  The dynamics of the core of the Sagittarius (Sgr) dwarf spheroidal (dSph)
galaxy are explored using high-resolution (R~22,500), H-band, near-infrared
spectra of over 1,000 giant stars in the central 3 deg^2 of the system, of
which 328 are identified as Sgr members. These data, among some of the earliest
observations from the SDSS-III/Apache Point Observatory Galactic Evolution
Experiment (APOGEE) and the largest published sample of high resolution Sgr
dSph spectra to date, reveal a distinct gradient in the velocity dispersion of
Sgr from 11-14 km/s for radii >0.8 degrees from center to a dynamical cold
point of 8 km/s in the Sgr center --- a trend differing from that found in
previous kinematical analyses of Sgr over larger scales that suggest a more or
less flat dispersion profile at these radii. Well-fitting mass models with
either cored and cusped dark matter distributions can be found to match the
kinematical results, although the cored profile succeeds with significantly
more isotropic stellar orbits than required for a cusped profile. It is
unlikely that the cold point reflects an unusual mass distribution. The
dispersion gradient may arise from variations in the mixture of populations
with distinct kinematics within the dSph; this explanation is suggested (e.g.,
by detection of a metallicity gradient across similar radii), but not
confirmed, by the present data. Despite these remaining uncertainties about
their interpretation, these early test data (including some from instrument
commissioning) demonstrate APOGEE's usefulness for precision dynamical studies,
even for fields observed at extreme airmasses.
