Protostellar outflows with Smoothed Particle Magnetohydrodynamics   (SPMHD)
  The protostellar collapse of a molecular cloud core is usually accompanied by outflow phenomena. The latter are thought to be driven by magnetorotational processes from the central parts of the protostellar disc. While several 3D AMR/nested grid studies of outflow phenomena in collapsing magnetically supercritical dense cores have been reported in the literature, so far no such simulation has been performed using the Smoothed Particle Hydrodynamics (SPH) method. This is mainly due to intrinsic numerical difficulties in handling magnetohydrodynamics within SPH, which only recently were partly resolved. In this work, we use an approach where we evolve the magnetic field via the induction equation, augmented with stability correction and divergence cleaning schemes. We consider the collapse of a rotating core of one solar mass, threaded by a weak magnetic field initially parallel to the rotation axis so that the core is magnetically supercritical. We show, that Smoothed Particle Magnetohydrodynamics (SPMHD) is able to handle the magnetorotational processes connected with outflow phenomena, and to produce meaningful results which are in good agreement with findings reported in the literature. Especially, our numerical scheme allows for a quantitative analysis of the evolution of the ratio of the toroidal to the poloidal magnetic field, which we performed in this work. 
Florian B\"urzle, Paul C. Clark, Federico Stasyszyn, Klaus Dolag and   Ralf S. Klessen
astro-ph.SR