  The ability to perform detailed chemical analysis of Sun-like F-, G-, and
K-type stars is a powerful tool with many applications including studying the
chemical evolution of the Galaxy and constraining planet formation theories.
Unfortunately, complications in modeling cooler stellar atmospheres hinders
similar analysis of M-dwarf stars. Empirically-calibrated methods to measure M
dwarf metallicity from moderate-resolution spectra are currently limited to
measuring overall metallicity and rely on astrophysical abundance correlations
in stellar populations. We present a new, empirical calibration of synthetic M
dwarf spectra that can be used to infer effective temperature, Fe abundance,
and Ti abundance. We obtained high-resolution (R~25,000), Y-band (~1 micron)
spectra of 29 M dwarfs with NIRSPEC on Keck II. Using the PHOENIX stellar
atmosphere modeling code (version 15.5), we generated a grid of synthetic
spectra covering a range of temperatures, metallicities, and
alpha-enhancements. From our observed and synthetic spectra, we measured the
equivalent widths of multiple Fe I and Ti I lines and a temperature-sensitive
index based on the FeH bandhead. We used abundances measured from
widely-separated solar-type companions to empirically calibrate transformations
to the observed indices and equivalent widths that force agreement with the
models. Our calibration achieves precisions in Teff, [Fe/H], and [Ti/Fe] of 60
K, 0.1 dex, and 0.05 dex, respectively and is calibrated for 3200 K < Teff <
4100 K, -0.7 < [Fe/H] < +0.3, and -0.05 < [Ti/Fe] < +0.3. This work is a step
toward detailed chemical analysis of M dwarfs at a similar precision achieved
for FGK stars.
