THE MILKY WAY'S CIRCULAR-VELOCITY CURVE BETWEEN 4 AND 14 kpc FROM APOGEE DATA

Abstract

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 • 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 φ,⊙ = 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 × 10 11 M ⊙ .

Radial migration of the Sun in the Milky Way: a statistical study

“…This means that translated to a Sun-centred reference frame the x-axis points toward the Galactic centre, the yaxis in the direction of Galactic rotation, and the z-axis completes the right-handed coordinate system. Recently Bovy et al (2012) found an offset between the rotational velocity of the Sun and VLSR of 26 ± 3 km s −1 , which is larger than the value measured by Schönrich et al (2010). We also use this value to trace back the Sun's orbit.…”

“…The green line is the resulting radial migration of the Sun when we assume a tangential velocity of 12.4 ± 2.1 kms −1 (Schönrich et al 2010) in the orbit integration backwards in time. The blue line is the radial migration of the Sun when we assume a tangential velocity of 26 ± 3 kms −1 (Bovy et al 2012). The blue shaded region corresponds to the RSE of p(Rp − R b ) for this latter case.…”

“…For comparison we have also plotted the median of the distribution p(Rp − R b ) when the tangential velocity of the Sun is taken from Schönrich et al (2010). As can be observed, the migration of the Sun on average is approximately 1 kpc higher when V is taken from Bovy et al (2012). In the latter case, the median of the distribution p(Rp −R b ) is negative for both m = 2 and m = 4 meaning that the Sun has migrated from outer regions of the Galactic disk to R .…”

“…In this simulation the amplitude of the main spiral structure is Asp 1 = 1300 km 2 s −2 kpc −1 . We used the tangential velocity of the Sun from Bovy et al (2012). As can be seen, the median of the distribution p(Rp − R b ) is smaller than 1 kpc, meaning that the migration of the Sun on average is not significant.…”

“…In this section we explore the motion of the Sun backwards in time when assuming the rotational velocity suggested by Bovy et al (2012). In Fig.…”