On the role of outer boundary condition in the collapse of molecular clouds

In this paper, we investigate the influence of the outer boundary condition on the collapse of dense molecular clouds. Observational data confirm subsonic inward contraction both before and after the formation of a central protostar. Here, we study the problem of steady, spherical accretion of gas onto a protostar with the polytropic equation of state. Our model include self-gravity of the cloud and has an open outer boundary condition in which the velocity is no longer zero there. Thus, matter continuously drifts across this outer boundary. Since we study the early protostellar cloud evolution, the central protostar is highly less massive than the surrounding cloud. We assume the cloud radius is very large and impose a finite, subsonic velocity at the cloud’s outer boundary and ignore magnetic field effects entirely. Our assumptions, while highly idealized, show supersonic infall is confined to the small central region of cloud.