Gravitational Collapse for Polytropic Gaseous Stars: Self-similar Solutions

Abstract

In the supercritical range of the polytropic indices $\gamma \in (1,\frac{4}{3})$ we show the existence of smooth radially symmetric self-similar solutions to the gravitational Euler-Poisson system. These solutions exhibit gravitational collapse in the sense that the density blows-up in finite time. Some of these solutions were numerically found by Yahil in 1983 and they can be thought of as polytropic analogues of the Larson-Penston collapsing solutions in the isothermal case $\gamma =1$. They each contain a sonic point, which leads to numerous mathematical difficulties in the existence proof.

92 pages

References in corpus (2)

• Larson-Penston Self-similar Gravitational Collapse
• Self-Similar Solutions to the Compressible Euler Equations and their Instabilities

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• On the Stability of the Euler-Poisson Dark-Fluid Model