Transport and influence of angular momentum in collapsing dense cores

Angular momentum is playing a key role during the collapse of prestellar cores since it is leading to disk formation and to some extent to binary formation. On the other hand, it has long been recognized that the stars possess a tiny fraction of the initial momentum that their parent clouds retain, an issue known as the “angular momentum problem”. In these lectures, we attempt to present the most recent calculations performed to investigate the angular momentum transport and the influence angular momentum has, during the collapse of prestellar cores. After a brief introduction of the star formation context and a broad description of the important features within collapsing cores, we discuss the so-called catastrophic braking. Indeed when magnetic field and rotation axis are aligned, the magnetic braking is so efficient that the formation of early disks is completely prevented. We then present the various studies which have attempted to explore the robustness of this efficient transport including influence of non-ideal MHD, misalignment between magnetic field and rotation axis and turbulence. While the role of the first, is not entirely clear; the two other effects diminish the efficacity of the magnetic braking making the issue less severe than in the pure ideal MHD aligned configuration. Finally, we discuss the fragmentation of low and high mass cores with particular emphasis on the impact of the magnetic field. In particular, we discuss the drastic stabilization that magnetic field has on low mass cores and the possible solution to this apparent conundrum. In the context of high mass stars, its influence is much more limited reducing the number of fragments by a factor of the order of two. However when both radiative feedback and magentic field are included, the fragmentation is very significantly reduced