Characterizing 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 survey. These stars are detected to radii similar to 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 similar to a'2 to similar to a'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 similar to a'0.001 dex kpc(-1), a small gradient in the dispersion in [Fe/H] of similar to 0.001 dex kpc(-1), and a higher degree of radial anisotropy in metal-richer stars result. Lognormal components with peaks at similar to a'1.5 and similar to a'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.