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The radial profile and flattening of the Milky Way's stellar halo to $\rm 80~$kpc from the SEGUE K-giant Survey

We characterise the radial density, metallicity and flattening profile of the Milky Way's stellar halo, based on the large sample of 1757 spectroscopically confirmed giant stars from SDSS/SEGUE-2 after excising stars that were algorithmically attributed to apparent halo substructure (including the Sagittarius stream). Compared to BHB stars or RR Lyrae, 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 modelling 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 $n=3.1\pm 0.5$ with an effective radius $\rm r_{eff} = 15\pm2~$kpc and a flattening of $q=0.7\pm 0.02$; or comparably well by an equally flattened broken power-law, with radial slopes of $α_{in}=2.1\pm 0.3$ and $α_{out}=3.8\pm 0.1$, with a break-radius of $r_{break}=18\pm1$~kpc; this is largely consistent with earlier work. We find a modest, but significant metallicity gradient within the "outer" stellar halo, $\rm [Fe/H]$ decreasing outward. If we allow for a variable flattening $q = f(r_{GC} )$, we find the distribution of halo giants to be considerably more flattened at small radii, $q({\rm 10~kpc})\sim 0.57$, compared to $q(>30{\rm kpc})\sim 0.8$. Remarkably, the data are then very well fit by a single power-law of index $\rm \sim 4.2\pm0.1$ of the variable $r_q\equiv\sqrt{R^2+(z/q(r))^2}$. In this simple and better fitting model, there is a break in flattening at $\sim 20$~kpc, instead of a break in the radial density function.