The Fractions of Inner- and Outer-Halo Stars in the Local Volume
  We obtain a new determination of the metallicity distribution function (MDF)
of stars within $\sim5$-$10$ kpc of the Sun, based on recently improved co-adds
of $ugriz$ photometry for Stripe 82 from the Sloan Digital Sky Survey. Our new
estimate uses the methodology developed previously by An et al. to study in
situ halo stars, but is based on a factor of two larger sample than available
before, with much-improved photometric errors and zero-points. The newly
obtained MDF can be divided into multiple populations of halo stars, with peak
metallicities at [Fe/H] $\approx -1.4$ and $-1.9$, which we associate with the
inner-halo and outer-halo populations of the Milky Way, respectively. We find
that the kinematics of these stars (based on proper-motion measurements at high
Galactic latitude) supports the proposed dichotomy of the halo, as stars with
retrograde motions in the rest frame of the Galaxy are generally more
metal-poor than stars with prograde motions, consistent with previous claims.
In addition, we generate mock catalogs of stars from a simulated Milk Way halo
system, and demonstrate for the first time that the chemically- and
kinematically-distinct properties of the inner- and outer-halo populations are
qualitatively in agreement with our observations. The decomposition of the
observed MDF and our comparison with the mock catalog results suggest that the
outer-halo population contributes on the order of $\sim35\%$-$55\%$ of halo
stars in the local volume.
