Magnetohydrodynamical modeling of star-disk formation: from isolated spherical collapse towards incorporation of external dynamics

The formation of protostars and their disks has been understood as the result of the gravitational collapse phase of an accumulation of dense gas that determines the mass reservoir of the star-disk system. Against this background, the broadly applied scenario of considering the formation of disks has been to model the collapse of a dense core assuming spherical spherical symmetry. Our understanding of the formation of star-disk systems is currently undergoing a reformation though. The picture evolves from interpreting disks as the sole outcome of the collapse of an isolated prestellar core to a more dynamic picture where disks are affected by the molecular cloud environment in which they form. In this review, we provide a status report of the state-of-the-art of spherical collapse models that are highly advanced in terms of the incorporated physics together with constraints from models that account for the possibility of infall onto star-disk systems in simplified test setups, as well as in multi-scale simulations that cover a dynamical range from the Giant Molecular Cloud environment down to the disk. Considering the observational constraints that favor a more dynamical picture of star formation, we finally discuss the challenges and prospects in linking the efforts of tackle the problem of star-disk formation in combined multi-scale, multi-physics simulations.