Characterising stellar halo populations I: An extended distribution
  function for halo K giants
  We fit an Extended Distribution Function (EDF) to K giants in the Sloan
Extension for Galactic Understanding and Exploration (SEGUE) survey. These
stars are detected to radii ~80 kpc and span a wide range in [Fe/H]. Our EDF,
which depends on [Fe/H] in addition to actions, encodes the entanglement of
metallicity with dynamics within the Galaxy's stellar halo. Our
maximum-likelihood fit of the EDF to the data allows us to model the survey's
selection function. The density profile of the K giants steepens with radius
from a slope ~-2 to ~-4 at large radii. The halo's axis ratio increases with
radius from 0.7 to almost unity. The metal-rich stars are more tightly confined
in action space than the metal-poor stars and form a more flattened structure.
A weak metallicity gradient ~-0.001 dex/kpc, a small gradient in the dispersion
in [Fe/H] of ~0.001 dex/kpc, and a higher degree of radial anistropy in
metal-richer stars result. Lognormal components with peaks at ~-1.5 and ~-2.3
are required to capture the overall metallicity distribution, suggestive of the
existence of two populations of K giants. The spherical anisotropy parameter
varies between 0.3 in the inner halo to isotropic in the outer halo. If the
Sagittarius stream is included, a very similar model is found but with a
stronger degree of radial anisotropy throughout.
