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

@article{Jalali2002ScalefreeEO,
  title={Scale-free Equilibria of Self-gravitating Gaseous Disks with Flat Rotation Curves},
  author={Mir Abbas Jalali and Mehdi Abolghasemi},
  journal={The Astrophysical Journal},
  year={2002},
  volume={580},
  pages={718 - 724}
}
We introduce exact analytical solutions of the steady state hydrodynamic equations of scale-free, self-gravitating gaseous disks with flat rotation curves. We express the velocity field in terms of a stream function and obtain a third-order ordinary differential equation (ODE) for the angular part of the stream function. We present the closed-form solutions of the obtained ODE and construct hydrodynamical counterparts of the power-law and elliptic disks, for which self-consistent stellar… 
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