Is the dark halo of the Milky Way prolate?

Abstract

We introduce the flattening equation, which relates the shape of the dark halo to the angular velocity dispersions and the density of a tracer population of stars. It assumes spherical alignment of the velocity dispersion tensor, as seen in the data on stellar halo stars in the Milky Way. The angular anisotropy and gradients in the angular velocity dispersions drive the solutions towards prolateness, whilst the gradient in the stellar density is a competing effect favouring oblateness. We provide an efficient numerical algorithm to integrate the flattening equation. Using tests on mock data, we show that the there is a strong degeneracy between circular speed and flattening, which can be circumvented with informative priors. Therefore, we advocate the use of the flattening equation to test for oblateness or prolateness, though the precise value of q can only be measured with the addition of the radial Jeans equation. We apply the flattening equation to a sample extracted from the Sloan Digital Sky Survey of ∼ 15000 halo stars with full phase space information and errors. We find that between Galactocentric radii of 5 and 10 kpc, the shape of the dark halo is prolate, whilst even mildly oblate models are disfavoured. Strongly oblate models are ruled out. Specifically, for a logarithmic halo model, if the asymptotic circular speed v 0 lies between 210 and 250 kms −1 , then we find the axis ratio of the equipotentials q satisfies 1.5 q 2.

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

“…Similarly, there has also been some work on the shape of the total gravitational potential. While a proper comparison taking into account the systematics induced by tracers and methods is not straightforward, here we note that our estimate roughly agrees with other studies of the Sagittarius stream (Helmi 2004), the flaring of the HI disc (Banerjee & Jog 2011), or the kinematics of halo stars (Bowden, Evans, & Williams 2016), while being apparently inconsistent with studies modelling the GD-1 stream (Koposov, Rix, & Hogg 2010;Bowden, Belokurov, & Evans 2015, which, however, probes a region much closer to the Galactic centre) and studies of the tilt of the local velocity ellipsoid (Smith, Wyn Evans, & An 2009;Posti et al 2018).…”

Bayesian Mass Estimates of the Milky Way: The Dark and Light Sides of Parameter Assumptions

“…However, the geometry of the MW's DM halo is not well known. Some studies favor a triaxial shape or oblate shape (Law & Majewski 2010b;Deg & Widrow 2013;Loebman et al 2014), others a prolate shape (Bowden et al 2016), and still others show that a spherical shape is not ruled out (Smith et al 2009). The ideal way to allow for a nonspherical halo under the methodology of EHW would be to use a DF that includes an angular-dependent dark matter potential through extra model parameters.…”

Efficient solution of the anisotropic spherically aligned axisymmetric Jeans equations of stellar hydrodynamics for galactic dynamics

“…To find a solution for the Jeans equations I start from equation (3) and assume that the velocity ellipsoid is aligned with the spherical coordinate system. The cross-terms of the second velocity moment tensor vanishes and the Jeans equations become Bowden et al (2016) pointed out that equation (5b) "does not involve the radial velocity dispersion at all" and solved it by itself to study the flattening of the gravitational potential. Their solution involves expanding in a Fourier series the angular variation of the v 2 φ /v 2 θ ratio.…”