The radial profile and flattening of the Milky Way's stellar halo to 80 kpc from the SEGUE K-giant survey

We characterize the radial density, metallicity, and flattening profile of the Milky Way's stellar halo, based on the large sample of spectroscopically confirmed giant stars from SDSS/SEGUE-2, spanning galactocentric radii 10 kpc ≤ r_GC ≤ 80 kpc. After excising stars that were algorithmically attributed to apparent halo substructure (including the Sagittarius stream), the sample has 1757 K giants, with a typical metallicity precision of 0.2 dex and a mean distance accuracy of 16%. Compared to blue horizontal branch stars or RR Lyrae variables, giants are more readily understood tracers of the overall halo star population, with less bias in age or metallicity. The well-characterized selection function of the sample enables forward modeling of those data, based on ellipsoidal stellar density models, ν_*(R, z), with Einasto profiles and (broken) power laws for their radial dependence, combined with a model for the metallicity gradient and the flattening profile. Among models with constant flattening, these data are reasonably well fit by an Einasto profile of n = 3.1 ± 0.5 with an effective radius $r_{eff}=15\pm 2kpc$ and a flattening of q = 0.7 ± 0.02, or comparably well by an equally flattened broken power law, with radial slopes of α_in = 2.1 ± 0.3 and α_out = 3.8 ± 0.1, with a break radius of r_break = 18 ± 1 kpc; this is largely consistent with earlier work. We find a modest but significant metallicity gradient within the "outer" stellar halo, [Fe/H] decreasing outward. If we allow for a variable flattening $q=f\left(r_{GC}\right)$, we find the distribution of halo giants to be considerably more flattened at small radii, q(10 kpc) = 0.55 ± 0.02, compared to q(>30 kpc) = 0.8 ± 0.03. Remarkably, the data are then very well fit by a single power law with index of 4.2 ± 0.1 on the variable $r_q\equiv \sqrt{R^2+{\left(z/q\right(r\left)\right)}^2}$. In this simple and better-fitting model, there is a break in flattening at ∼20 kpc, instead of a break in the radial density function. While different parameterizations of the radial profile vary in their parameters, their implied density gradient, $\partial ln{\nu }_{\ast }/\partial lnr$, is stable along a direction intermediate between major and minor axis; this gradient is crucial in any dynamical modeling that uses halo stars as tracers.