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 the flattening $q$ 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 $\sim 15000$ 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 $1.5\lesssim q\lesssim 2$.

arXiv commentMNRAS, submitted

References in corpus (32)

• emcee: The MCMC Hammer
• The Milky Way Tomography with SDSS: I. Stellar Number Density Distribution
• The Milky Way Tomography with SDSS: II. Stellar Metallicity
• The Sagittarius Dwarf Galaxy: a Model for Evolution in a Triaxial Milky Way Halo
• Measuring the inclination and mass-to-light ratio of axisymmetric galaxies via anisotropic Jeans models of stellar kinematics
• Great Circle tidal streams: evidence for a nearly spherical massive dark halo around the Milky Way
• Constraining the Milky Way potential with a 6-D phase-space map of the GD-1 stellar stream
• Dark matter in elliptical galaxies: II. Estimating the mass within the virial radius
• The Milky Way stellar halo out to 40 kpc : Squashed, broken but smooth
• Substructure revealed by RR Lyraes in SDSS Stripe 82
• The Origin of the Bifurcation in the Sagittarius Stream
• Velocity trends in the debris of Sagittarius and the shape of the dark-matter halo of the Galaxy
• The Milky Way Tomography with SDSS: III. Stellar Kinematics
• Kinematics of SDSS subdwarfs: Structure and substructure of the Milky Way halo
• Two measures of the shape of the Milky Way's dark halo
• Constraints on the shape of the Milky Way dark matter halo from the Sagittarius stream
• Optimal Data-Based Binning for Histograms
• Halo Star Streams in the Solar Neighborhood
• Dipping Our Toes in the Water: First Models of GD-1 as a Stream
• More dynamical models of our Galaxy
• High Resolution Chandra HETG spectroscopy of V404 Cygni in Outburst
• The Tilt of the Halo Velocity Ellipsoid and the Shape of the Milky Way Halo
• Distribution function of the dark matter
• Simple Three-Integral Scale-Free Galaxy Models
• The Milky Way Tomography with SDSS. V. Mapping the Dark Matter Halo
• Analysing surveys of our Galaxy -- II. Determining the potential
• A skewer survey of the Galactic halo from deep CFHT and INT images
• Dynamical Models of Elliptical Galaxies -- I. Simple Methods
• Progressively more prolate dark matter halo in the outer Galaxy as traced by flaring HI gas
• Stellar Velocity Dispersion and Anisotropy of the Milky Way Inner Halo
• What can the alignments of the velocity moments tell us about the nature of the potential?
• Extremely Flat Haloes and the Shape of the Galaxy

Cited by in corpus (27)

• Streams, substructures and the early history of the Milky Way
• Mass and shape of the Milky Way's dark matter halo with globular clusters from Gaia and Hubble
• The shape of the inner Milky Way halo from observations of the Pal 5 and GD-1 stellar streams
• Shape of Dark Matter Haloes in the Illustris Simulation: Effects of Baryons
• The Gravitational Force Field of the Galaxy Measured From the Kinematics of RR Lyrae in Gaia
• The Halo's Ancient Metal-Rich Progenitor Revealed with BHB Stars
• The information content in cold stellar streams
• Efficient solution of the anisotropic spherically-aligned axisymmetric Jeans equations of stellar hydrodynamics for galactic dynamics
• Updating the MACHO fraction of the Milky Way dark halo with improved mass models
• The first all-sky view of the Milky Way stellar halo with Gaia+2MASS RR Lyrae
• On the Run: mapping the escape speed across the Galaxy with SDSS
• Merger-induced galaxy transformations in the ARTEMIS simulations
• Bayesian Mass Estimates of the Milky Way II: The dark and light sides of parameter assumptions
• Dark matter halo shapes in the Auriga simulations
• Dark Matter Interpretation of the Fermi-LAT Observations Toward the Outer Halo of M31
• Action-based distribution function modelling for constraining the shape of the Galactic dark matter halo
• The impact of galactic feedback on the shapes of dark-matter haloes
• The twisted dark matter halo of the Milky Way
• On measuring the Galactic dark matter halo with hypervelocity stars
• The oblateness of the Milky Way dark matter halo from the stellar streams of NGC 3201, M68, and Palomar 5
• Galactic googly: the rotation-metallicity bias in the inner stellar halo of the Milky Way
• Around The Way: Testing $\Lambda$CDM with Milky Way Stellar Stream Constraints
• Charting Galactic Accelerations: When and How to Extract a Unique Potential from the Distribution Function
• A 6-d View of Stellar Shells
• On Filaments, Prolate Halos and Rotation Curves
• The shape of the dark matter halo revealed from a hypervelocity star
• A Tilt in the Dark Matter Halo of the Galaxy