A Statistical Model for the Cloud Structure of the Interstellar Medium

Abstract

We have formulated and studied the properties of a mathematical model intended to span between the hydrodynamical and discontinuous regimes. Model parameters and predictions permit matching the observed mass spectrum of those interstellar clouds with masses between 10³ and 10⁶M⊙. The central element of the theory is the specification of P (m, m′, μ, μ′, … μ″), the conditional probability that once a collision has occurred between clouds of mass m, m′ the result is clouds of mass μ, μ′, … μ″. For stable solutions to exist we require that the total mass in the system be conserved. Such simple models as total coalescence, geometric overlap and partition statistics were considered for P as well as several probabilities based on possible physical conditions that might prevail in cloud-cloud collisions. One immediate numerical result of these models is that nearly total coalescence must obtain in actual cloud-cloud collisions before one can build up a non-infinitesimal concentration of large mass couds. Field and coworkers (1965, 1968) indicate that total coalescence would produce a minimum in the mass spectrum and that as the position of the minimum went to infinity the spectrum itself more closely approximates a power law curve with index − 3/2. In none of our calculations was anything but strict monotonic decrease observed and under the same physical assumptions as Field the curve we obtain (analytically) has no minimum, independent of the largest mass in the system. Both of these spectra are flatter than recent observational evidence indicate. True equilibrium solutions exist in our formulation with an e-folding time ≃ 10⁷ yr for objects such as these. We are continuing work on the detailed time evolution of interstellar clouds in particular and formulating other astronomically interesting applications of the general theory.