The spatial variations of the velocity field of local stars provide direct evidence of Galactic differential rotation .
The local divergence , shear , and vorticity of the velocity field—the traditional Oort constants—can be measured based purely on astrometric measurements and in particular depend linearly on proper motion and parallax .
I use data for 304,267 main-sequence stars from the Gaia DR1 Tycho- Gaia Astrometric Solution to perform a local , precise measurement of the Oort constants at a typical heliocentric distance of 230 pc .
The pattern of proper motions for these stars clearly displays the expected effects from differential rotation .
I measure the Oort constants to be : A = 15.3 \pm 0.4 \mathrm { km s } ^ { -1 } \mathrm { kpc } ^ { -1 } , B = -11.9 \pm 0.4 \mathrm { km s } ^ { -1 } \mathrm { kpc } ^ { -1 } , C = -3.2 \pm 0.4 \mathrm { km s } ^ { -1 } \mathrm { kpc } ^ { -1 } and K = -3.3 \pm 0.6 \mathrm { km s } ^ { -1 } \mathrm { kpc } ^ { -1 } , with no color trend over a wide range of stellar populations .
These first confident measurements of C and K clearly demonstrate the importance of non-axisymmetry for the velocity field of local stars and they provide strong constraints on non-axisymmetric models of the Milky Way .