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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-addsof $ugriz$ photometry for Stripe 82 from the Sloan Digital Sky Survey. Our newestimate uses the methodology developed previously by An et al. to study insitu halo stars, but is based on a factor of two larger sample than availablebefore, with much-improved photometric errors and zero-points. The newlyobtained MDF can be divided into multiple populations of halo stars, with peakmetallicities at [Fe/H] $\approx -1.4$ and $-1.9$, which we associate with theinner-halo and outer-halo populations of the Milky Way, respectively. We findthat the kinematics of these stars (based on proper-motion measurements at highGalactic latitude) supports the proposed dichotomy of the halo, as stars withretrograde motions in the rest frame of the Galaxy are generally moremetal-poor than stars with prograde motions, consistent with previous claims.In addition, we generate mock catalogs of stars from a simulated Milk Way halosystem, and demonstrate for the first time that the chemically- andkinematically-distinct properties of the inner- and outer-halo populations arequalitatively in agreement with our observations. The decomposition of theobserved MDF and our comparison with the mock catalog results suggest that theouter-halo population contributes on the order of $\sim35\%$-$55\%$ of halostars in the local volume.

The Fractions of Inner- and Outer-Halo Stars in the Local Volume