GRAVITATIONAL COLLAPSE OF AN ISOTHERMAL SPHERE

We investigate the spherical gravitational collapse of isothermal sphe res using numerical hydrodynamics. The initial configuration is close to hydrostatic equilibrium. If the initial density profile has a finit e core radius (i.e., it is not singular), supersonic velocities develo p during the initial collapse. At the time of central core formation, when the central density diverges, the central inflow velocity approac hes -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-si milar 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. F or the marginally stable equilibrium isothermal sphere, with an initia l outer cloud radius to core radius ratio of 3.2, the central mass acc retion rate steadily declines after core formation. Only if this ratio is greater than or similar to 20 does the collapse enter a constant m ass accretion rate, as occurs in the self-similar solutions developed by Shu. Assuming optical transparency, we calculate line profiles for the computed collapse.