2006ApJ...641..347S

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 have on the derived global properties. We calculate the masses, sizes, and average densities of the clumps as a function of the fractal dimension (D_f) and the fraction of the total mass in the form of clumps (ε). In general, clump mass does not fulfill a simple power law with size of the type M_cl{vprop}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 N_cl{vprop}M^–αM_cl in the range of relatively large masses, and the corresponding size distribution is N_cl{vprop}R^–αR_clat large sizes. When all the mass is forming clumps (ε=1), we obtain that as D_fincreases from 2 to 3, α_Mincreases from ∼0.3 to ∼0.6 and α_Rincreases from ∼1.0 to ∼2.1. Comparison with observations suggests that D_f≃2.6 is roughly consistent with the average properties of the ISM. On the other hand, as the fraction of mass in clumps decreases (ε<1), α_M increases and α_Rdecreases. When only ∼10% of the complex mass is in the form of dense clumps, we obtain α_M≃1.2 for D_f=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.