The Milky Way's circular velocity curve between 4 and 14 kpc from APOGEE
  data
  We measure the Milky Way's rotation curve over the Galactocentric range 4 kpc
<~ R <~ 14 kpc from the first year of data from the Apache Point Observatory
Galactic Evolution Experiment (APOGEE). We model the line-of-sight velocities
of 3,365 stars in fourteen fields with b = 0 deg between 30 deg < l < 210 deg
out to distances of 10 kpc using an axisymmetric kinematical model that
includes a correction for the asymmetric drift of the warm tracer population
(\sigma_R ~ 35 km/s). We determine the local value of the circular velocity to
be V_c(R_0) = 218 +/- 6 km/s and find that the rotation curve is approximately
flat with a local derivative between -3.0 km/s/kpc and 0.4 km/s/kpc. We also
measure the Sun's position and velocity in the Galactocentric rest frame,
finding the distance to the Galactic center to be 8 kpc < R_0 < 9 kpc, radial
velocity V_{R,sun} = -10 +/- 1 km/s, and rotational velocity V_{\phi,sun} =
242^{+10}_{-3} km/s, in good agreement with local measurements of the Sun's
radial velocity and with the observed proper motion of Sgr A*. We investigate
various systematic uncertainties and find that these are limited to offsets at
the percent level, ~2 km/s in V_c. Marginalizing over all the systematics that
we consider, we find that V_c(R_0) < 235 km/s at >99% confidence. We find an
offset between the Sun's rotational velocity and the local circular velocity of
26 +/- 3 km/s, which is larger than the locally-measured solar motion of 12
km/s. This larger offset reconciles our value for V_c with recent claims that
V_c >~ 240 km/s. Combining our results with other data, we find that the Milky
Way's dark-halo mass within the virial radius is ~8x10^{11} M_sun.
