On the properties of fractal cloud complexes

We study the physical properties derived from interstellar cloud complexes having a fractal structure. We first generate fractal clouds with a given fractal dimension and associate each clump with a maximum in the resulting density field. Then, we discuss the effect that different criteria for clump selection has on the derived global properties. We calculate the masses, sizes and average densities of the clumps as a function of the fractal dimension (Df) and the fraction of the total mass in the form of clumps (ǫ). In general, clump mass does not fulfill a simple power law with size of the type Mcl ∝ R γ cl, instead the power changes, from γ ≃ 3 at small sizes to γ < 3 at larger sizes. The number of clumps per logarithmic mass interval can be fitted to a power law Ncl ∝ M −αM cl in the range of relatively large masses, and the corresponding size distribution is Ncl ∝ R −αR cl at large sizes. When all the mass is forming clumps (ǫ = 1) we obtain that as Df increases from 2 to 3 αM increases from ∼ 0.3 to ∼ 0.6 and αR increases from ∼ 1.0 to ∼ 2.1. Comparison with observations suggests that Df ≃ 2.6 is roughly consistent with the average properties of the ISM. On the other hand, as the fraction of mass in clumps decreases (ǫ < 1) αM increases and αR decreases. When only ∼ 10% of the complex mass is in the form of dense clumps we obtain αM ≃ 1.2 for Df = 2.6 (not very different from the Salpeter value 1.35), suggesting this a likely link between the stellar initial mass function and the internal structure of molecular cloud complexes. Subject headings: ISM: structure — ISM: clouds — ISM: general