Mass Functions in Fractal Clouds: The Role of Cloud Structure in the
  Stellar Initial Mass Function
  The possibility that the stellar initial mass function (IMF) arises mostly
from cloud structure is investigated with fractal Brownian motion (fBm) clouds
that have power-law power spectra. An fBm cloud with a realistic projected
power spectrum slope of $\beta=2.8$ is found to have a mass function for clumps
exceeding a threshold density that is a power-law with a slope of
$\alpha=2.35$, the same as in the Salpeter IMF. Any hierarchically structured
cloud has a clump mass function with about the same slope. This result implies
that turbulent interstellar clouds produce dense substructure with the observed
pre-stellar core mass function built in from the start. Details of the clump
formation processes are not critical. The conversion of clumps into stars
involves a second step. A one-to-one correspondence between clump mass and star
mass is not necessary to convert the clump mass spectrum into an IMF with the
same power-law slope. As long as clumps have an internal stellar IMF from
sub-fragmentation, protostellar accretion, coalescence and other processes, and
the characteristic mass for this internal IMF scales with the clump mass, then
the IMF slope above the minimum characteristic mass will equal the clump mass
slope. A detailed review of IMF models illustrates the prominence of cloud
structure as a major component in a wide class of theories. Tests are proposed
to determine the relative importance of cloud structure and competitive
accretion in the IMF.
