Galactic Rotation and the Oort Constants in the Solar Vicinity

Gaia DR2 data are used to calculate the Oort constants and derive the Galactic rotational properties in this work. We choose the solar vicinity stars with a clean sample within 500 pc. The Oort constants are then fitted through the relation between the proper motions as a function of Galactic longitude l. A maximum likelihood method is adopted to obtain the Oort constants and the uncertainties are produced by a Markov Chain Monte Carlo technique with the sample. Our results for the Oort constants are A = 15.1 +/- 0.1 kms(-1) kpc(-1), B = -13.4 +/- 0.1 kms(-1) kpc(-1), C = -2.7 +/- 0.1 kms(-1) kpc(-1), and K = -1.7 +/- 0.2 kms(-1) kpc(-1) respectively. The nonzero values of C and K represent a nonaxisymmetric model for the Galaxy. According to our results, the angular velocity Omega = vertical bar A - B vertical bar = 28.5. 0.1 km s(-1) kpc(-1) and the circular velocity decreases in solar vicinity. The local radial velocity also decreases along the radial direction due to C + K being negative.