Oort Constants and Local Stellar Kinematics from GCNS

Oort constants and local kinematics are vital parameters with which to study the structure and dynamics of the Milky Way. When GCNS was published, it provided a clean sample of stars in the solar vicinity, which gives us an ideal tool with which to determine these parameters. Our aim was to calculate the reliable Oort constants with GCNS. We determined the Oort constants using the GCNS from Gaia EDR3 with $d<100$$\mathrm{pc}$. The proper motions and radial velocities were fitted with a maximum likelihood model. The uncertainties were obtained with an MCMC method. The sample was carefully selected to obtain a reliable result. The result yields the Oort constants $A=15.6\pm 1.6\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{kpc}}^{-1}$, $B=-15.8\pm 1.7\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{kpc}}^{-1}$, $C=-3.5\pm 1.6\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{kpc}}^{-1}$, and $K=2.7\pm 1.5\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{kpc}}^{-1}$. The non-zero C and K imply that the local disc is in a non-asymmetric potential. With the Oort constants, we derived the local angular velocity ${\Omega }_0\approx A-B=31.4\pm 2.3\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{kpc}}^{-1}$. The solar motion ($U_{\odot }$, $V_{\odot }$, $W_{\odot }$) was calculated as ($10.1\pm 0.1$, $22.8\pm 0.1$, $7.8\pm 0.1$) $\mathrm{km}{\mathrm{s}}^{-1}$.