  Characterizing turbulence in protoplanetary disks is crucial for
understanding how they accrete and spawn planets. Recent measurements of
spectral line broadening promise to diagnose turbulence, with different lines
probing different depths. We use 3D local hydrodynamic simulations of cooling,
self-gravitating disks to resolve how motions driven by "gravito-turbulence"
vary with height. We find that gravito-turbulence is practically as vigorous at
altitude as at depth: even though gas at altitude is much too rarefied to be
itself self-gravitating, it is strongly forced by self-gravitating
overdensities at the midplane. The long-range nature of gravity means that
turbulent velocities are nearly uniform vertically, increasing by just a factor
of 2 from midplane to surface, even as the density ranges over nearly three
orders of magnitude. The insensitivity of gravito-turbulence to height
contrasts with the behavior of disks afflicted by the magnetorotational
instability (MRI); in the latter case, non-circular velocities increase by at
least a factor of 15 from midplane to surface, with various non-ideal effects
only magnifying this factor. The distinct vertical profiles of
gravito-turbulence vs. MRI turbulence may be used in conjunction with
measurements of non-thermal linewidths at various depths to identify the source
of transport in protoplanetary disks.
