Gravitational Contraction of Rotating Clouds: Formation of Self‐similarly Collapsing Disks

Abstract

We investigate the isothermal gravitational collapse of rotating interstellar clouds with axisymmetric numerical simulations. The simulations show that a filamentary cloud fragments owing to the gravitational instability and the fragment evolves into a dynamically contracting disk. The disk contraction is followed until the central density increases by a factor of 1016 at most. The disk evolution shows similarity: the disk structure at a given time is similar to that at another time except for the scale. We construct various models, in which we change the wavelength of the perturbation and the initial rotation velocity, and study the dependences of the disk evolution on these model parameters. The surface density of the disk is proportional to the square of the sound speed, Σ∝c2s and almost independent of the wavelength of the perturbation imposed, i.e., the mass contained in the fragment. It indicates that the mass of the gravitationally contracting disk is independent of the parent cloud mass. When the initial cloud rotates slowly, the dense part of the fragment is nearly spherical in the early contraction phase and evolves into a disk. When the initial cloud rotates fast, the fragment has a disk shape from the early contraction phase. In the late contraction phase, the surface density and the rotation velocity do not depend strongly on the initial rotation velocity and depend weakly on it when it is small. Although the disk evolution is well understand by similarity collapse, it shows an oscillation around similarity collapse. A new shock wave forms each cycle of oscillation.