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We introduce exact analytical solutions of the steady-state hydrodynamicequations of scale-free, self-gravitating gaseous disks with flat rotationcurves. We express the velocity field in terms of a stream function and obtaina third-order ordinary differential equation (ODE) for the angular part of thestream function. We present the closed-form solutions of the obtained ODE andconstruct hydrodynamical counterparts of the power-law and elliptic disks, forwhich self-consistent stellar dynamical models are known. We show that thekinematics of the Large Magellanic Cloud can well be explained by our findingsfor scale-free elliptic disks.Comment: AAS preprint format, 21 pages, 8 figures, accepted for publication in  The Astrophysical Journa

Scale‐free Equilibria of Self‐gravitating Gaseous Disks with Flat Rotation Curves