Kinematics of the molecular interstellar medium probed by Gaia: steep
  velocity dispersion-size relation, isotropic turbulence, and
  location-dependent energy dissipation
  The evolution of the molecular interstellar medium is controlled by processes
such as turbulence, gravity, stellar feedback, and Galactic shear. AL a part of
the ISM-6D https://gxli.github.io/ISM-6D/ project, using Gaia astrometric
measurements towards a sample of young stellar objects (YSOs), we study
morphology and kinematic structure of the associated molecular gas. We identify
150 YSO associations with distance $d \lesssim 3 \;\rm kpc$. The YSO
associations are elongated, with a median aspect ratio of 1.97, and are
oriented parallel to the disk midplane, with a median angle of 30$^{\circ}$.
The turbulence in the molecular clouds as probed by the YSOs is isotropic, and
the velocity dispersions are related to the sizes by $\sigma_{v,{\rm 2D}} =
0.74\;(r/{\rm pc})^{0.67} \;({\rm km/s})\;$. The slope is on the steeper side,
yet consistent with previous measurements. The energy dissipation rate of
turbulence $\dot{\epsilon} = \sigma_{v,{\rm 3D}}^3 /L$ decreases with the
Galactocentric distance, with a gradient of 0.2 $\rm dex
  \; kpc^{-1}$, which can be explained if turbulence is driven by cloud
collisions. In this scenario, the clouds located in the inner Galaxy have
higher chances to accrete smaller clouds and are more turbulent. Although the
density structures of the complexes are anisotropic, the turbulence is
consistent with being isotropic. If the alignment between density structures
and the Galactic-disk mid-plane is due to shear, we expect $t_{\rm cloud}
\gtrsim t_{\rm shear}\approx 30\; \rm Myr$. This cloud lifetime is longer than
the turbulence crossing time, and a continuous energy injection is required to
maintain the turbulence.
