Determination of Sodium Abundance Ratio from Low-Resolution Stellar
  Spectra and Its Applications
  We present a method to determine sodium-abundance ratios ([Na/Fe]) using the
Na I D doublet lines in low-resolution ($R \sim$ 2000) stellar spectra. As
stellar Na I D lines are blended with those produced by the interstellar medium
(ISM), we developed a technique for removing the interstellar Na I D lines
using the relationship between extinction, which is proportional to $E(B-V)$,
and the equivalent width (EW) of the interstellar Na I D absorption lines. When
measuring [Na/Fe], we also considered corrections for non-local thermodynamic
equilibrium (NLTE) effects. Comparisons with data from high-resolution
spectroscopic surveys suggest that the expected precision of [Na/Fe] from
low-resolution spectra is better than 0.3 dex for stars with [Fe/H] $>$ $-$3.0.
We also present a simple application employing the estimated [Na/Fe] values for
a large number of stellar spectra from the Sloan Digital Sky Survey (SDSS).
After classifying the SDSS stars into Na-normal, Na-high, and Na-extreme, we
explore their relation to stars in Galactic globular clusters (GCs). We find
that, while the Na-high SDSS stars exhibit a similar metallicity distribution
function (MDF) to that of the GCs, indicating that the majority of such stars
may have originated from GC debris, the MDF of the Na-normal SDSS stars follows
that of typical disk and halo stars. As there is a high fraction of
carbon-enhanced metal-poor stars among the Na-extreme stars, they may have a
non-GC origin, perhaps due to mass-transfer events from evolved binary
companions.
