GRAVITATIONAL COLLAPSE OF AN ISOTHERMAL SPHERE

We investigate the spherical gravitational collapse of isothermal spheres using numerical hydrodynamics. The initial configuration is close to hydrostatic equilibrium. If the initial density profile has a finite core radius (i.e., it is not singular), supersonic velocities develop during the initial collapse. At the time of central core formation, when the central density diverges, the central inflow velocity approaches -3.3 times the sound speed and the central density approaches an r-2 profile. These conditions are similar to those found in the self-similar solution of Larson and Penston, but occur only at the center and not at all radii as in the self-similar solution at core formation. For the marginally stable equilibrium isothermal sphere, with an initial outer cloud radius to core radius ratio of 3.2, the central mass accretion rate steadily declines after core formation. Only if this ratio is greater than or similar to 20 does the collapse enter a constant mass accretion rate, as occurs in the self-similar solutions developed by Shu. Assuming optical transparency, we calculate line profiles for the computed collapse.