A Fractal Origin for the Mass Spectrum of Interstellar Clouds

Abstract

Interstellar molecular clouds have power-law size L and mass M distributions of the form n ( L ) dL = L −α L dL and n ( M ) dM = M −α M dM , where M ∝ L k is also a power law. These relations are shown to result from the fractal and scale-free nature of interstellar gas with power indices that are independent of distance. The results are α L = 1 + D and α M = 1 + D / κ for interstellar fractal dimension D = 2.3 ± 0.3 and a value of κ in the range 2.4-3.7, as determined from cloud surveys in the literature. The same fractal dimension also results from the expected relation D = κ when the M ( L ) correlation includes many different surveys, spanning a range of 10 10 in mass. These results imply that interstellar CO clouds are the unresolved parts of a pervasive fractal structure in the interstellar gas. The similarity between n ( M ) for interstellar clouds and n ( M ) for globular clusters suggests that the clusters formed inside fractal progenitor clouds at a nearly constant efficiency.