We measure the Milky Way ’ s rotation curve over the Galactocentric range 4 \mathrm { kpc } \lesssim R \lesssim 14 \mathrm { 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 ^ { \circ } between 30 ^ { \circ } \leq l \leq 210 ^ { \circ } out to distances of 10 \mathrm { kpc } using an axisymmetric kinematical model that includes a correction for the asymmetric drift of the warm tracer population ( \sigma _ { R } \approx 35 \mathrm { km s } ^ { -1 } ) .
We determine the local value of the circular velocity to be V _ { c } ( R _ { 0 } ) = 218 \pm 6 \mathrm { km s } ^ { -1 } and find that the rotation curve is approximately flat with a local derivative between -3.0 \mathrm { km s } ^ { -1 } \mathrm { kpc } ^ { -1 } and 0.4 \mathrm { km s } ^ { -1 } \mathrm { kpc } ^ { -1 } .
We also measure the Sun ’ s position and velocity in the Galactocentric rest frame , finding the distance to the Galactic center to be 8 \mathrm { kpc } < R _ { 0 } < 9 \mathrm { kpc } , radial velocity V _ { R, \odot } = -10 \pm 1 \mathrm { km s } ^ { -1 } , and rotational velocity V _ { \phi, \odot } = 242 ^ { +10 } _ { -3 } \mathrm { km s } ^ { -1 } , 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 , \sim 2 \mathrm { km s } ^ { -1 } in V _ { c } .
Marginalizing over all the systematics that we consider , we find that V _ { c } ( R _ { 0 } ) < 235 \mathrm { km s } ^ { -1 } at > 99 \% confidence .
We find an offset between the Sun ’ s rotational velocity and the local circular velocity of 26 \pm 3 \mathrm { km s } ^ { -1 } , which is larger than the locally-measured solar motion of 12 \mathrm { km s } ^ { -1 } .
This larger offset reconciles our value for V _ { c } with recent claims that V _ { c } \gtrsim 240 \mathrm { km s } ^ { -1 } .
Combining our results with other data , we find that the Milky Way ’ s dark-halo mass within the virial radius is \sim 8 \times 10 ^ { 11 } M _ { \odot } .