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 (σ _R ≈ 35 km s^-1). We determine the local value of the circular velocity to be V_c (R ₀) = 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 < R ₀ < 9 kpc, radial velocity V _{R, ⊙} = -10 ± 1 km s^-1, and rotational velocity V _{phi, ⊙} = 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 V_c . Marginalizing over all the systematics that we consider, we find that V_c (R ₀) < 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 V_c with recent claims that V_c >~ 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 _⊙.