Self-consistent equilibrium models for the perfect elliptic disc

Computer Science – Numerical Analysis

Scientific paper

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18

Angular Momentum, Distribution Functions, Elliptical Cylinders, Equilibrium Equations, Orbital Mechanics, Elliptical Galaxies, Kinematics, Mathematical Models, Numerical Analysis, Radial Velocity, Schwarzschild Metric, Velocity Distribution

Scientific paper

Schwarzchild's linear programming method is used to develop numerical self-consistent models for the perfect elliptic disc. The maximum angular momentum solutions are found to have smooth distribution functions in action space (apart from an allowed discontinuity in the closed loop orbits), and the minimum angular momentum solutions are shown to be discontinuous over the marginal unstable orbits, suggesting that these solutions are probably unphysical. Mean streaming and velocity dispersion fields for the star and gas have been obtained. A significant difference is noted in the kinematics of the stars and gas which may have some relevance to hot ovally distorted discs with little or no figure pattern, or to the gas in the principal plane of a triaxial elliptical galaxy.

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