Chemistry in Disks VIII: the CS molecule as an analytic tracer of
  turbulence in disks
  Turbulence is thought to be a key driver of the evolution of protoplanetary
disks, regulating the mass accretion process, the transport of angular
momentum, and the growth of dust particles.
  We intend to determine the magnitude of the turbulent motions in the outer
parts (> 100 AU) of the disk surrounding DM Tau. Turbulent motions can be
constrained by measuring the nonthermal broadening of line emission from heavy
molecules. We used the IRAM Plateau de Bure interferometer to study emission
from the CS molecule in the disk of DM Tau. High spatial (1.4 x 1 ") and
spectral resolution (0.126 km/s) CS J=3-2 images provide constraints on the
molecule distribution and velocity structure of the disk. A low sensitivity CS
J=5-4 image was used in conjunction to evaluate the excitation conditions. We
analyzed the data in terms of two parametric disk models, and compared the
results with detailed time-dependent chemical simulations.
  The CS data confirm the relatively low temperature suggested by observations
of other simple molecules. The intrinsic linewidth derived from the CS J=3-2
data is much larger than expected from pure thermal broadening. The magnitude
of the derived nonthermal component depends only weakly on assumptions about
the location of the CS molecules with respect to the disk plane. Our results
indicate turbulence with a Mach number around 0.4 - 0.5 in the molecular layer.
Geometrical constraints suggest that this layer is located near one scale
height, in reasonable agreement with chemical model predictions.
