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Self-similar collapse of isothermal spheres and star formation
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1977
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Similarity solutions describe the gravitational collapse of isothermal spheres originating from gas clouds near marginal stability. The study argues that post‑core‑formation gas dynamics are self‑similar and explores applications to fragmentation stability and energy radiated during protostar formation. The authors derive similarity solutions for singular isothermal spheres, impose negligible initial fluid velocities to eliminate noncritical solutions, and evaluate an expansion‑wave collapse solution. A numerical example demonstrates the solutions under conditions representative of Bok globules or the central regions of nonmagnetic molecular clouds. Published in The Astrophysical Journal (1977), DOI 10.1086/155274.
view Abstract Citations (1574) References (29) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Self-similar collapse of isothermal spheres and star formation. Shu, F. H. Abstract Similarity solutions are obtained which describe the gravitational collapse of isothermal spheres that originated as gas clouds not far removed from the condition of marginal stability. It is argued that the similarity solution of Larson and Penston (1969) for the stages before core formation is physically artificial, but the gasdynamic flow subsequent to core formation exhibits self-similar properties. Similarity solutions are determined for the collapse of singular isothermal spheres, minus solutions without critical points are obtained by imposing the condition that the fluid velocities are negligible at the 'initial instant', and an expansion-wave collapse solution is evaluated. The results are illustrated with a numerical example roughly corresponding to conditions appropriate for Bok globules or the central regions of a nonmagnetic molecular cloud. Two possible applications of the solutions are discussed: analyzing the stability to gravitational fragmentation of collapsing pressure-free gas spheres and determining the amount of energy radiated away during protostar formation. Publication: The Astrophysical Journal Pub Date: June 1977 DOI: 10.1086/155274 Bibcode: 1977ApJ...214..488S Keywords: Density Distribution; Gravitational Collapse; Isothermal Flow; Protostars; Star Formation; Stellar Structure; Critical Point; Runge-Kutta Method; Similarity Theorem; Steady State; Stellar Envelopes; Astrophysics full text sources ADS |