Density bifurcation in a homogeneous isotropic collapsing star

Details Density bifurcation in a homogeneous isotropic collapsing star Density bifurcation in a homogeneous isotropic collapsing star

Jun 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985apj...293..494b&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 293, June 15, 1985, p. 494-503.

Mathematics

40

Density Distribution, Gravitational Collapse, Hydrodynamics, Stellar Structure, Branching (Mathematics), Eigenvectors, Isotropism, Linear Equations, Mach Number, Polytropic Processes, Stellar Models

Scientific paper

The collapse of an isotropic nonradiating sphere of perfect gas submitted to a polytropic equation of state is studied from the point of view of similarity solutions. The equations representing the evolution of the sphere throughout the collapse are shown to have a critical point. An analytic study of this critical point is made possible in the simple case of the homogeneous solution. In this special case, a mathematical and numerical bifurcation is shown to exist.

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