Infall Collapse Solutions in the Inner Limit: Radiation Pressure and its Effects on Star Formation

In this paper, we study infall collapse solutions for star formation in the small radius limit where the particle orbits become nearly pressure-free. We generalize previous solutions to simultaneously include the effects of both radiation pressure and angular momentum. The effects of radiation pressure can be modeled using a modified potential; for representative cases of such potentials, we obtain analytical solutions for the density and velocity fields. In general, radiation pressure limits the maximum mass of a forming star by reversing the infall when the star becomes sufficiently large. Our results imply that this maximum mass scale is given by the condition that the turnaround radius $R_R$ (the radius at which the radiation pressure force exceeds the gravitational force) exceeds the centrifugal radius $R_C$ (the angular momentum barrier). The maximum mass scale for a star forming within a rotating collapse flow with radiation pressure depends on the initial conditions, but is generally much larger than for the case of spherical infall considered previously. In particular, stars with masses $M_\ast$ $\sim 100$ $M_\odot$ can form for a fairly wide range of initial conditions.