Protostellar birth with ambipolar and ohmic diffusion

Context. The transport of angular momentum is fundamental during the formation of low-mass stars; too little removal and rotation ensures stellar densities are never reached, too much and the absence of rotation means no protoplanetary disks can form. Magnetic diffusion is seen as a pathway to resolving this long-standing problem. Aims. We aim to investigate the impact of including resistive magnetohydrodynamics (MHD) in simulations of the gravitational collapse of a 1 M-circle dot gas sphere, from molecular cloud densities to the formation of the protostellar seed; the second Larson core. Methods. We used the adaptive mesh refinement code RAMSES to perform two 3D simulations of collapsing magnetised gas spheres, including self-gravity, radiative transfer in the form of flux-limited diffusion, and a non-ideal gas equation of state to describe H-2 dissociation which leads to the second collapse. The first run was carried out under the ideal MHD approximation, while ambipolar and ohmic diffusion was incorporated in the second calculation using resistivities computed from an equilibrium chemical network. Results. In the ideal MHD simulation, the magnetic field dominates the energy budget everywhere inside and around the first hydrostatic core, fueling interchange instabilities and driving a low-velocity outflow above and below the equatorial plane of the system. High magnetic braking removes essentially all angular momentum from the second core. On the other hand, ambipolar and ohmic diffusion create a barrier which prevents amplification of the magnetic field beyond 0.1 G in the first Larson core which is now fully thermally supported. A significant amount of rotation is preserved and a small Keplerian-like disk forms around the second core. The ambipolar and ohmic diffusions are effective at radii below 10 AU, indicating that a spatial resolution of at least similar to 1 AU is necessary to investigate the angular momentum transfer and the formation of rotationally supported disks. Finally, when studying the radiative efficiency of the first and second core accretion shocks, we found that it can vary by several orders of magnitude over the 3D surface of the cores. Conclusions. This proves that magnetic diffusion is a prerequisite to star formation. Not only does it enable the formation of protoplanetary disks in which planets will eventually form, it also plays a determinant role in the formation of the protostar itself.