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. We model the line-of-sight velocities of 3365 stars in 14 fields with b = 0° between 30° ⩽ l ⩽ 210° out to distances of 10 kpc using an axisymmetric kinematical model that includes a correction for the asymmetric drift of the warm tracer population (σR ≈ 35 km s−1). We determine the local value of the circular velocity to be Vc(R0) = 218 ± 6 km s−1 and find that the rotation curve is approximately flat with a local derivative between −3.0 km s−1 kpc−1 and 0.4 km s−1 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 kpc < R0 < 9 kpc, radial velocity VR, ☉ = −10 ± 1 km s−1, and rotational velocity Vϕ, ☉ = 242+10− 3 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, ∼2 km s−1 in Vc. Marginalizing over all the systematics that we consider, we find that Vc(R0) < 235 km s−1 at >99 % confidence. We find an offset between the Sun's rotational velocity and the local circular velocity of 26 ± 3 km s−1, which is larger than the locally measured solar motion of 12 km s−1. This larger offset reconciles our value for Vc with recent claims that Vc ≳ 240 km s−1. Combining our results with other data, we find that the Milky Way's dark-halo mass within the virial radius is ∼8 × 1011 M☉.