Action-based distribution function modelling for constraining the shape
  of the Galactic dark matter halo
  We estimate the 3D density profile of the Galactic dark matter (DM) halo
within $r \lesssim 30$ kpc from the Galactic centre by using the astrometric
data for halo RR Lyrae stars from Gaia DR2. We model both the stellar halo
distribution function and the Galactic potential, fully taking into account the
survey selection function, the observational errors, and the missing
line-of-sight velocity data for RR Lyrae stars. With a Bayesian MCMC method, we
infer the model parameters, including the density flattening of the DM halo
$q$, which is assumed to be constant as a function of radius. We find that 99\%
of the posterior distribution of $q$ is located at $q>0.963$, which strongly
disfavours a flattened DM halo. We cannot draw any conclusions as to whether
the Galactic DM halo at $r \lesssim 30$ kpc is prolate, because we restrict
ourselves to axisymmetric oblate halo models with $q\leq1$. Our result is
inconsistent with predictions from cosmological hydrodynamical simulations that
advocate more oblate ($\langle{q}\rangle \sim0.8 \pm 0.15$) DM halos within
$\sim 15\%$ of the virial radius for Milky-Way-sized galaxies. An alternative
possibility, based on our validation tests with a cosmological simulation, is
that the true value $q$ of the Galactic halo could be consistent with
cosmological simulations but that disequilibrium in the Milky Way potential is
inflating our measurement of $q$ by 0.1-0.2. As a by-product of our analysis,
our model constrains the DM density in the Solar neighbourhood to be
$\rho_{\mathrm{DM},\odot} = (9.01^{+0.18}_{-0.20})\times10^{-3}M_\odot
\mathrm{pc}^{-3} = 0.342^{+0.007}_{-0.007}$ $\;\mathrm{GeV} \mathrm{cm}^{-3}$.
