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Aims. We investigate the influence of turbulent viscosity on the collapse of a rotating molecular cloud core with axial symmetry, in particular, on the first and second collapse phase, as well as the evolution of the second (protostellar) core during its first accretion period. By using extensive numerical calculations, we monitor the intricate interactions between the newly formed protostar and the surrounding accretion disk (the first core) in which the star is embedded. Methods. We use a grid-based radiation-hydrodynamics code with a spatial grid designed to meet the high resolution required to study the second core. The radiative transfer is treated in the flux-limited diffusion approximation. A slightly supercritical Bonnor-Ebert sphere of 1 M ⊙ and uniform rotation according to a fixed centrifugal radius of 100 AU serves as the initial condition without exception. In a parameter study, we vary the β-viscosity driving the angular momentum transport. Results. Without viscosity (β = 0), a highly flattened accretion disk forms that fragments into several "cold" rings. For β = 10- 4 , a single "warm" ring forms that undergoes collapse due to hydrogen dissociation. For β = 10- 3 , ring formation is suppressed completely. The second collapse proceeds on the local thermal timescale, which is in contrast to the current view of a generally dynamical second collapse. During the first accretion period of the second core, the first core heats up globally and, as a consequence, a nearly spherical outflow occurs, destroying the structure of the former accretion disk completely. Finally, for β = 10 ―2 , we see the classical dynamical second collapse and a shorter but more rapid accretion phase. The impact on the surrounding accretion disk is even more pronounced. We follow the resulting massive outflow up to several kyr after the second collapse, where the central parts (R < 0.7 AU) are now cut out and replaced with an appropriate inner boundary condition. Matter is found to turn back to the center at a radius of 500 AU after about 4 kyr and to reach the protostar again after approximately 7 kyr. The results suggest that the star formation process consists of short and rapid accretion phases (lasting on the order of 100 yr) between long and quiet outflow periods (lasting several kyr).

Protostellar collapse of rotating cloud cores