Abstract
Astrophys.J. 551 (2001) 712-729 Multifractal scaling (MFS) refers to structures that can be described as a
collection of interwoven fractal subsets which exhibit power-law spatial
scaling behavior with a range of scaling exponents (concentration, or
singularity, strengths) and dimensions. The existence of MFS implies an
underlying multiplicative (or hierarchical, or cascade) process. Panoramic
column density images of several nearby star- forming cloud complexes,
constructed from IRAS data and justified in an appendix, are shown to exhibit
such multifractal scaling, which we interpret as indirect but quantitative
evidence for nested hierarchical structure. The relation between the dimensions
of the subsets and their concentration strengths (the "multifractal spectrum'')
appears to satisfactorily order the observed regions in terms of the mixture of
geometries present: strong point-like concentrations, line- like filaments or
fronts, and space-filling diffuse structures. This multifractal spectrum is a
global property of the regions studied, and does not rely on any operational
definition of "clouds.'' The range of forms of the multifractal spectrum among
the regions studied implies that the column density structures do not form a
universality class, in contrast to indications for velocity and passive scalar
fields in incompressible turbulence, providing another indication that the
physics of highly compressible interstellar gas dynamics differs fundamentally
from incompressible turbulence. (Abstract truncated)