Characteristic structure of star-forming clouds
  This paper gives a new way to diagnose the star-forming potential of a
molecular cloud region from the probability density function of its column
density (N-pdf). It gives expressions for the column density and mass profiles
of a symmetric filament having the same N-pdf as a filamentary region. The
central concentration of this characteristic filament can distinguish regions
and can quantify their fertility for star formation. Profiles are calculated
for N-pdfs which are pure lognormal, pure power law, or a combination. In
relation to models of singular polytropic cylinders, characteristic filaments
can be unbound, bound, or collapsing depending on their central concentration.
Such filamentary models of the dynamical state of N-pdf gas are more relevant
to star-forming regions than are models of spherical collapse. The star
formation fertility of a bound or collapsing filament is quantified by its mean
mass accretion rate when in radial free fall. For a given mass per length, the
fertility increases with the filament mean column density and with its initial
concentration. In selected regions the fertility of their characteristic
filaments increases with the level of star formation.
