| Summary: | 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 ∼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−1, a small gradient in the dispersion in [Fe/H] of ∼0.001 dex kpc−1, and a higher degree of radial anisotropy 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.
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