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A. Umnov (Kurchatov Inst.), M. V. Medvedev (Harvard & CITA), R. Narayan (Harvard)
Simple models of a self-gravitating gas are often used to describe or model the structure of molecular clouds, in studies of star formation, etc. Therefore, rigorous analytical results are welcome. Here we study and classify the structure of all possible axisymmetric self-similar equilibrium configurations of self-gravitating, rotating, isothermal systems. We show that there are two families: (1) Cylindrically symmetric solutions in which the density varies with cylindrical radius as R-2(n+1), with -1\le n\le0. (2) Axially symmetric solutions in which the density varies as f(\theta)/r2, where r is the spherical radius and \theta is the co-latitude. The singular isothermal sphere is a special case of the latter class with f(\theta)={\rm constant}. The axially symmetric equilibrium configurations form a two-parameter family of solutions and include equilibria which are asymmetric with respect to the equatorial plane. We investigate whether the asymmetric equilibria are force-free at the singular points r=0, \infty, as well as their relevance to real systems. For each hydrodynamic equilibrium, we determine the phase-space distribution of the collisionless analog.
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