Equilibrium of rotating gaseous disks of finite thickness

Astronomy and Astrophysics – Astronomy

Scientific paper

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Astronomical Models, Dynamic Stability, Equilibrium Equations, Gravitation Theory, Rotating Fluids, Asymptotic Methods, Galactic Evolution, Galactic Rotation, Poisson Equation, Polytropic Processes, Roche Limit, Rotating Disks, Rotating Liquids, Spatial Distribution, Spiral Galaxies, Stellar Rotation

Scientific paper

An analysis is presented of the equilibrium of self-gravitating gaseous disks of finite thickness, with allowance for all corrections of the order h/R, where h and R are the characteristic values of half-thickness and radius. It is shown that it is necessary to take into account corrections of gravitational force to the same order as pressure terms in the radial equilibrium. For a specified polytropic equation of state, a closed system of equations is obtained determining the distribution of surface density in the main part of the disk for a given rotation law. It is also shown that there is a limit of uniform rotation for any polytropic figure of equilibrium, except for an incompressible fluid. An asymptotic relationship is obtained for the maximum oblateness of a figure in the case of limiting rotation.

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