The Structure of Self-Gravitating Polytropic Systems with n around 5

Abstract

We investigate the structure of self-gravitating polytropic stellar systems. We present a method which allows to obtain approximate analytical solutions, ${\psi }_{n+\epsilon }(\mathbf{x})$, of the nonlinear Poisson equation with the polytropic index $n+\epsilon$, given the solution ${\psi }_n(\mathbf{x})$ with the polytropic index n, for any positive or negative $\epsilon$ such that $|\epsilon |\ll 1$. Application of this method to the spherically symmetric stellar polytropes with $n\simeq 5$ yields the solutions which describe spatially bound systems if n<5 and the formation of a second core if n>5. A heuristic approximate expressions for the radial profiles are also presented. Due to the duality between stellar and gas polytropes, our results are valid for gaseous, self-gravitating polytropic systems (e.g., molecular clouds) with the index $\gamma \simeq 6/5$. Stability of such systems and observational consequences for both stellar and gaseous systems are discussed.

LaTeX, emulateapj, 5 pages, 2 PS figures. ApJ,accepted version. Other works are at http://www.cita.utoronto.ca/~medvedev/

References in corpus (2)

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