Deep SDSS optical spectroscopy of distant halo stars I. Atmospheric
  parameters and stellar metallicity distribution
  We analyze a sample of tens of thousands of spectra of halo turnoff stars,
obtained with the optical spectrographs of the Sloan Digital Sky Survey (SDSS),
to characterize the stellar halo population "in situ" out to a distance of a
few tens of kpc from the Sun. In this paper we describe the derivation of
atmospheric parameters. We also derive the overall stellar metallicity
distribution based on F-type stars observed as flux calibrators for the
Baryonic Oscillations Spectroscopic Survey (BOSS). Our analysis is based on an
automated method that determines the set of parameters of a model atmosphere
that reproduces each observed spectrum best. We used an optimization algorithm
and evaluate model fluxes by means of interpolation in a precomputed grid. In
our analysis, we account for the spectrograph's varying resolution as a
function of fiber and wavelength. Our results for early SDSS (pre-BOSS upgrade)
data compare well with those from the SEGUE Stellar Parameter Pipeline (SSPP),
except for stars with logg (cgs units) lower than 2.5. An analysis of stars in
the globular cluster M13 reveals a dependence of the inferred metallicity on
surface gravity for stars with logg < 2.5, confirming the systematics
identified in the comparison with the SSPP. We find that our metallicity
estimates are significantly more precise than the SSPP results. We obtain a
halo metallicity distribution that is narrower and more asymmetric than in
previous studies. The lowest gravity stars in our sample, at tens of kpc from
the Sun, indicate a shift of the metallicity distribution to lower abundances,
consistent with what is expected from a dual halo system in the Milky Way.
