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 \leq r _ { GC } \leq 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 , \nu _ { * } ( 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 \mathrm { r } _ { \mathrm { eff } } = 15 \pm 2 ~ { } 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 \alpha _ { in } = 2.1 \pm 0.3 and \alpha _ { out } = 3.8 \pm 0.1 , with a break radius of r _ { break } = 18 \pm 1 kpc ; this is largely consistent with earlier work .
We find a modest but significant metallicity gradient within the ‘ outer ’ stellar halo , \mathrm { [ Fe / H ] } decreasing outward .
If we allow for a variable flattening q = f ( \mathrm { r } _ { GC } ) , we find the distribution of halo giants to be considerably more flattened at small radii , q ( { 10 ~ { } kpc } ) = 0.55 \pm 0.02 , compared to q ( > 30 { kpc } ) = 0.8 \pm 0.03 .
Remarkably , the data are then very well fit by a single power law with index of 4.2 \pm 0.1 on 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 .
While different parameterizations of the radial profile vary in their parameters , their implied density gradient , \partial { \ln \nu _ { * } } / \partial { \ln r } , 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 .