Rotating self-gravitating cylinders with oscillating density structures.

Details Rotating self-gravitating cylinders with oscillating density structures. Rotating self-gravitating cylinders with oscillating density structures.

Sep 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...301..933s&link_type=abstract

Astronomy and Astrophysics, v.301, p.933

Astronomy and Astrophysics

Astrophysics

1

Hydrodynamics, Ism: Kinematics And Dynamics, Ism: Structure

Scientific paper

Specific properties of differentially rotating selfgravitating gases are investigated by studying the structure of infinitely long rotating cylinders. The combined effect of rotation, gravitation, and gaseous pressure leads to the formation of radial density oscillations. For a given simple rotation law, the equilibrium equations of self-gravitating differentially rotating gases yield solutions with a series of density maxima and minima in the radial direction. As the occurrence of such structures set limits to the numerical calculation of the equilibrium equations, we study rotating cylinders the structure of which is governed by ordinary differential equations. The discussion of a rigidly rotating polytropic cylinder with index n=1 introduces into the problem, and gives representative results. We study polytropic cylinders with negative polytropic index n<-1 as the behavior of these configurations corresponds to that of spherical or flattened polytropic configurations with n>5. As in the case of static polytropic spheres or cylinders, the equilibrium equations of rotating cylinders have singular solutions with infinite central density, which are limiting cases of solutions with finite central density. The latter oscillate about the corresponding singular solution. The asymptotic form of the oscillations is calculated analytically. For a given rotation law which approaches the rotation law of the singular solution asymptotically, the solutions of the equilibrium equation are calculated numerically. The strength of the oscillations depends on the central density. Further, we use a rotation law calculated from a given smooth density distribution, to study the behavior of a family of solutions with at least one member with a monotonic density. The analytical calculation of neighbouring solutions shows the particularity of a smooth density stratification. In general, a smooth rotation law produces oscillating density stratifications rather than monotonic configurations. A brief discussion of the stability of cylinders against adiabatic axi-symmetric perturbations shows that rotating configurations with oscillating densities should not be ruled out.

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