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

Abstract

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 +0.18 −0.17 × 10 11 M , of which M DM (< 20 kpc) = 1.37 +0.18 −0.17 × 10 11 M is in dark matter, and the density axis ratio of the dark matter halo to be q = 1.30 ± 0.25. Assuming a concentrationmass relation, this implies a virial mass M vir = 1.3 ± 0.3 × 10 12 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 V rot −14 km 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.

Local Group Analogs in ΛCDM Cosmological Simulations

“…For the radial orbits, the median halo mass of M31 is about 2.5×10 12 M , which is consistent with former works (Watkins et al 2010;Fardal et al 2013), while the median halo mass of the MW is about 1.5×10 12 M , slightly higher than the results in the literature (e.g. Wilkinson & Evans 1999;Smith et al 2007;Xue et al 2008;Zhai et al 2018;Posti & Helmi 2019). A further constraint on the bulge-mass fraction reduces the corresponding host halo mass slightly (see Table 3).…”

The milky way total mass profile as inferred from Gaia DR2

“…Figure 10 shows that the contracted NFW halo model matches well the Eilers et al (2019) and Callingham et al (2019b) measurements, which were the ones used for the fitting procedure. The model also agrees well with the mass measurements by Posti & Helmi (2019) and Watkins et al (2019). However, it does not match the Eadie & Jurić (2019) data particularly well, which may be due to the assumption by these authors of a power-law model for the MW potential, which is an oversimplification.…”

“…The resulting 68 and 95% confidence limits for M DM 200 and c NFW are shown in Figure 8. locity measurement, Vcirc(r = 8 kpc) = (230 ± 5) km s −1 , and the enclosed total mass measurement of Posti & Helmi (2019), M tot (< r = 20 kpc) = (1.91 ± 0.18) × 10 11 M . Using a single mass measurement results in a degeneracy between the inferred halo mass and concentration since different (M DM 200 , c NFW ) pairs can produce the same enclosed DM mass, as may be seen from the coloured shaded regions in Figure 8.…”

“…The black data points are the Eilers et al (2019) Vcirc data and the dark blue square is the Callingham et al (2019b) total mass estimate converted to a Vcirc value at the halo radius, R200. The other colour data points are the Posti & Helmi (2019), Watkins et al (2019) and Eadie & Jurić (2019) estimates of the enclosed mass at various Galactocentric radii, which were converted to circular velocities as GM (< r)/r, where G is Newton's gravitational constant and M (< r) is the enclosed mass within radius, r. The latter measurements are inferred from the dynamics of globular clusters with proper motions measured by Gaia DR2 and several various HST programs (for details see Eadie & Jurić 2019). Figure 10 shows that the contracted NFW halo model matches well the Eilers et al (2019) and Callingham et al (2019b) measurements, which were the ones used for the fitting procedure.…”

“…Xue et al 2008;Deason et al 2012;Kafle et al 2012), globular clusters (e.g. Eadie & Harris 2016;Posti & Helmi 2019;Watkins et al 2019) and satellite galaxies (e.g. Watkins et al 2010;Li et al 2017;Patel et al 2017;Callingham et al 2019b), high velocity stars (e,g, Smith et al 2007;Piffl et al 2014;Fragione & Loeb 2017;Rossi et al 2017;Deason et al 2019b), the orbits of tidal streams (e.g.…”