On the quasi-hydrostatic flows of radiatively cooling self-gravitating gas clouds

Two model problems are considered, illustrating the dynamics of quasi-hydrostatic flows of radiatively cooling, optically thin self-gravitating gas clouds. In the first problem, spherically symmetric flows in an unmagnetized plasma are considered. For a power-law dependence of the radiative loss function on the temperature, a one-parameter family of similarity solutions is found. We concentrate on a constant-mass cloud, one of the cases when the similarity indices are uniquely selected. In this case, the problem can be formally reduced to the classical Lane-Emden equation and therefore solved analytically. The cloud is shown to undergo radiative condensation, if the gas specific heat ratio γ is greater than 4/3. The condensation proceeds either gradually or in the form of (quasi-hydrostatic) collapse. For γ < 4/3, the cloud is shown to expand. The second problem addresses a magnetized plasma slab that undergoes quasi-hydrostatic radiative cooling and condensation. The problem is solved analytically, employing the Lagrangian mass coordinate.