Vertical structure of Galactic disk kinematics from LAMOST K giants

We examine the vertical structure of Galactic disk kinematics over a Galactocentric radial distance range of $R=5-15$ $\rm{kpc}$ and up to $3$ $\rm{kpc}$ away from the Galactic plane, using the K-type giants surveyed by LAMOST. Based on robust measurements of three-dimensional velocity moments, a wobbly disk is detected in a phenomenological sense. An outflow dominates the radial motion of the inner disk, while in the outer disk there exist alternate outward and inward flows. The vertical bulk velocities is a combination of breathing and bending modes. A contraction-like breathing mode with amplitudes increasing with the distance to the plane and an upward bending mode dominate the vertical motion outside $R_0$, and there are reversed breathing mode and bending mode at $R<R_0$, with amplitudes much smaller than those outside $R_0$. The mean azimuthal velocity decreases with the increasing distance to the plane, with gradients shallower for larger $R$. Stars in the south disk are rotating faster than stars in the north. The velocity ellipsoid orientation differs between different $R$: in the range of $5<R<9$ $\rm{kpc}$, the gradient of the tilt angle with respect to $\arctan(Z/R)$ decreases from $\sim0.83$ for the inner disk to $\sim0.52$ for the outer disk; within $9<R<15$ $\rm{kpc}$, the tilt of velocity ellipsoid deviates from vertical antisymmetry. A clear flaring signature is found for both north and south disks based on the observed vertical structures of velocity ellipsoid.