Evolution of superbubbles in a self-gravitating disk

The expansion of a superbubble is investigated both analytically and numerically. Our model implements the thin layer approximation in a vertical profile of density as given by an isothermal self-gravitating disk. A precise comparison with the results of numerical hydro-dynamics is given. Analogies are drawn with the Kompaneets equation that includes the quadratic hyperbolic-secant law in the list of the plane-parallel stratified media. An astrophysical application is made to the superbubble connected with the two worms 46.4+5.5 and 39.7+5.7. The effects of the rotation of the galaxy on the simulated radius and on the velocity are introduced. The worms with their strong limb-brightening visible on astronomical maps are explained in the framework of image theory.