Do Lognormal Column-Density Distributions in Molecular Clouds Imply
  Supersonic Turbulence?
  Recent observations of column densities in molecular clouds find lognormal
distributions with power-law high-density tails. These results are often
interpreted as indications that supersonic turbulence dominates the dynamics of
the observed clouds. We calculate and present the column-density distributions
of three clouds, modeled with very different techniques, none of which is
dominated by supersonic turbulence. The first star-forming cloud is simulated
using smoothed particle hydrodynamics (SPH); in this case gravity, opposed only
by thermal-pressure forces, drives the evolution. The second cloud is
magnetically subcritical with subsonic turbulence, simulated using nonideal
MHD; in this case the evolution is due to gravitationally-driven ambipolar
diffusion. The third cloud is isothermal, self-gravitating, and has a smooth
density distribution analytically approximated with a uniform inner region and
an r^-2 profile at larger radii. We show that in all three cases the
column-density distributions are lognormal. Power-law tails develop only at
late times (or, in the case of the smooth analytic profile, for strongly
centrally concentrated configurations), when gravity dominates all opposing
forces. It therefore follows that lognormal column-density distributions are
generic features of diverse model clouds, and should not be interpreted as
being a consequence of supersonic turbulence.
