  We present arcsecond-scale Submillimeter Array observations of the CO(3-2)
line emission from the disks around the young stars HD 163296 and TW Hya at a
spectral resolution of 44 m/s. These observations probe below the ~100 m/s
turbulent linewidth inferred from lower-resolution observations, and allow us
to place constraints on the turbulent linewidth in the disk atmospheres. We
reproduce the observed CO(3-2) emission using two physical models of disk
structure: (1) a power-law temperature distribution with a tapered density
distribution following a simple functional form for an evolving accretion disk,
and (2) the radiative transfer models developed by D'Alessio et al. that can
reproduce the dust emission probed by the spectral energy distribution. Both
types of models yield a low upper limit on the turbulent linewidth (Doppler
b-parameter) in the TW Hya system (<40 m/s), and a tentative (3-sigma)
detection of a ~300 m/s turbulent linewidth in the upper layers of the HD
163296 disk. These correspond to roughly <10% and 40% of the sound speed at
size scales commensurate with the resolution of the data. The derived
linewidths imply a turbulent viscosity coefficient, alpha, of order 0.01 and
provide observational support for theoretical predictions of subsonic
turbulence in protoplanetary accretion disks.
