Evolution of interstellar clouds towards star formation. I. The density-mass diagram of polytropic models

Abstract

We discuss the meaning of the density-mass diagram (DM diagram) in the study of the evolution of interstellar clouds and point out three different forms of the diagram. Using the polytrope model, we take the mean density, total mass, surface conditions (pressure and temperature) and the polytropic index as the main model parameters and exemplify the various model series under different constraining conditions. We particularly point out the properties of the models under the critical state of gravitational instability and their behaviour on the DM diagram. For example, at fixed temperature, we have the relation between the critical mass and mean density, M cr ∝ < P> −0.5, and at fixed surface pressure, the relation M cr ∝ < P> −2. We give also the relation between the critical density contrast P cr /< P> and the polytropic index (Fig.4).