| Autors: Donkov, S. D., Stefanov, I. Z., Т. В. Велчев., R. S. Klessen. Title: Density profile of a self-gravitating polytropic turbulent fluid in the context of ensembles of molecular clouds Keywords: molecular clouds; star formation; polytropic equation of sta Abstract: We obtain an equation for the density profile in a self-gravitating polytropic spherically symmetric turbulent fluid. The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state changes from isothermal (in the outer cloud layers) with Γ=1 to one of `hard polytrope' with exponent Γ>1. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation reproduces the Bernoulli equation for the proposed model and describes the balance of the kinetic, thermal and gravitational energy of a fluid element. We propose as well a method to obtain approximate solutions in a power-law form which results in four solutions corresponding to different density profiles, polytropic exponents and energy balance equations for a fluid element. One of them matches with observations and numerical works. References Issue
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