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The Structure of Self-Gravitating Polytropic Systems with n around 5 | | Mikhail V. Medvedev
; George Rybicki
; | | Date: |
30 Oct 2000 | | Subject: | astro-ph | | Affiliation: | Harvard & CITA) and George Rybicki (Harvard | | Abstract: | We investigate the structure of self-gravitating polytropic stellar systems. We present a method which allows to obtain approximate analytical solutions, $psi_{n+epsilon}({f x})$, of the nonlinear Poisson equation with the polytropic index $n+epsilon$, given the solution $psi_n({f x})$ with the polytropic index n, for any positive or negative $epsilon$ such that $|epsilon|ll1$. Application of this method to the spherically symmetric stellar polytropes with $nsimeq5$ 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 $gammasimeq 6/5$. Stability of such systems and observational consequences for both stellar and gaseous systems are discussed. | | Source: | arXiv, astro-ph/0010621 | | Services: | Forum | Review | PDF | Favorites | |
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