Time stamps of vertical phase mixing in the Galactic disk from
  LAMOST-Gaia stars
  The perturbation mechanism of the Galactic disk has puzzled us for a long
time. The imprints from perturbations provide important diagnostics on the disk
formation and evolution. Here we try to constrain when the vertical
perturbation took place in the disk by tracking the phase mixing history.
Firstly, we clearly depict the spiral structures of radial ($v_R$) and
azimuthal ($v_{\phi}$) velocities in the phase space of the vertical position
and velocity ($z$-$v_z$) with 723,871 LAMOST-Gaia combined stars. Then, we
investigate the variation of the spirals with stellar age ($\tau$) by dividing
the sample into seven stellar age bins. Finally, we find that the spirals
explicitly exist in all the bins, even in the bin of $\tau<0.5$\,Gyr, except
for the bin of $\tau>6.0$\,Gyr. This constrains the vertical perturbation
probably starting no later than 0.5\,Gyr ago. But we can not rule out whether
the young stars ($\tau<0.5$\,Gyr) inherit the oscillations from the perturbed
ISM where they born from. This study provides some important observational
evidences to understand the disk perturbation mechanisms, even the formation
and evolution of our Galaxy.
