A fractal origin for the mass spectrum of interstellar clouds

Interstellar molecular clouds have power-law size L and mass M distributions of the form n(L)dL = L-(alpha L)dL and n(M)dM = M-(alpha M)dM, where M proportional to L(kappa) 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 alpha(L) = 1 + D and alpha(M) = 1 + D/kappa for interstellar fractal dimension D = 2.3 +/- 0.3 and a value of kappa 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 = kappa 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.