QUIPS - Time-dependent properties of quasi-invariant self-gravitating polytropes

Details QUIPS - Time-dependent properties of quasi-invariant self-gravitating polytropes QUIPS - Time-dependent properties of quasi-invariant self-gravitating polytropes

Apr 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983apj...267..344m&link_type=abstract

Astrophysical Journal, Part 1, vol. 267, Apr. 1, 1983, p. 344-357.

Astronomy and Astrophysics

Astrophysics

13

Hydrodynamics, Polytropic Processes, Stellar Gravitation, Stellar Oscillations, Stellar Structure, Time Dependence, Canonical Forms, Gas Expansion, Gravitational Effects, Hamiltonian Functions, Ideal Gas, Linear Transformations, Spheres, Stellar Models

Scientific paper

A time parameter is introduced into Emden's static solution in a quasi-invariant time-dependent analysis of the expansion and/or contraction of a self-gravitating sphere of perfect gas with a predetermined polytropic index. Oscillations of the gas sphere are ignored, and transformations are defined in a generalized canonical form, i.e., to ensure a linear time transformation. Additionally, the Hamiltonian is formulated to be invariant, and a dual space is defined which includes friction, a sink term, and a centripetal/centrifugal force. A characteristic frequency is obtained that is related to Jean's frequency, and is significant for the quasi-invariant polytrope. The internal structure of the gas sphere is found to be steady whether in contraction or expansion, whereas an expansion is stable while a contraction is not. It is noted that the numerical model developed is not periodic.

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