Linear and nonlinear dynamic instability of rotating polytropes

Details Linear and nonlinear dynamic instability of rotating polytropes Linear and nonlinear dynamic instability of rotating polytropes

Apr 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987apj...315..594w&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 315, April 15, 1987, p. 594-601. NASA-supported research.

Astronomy and Astrophysics

Astrophysics

46

Dynamic Stability, Linear Equations, Nonlinear Equations, Polytropic Processes, Stellar Models, Stellar Rotation, Density Distribution, Fourier Analysis, Kinetic Energy, Star Formation, Stellar Gravitation, Stellar Interiors

Scientific paper

A three-dimensional hydrodynamic computer program is used to study the growth of nonaxisymmetric structures in rapidly rotating, self-gravitating polytropes. Models with polytropic index n = 0.8, 1.0, 1.3, 1.5, and 1.8 are studied. The initially axisymmetric equilibria are constructed by the Ostriker-Mark self-consistent-field method. The nonaxisymmetric pattern that develops out of low-amplitude random noise is a two-armed spiral with a well-defined pattern speed and growth rate which closely match properties of the toroidal mode predicted from the linear, second-order tensor-virial equation. A Fourier analysis of each polytrope's azimuthal density distribution shows that, even in the linear amplitude regime, higher-order angular patterns also develop exponentially in time. The higher-order patterns ultimately move in synchronization with the broad two-armed spiral, creating a narrow two-armed spiral. As the polytropic index is decreased, a more open and centrally more barlike pattern develops.

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