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 alpha. 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 less than or similar to alpha less than or similar to 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, alpha greater than or similar to 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.