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 less than or similar to R less than or similar to 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 degrees between 30 degrees <= l <= 210 degrees 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) approximate to 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,V-circle dot = -10 +/- 1 km s(-1), and rotational velocity V-phi,V-circle dot = 242(-3)(+10) 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, similar to 2 kms(-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 greater than or similar to 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 similar to 8 x 10(11)M(circle dot).