  The distribution of Milky Way halo blue horizontal-branch (BHB) stars is
examined using action-based extended distribution functions (EDFs) that
describe the locations of stars in phase space, metallicity, and age. The
parameters of the EDFs are fitted using stars observed in the Sloan Extension
for Galactic Understanding and Exploration-II (SEGUE-II) survey that trace the
phase-space kinematics and chemistry out to ~70 kpc. A maximum a posteriori
probability (MAP) estimate method and a Markov Chain Monte Carlo method are
applied, taking into account the selection function in positions, distance, and
metallicity for the survey. The best-fit EDF declines with actions less steeply
at actions characteristic of the inner halo than at the larger actions
characteristic of the outer halo, and older ages are found at smaller actions
than at larger actions. In real space, the radial density profile steepens
smoothly from -2 at ~2 kpc to -4 in the outer halo, with an axis ratio ~0.7
throughout. There is no indication for rotation in the BHBs, although this is
highly uncertain. A moderate level of radial anisotropy is detected, with
$\beta_s$ varying from isotropic to between ~0.1 and ~0.3 in the outer halo
depending on latitude. The BHB data are consistent with an age gradient of
-0.03 Gyr kpc$^{-1}$, with some uncertainty in the distribution of the larger
ages. These results are consistent with a scenario in which older, larger
systems contribute to the inner halo, whilst the outer halo is primarily
comprised of younger, smaller systems.
