Interstellar gas mass functions: Fractality and scale dependence

We present a theoretical model for the observed mass functions (MF's) of interstellar clouds, and test it by comparison with interferometrically observed MF's. We consider the time evolution of velocities using the stochastic differential Langevin equation for the objects (in fact gas clumps of sizes below 1 pc) under Brownian motion, with friction and magnetic field. We also study geometrical binding, and hence the implications of sizes of the regions in which the gas clouds move, and also of the departures from sphericity of the clouds themselves. The size of the global region in which the objects move under the influence of the general dynamics of the galaxy leads to a box-effect modelled as a Chandrasekhar barrier, which naturally leads to the superposition of Gaussian distributions over different ranges of displacement, and with progressively decreasing amplitude. This accounts for the general power law trend observed for the MF's, as well as its accompanying peaked structure. These results fit well the observed distributions even in very low mass ranges, which show global power law characteristics (scale independence, fractality, departures from sphericity for individual clouds), accompanied by turnovers, for a wide range of masses, characteristics of Gaussians (scale dependence, a tendency for clouds to be spherical).