A SEARCH FOR SCALE-DEPENDENT MORPHOLOGY IN 5 MOLECULAR CLOUD COMPLEXES

We have analyzed IRAS 100 μm intensity images and 60 μm optical depth maps of five molecular clouds complexes (Chameleon, R CrA, p Oph, Taurus, and the Lynds 134/183/1778 group) using the area-perimeter analysis previously applied to terrestrial clouds by Lovejoy, and Rys and Waldvogel, and to the IRAS infrared cirrus by Bazell and Désert. In agreement with these workers, we find that cloud areas are generally a noninteger power of perimeter. The projected two-dimensional shapes of these objects are thus fractal. A noise analysis indicates that this result is not an artifact but reflects a fundamental property of the clouds. As in the case of terrestrial clouds, the fractal geometry almost certainly arises from the action of turbulence. Because turbulent fluctuations of equal energy might be expected to produce the most regular isodensity structure on the smallest scales within molecular clouds, we examine the dependence of fractal dimension on spatial scale in all five clouds. Even at the highest resolution of our analysis - approximately 0.3 pc - we find no evidence of completely smooth morphology. This implies that the correlation length of the turbulence driving the morphological irregularities within the clouds is less than 0.3 pc. However, we also find evidence of trends toward smoother geometries on smaller scales within the cloud complexes. This indicates either a decline in the amplitude of turbulent stress with scale (consistent with a correlation length not too far from the resolution of our analysis), the increasing dominance of self-gravity on smaller scales (as expected), or both. We examine the compatibility of our results with the theory of Hentschel and Procaccia, which was formulated to deal with the fractal geometries of terrestrial clouds and which is based on modifications of the Kolmogorov model of fully developed, incompressible turbulence. We find inconsistencies between the theory and what is currently known about turbulence in molecular clouds.