Gravitational Collapse of Spherical Interstellar Clouds

In this paper, the gravitational collapse of spherical interstellar clouds is discussed based on hydrodynamical simulations. The evolution is divided into two phases: former runaway collapse phase, in which the central density increases greatly on a finite time scale, and later contraction, associated with accretion onto a newborn star. The initial density distribution is expressed using a ratio of the gravitational force to the pressure force α. The equation of state for a polytropic gas is used. The central, high-density part of the solution converges on a self-similar solution, which was first derived for the runaway collapse by Larson and Penston (LP). In the later accretion phase, gas behaves like a particle, and the infall speed is accelerated by the gravity of the central object. The solution at this stage is qualitatively similar to the inside-out similarity solutions first found by Shu. However, it is shown that the gas-inflow (accretion) rate is time-dependent, in contrast to the constant rate of the inside-out similarity solutions. For isothermal models in which the pressure is important, 1 ≲ α ≲ 3.35, the accretion rate reaches its maximum when the central part, which obeys the LP solution, contracts and accretes. On the other hand, in isothermal models in which gravity is dominant, α ≳ 3.35, the accretion becomes most active at the epoch when the outer part of the cloud falls onto the center. The effect of the non-isothermal equation of state is discussed.