0.07, which varies significantly with radius only within the inner 15 kpc). We also find that our distinction between disc and halo clusters resembles, although not fully, the observed distinction in metal-rich ([Fe/H] > −0.8) and metal-poor ([Fe/H] ≤ −0.8) cluster populations.