Ambipolar diffusion in low-mass star formation I. General comparison with the ideal magnetohydrodynamic case

Angular momentum transport and the formation of rotationally supported structures are major issues in our understanding of protostellar core formation. Whereas purely hydrodynamical simulations lead to large Keplerian disks, ideal magnetohydrodynamics (MHD) models yield the opposite result, with essentially no disk formation. This stems from the flux-freezing condition in ideal MHD, which leads to strong magnetic braking. In this paper, we provide a more accurate description of the evolution of the magnetic flux redistribution by including resistive terms in the MHD equations. We focus more particularly on the effect of ambipolar diffusion on the properties of the first Larson core and its surrounding structure, exploring various initial magnetisations and magnetic field versus rotation axis orientations of a 1 M-circle dot collapsing prestellar dense core. We used the non-ideal magnetohydrodynamics version of the adaptive mesh refinement code RAMSES to carry out these calculations. The resistivities required to calculate the ambipolar diffusion terms were computed using a reduced chemical network of charged, neutral, and grain species. Including ambipolar diffusion leads to the formation of a magnetic diffusion barrier (also known as the decoupling stage) in the vicinity of the core, which prevents accumulation of magnetic flux in and around the core and amplification of the field above 0.1 G. The mass and radius of the first Larson core, however, remain similar between ideal and non-ideal MHD models. This diffusion plateau, preventing further amplification of the field and reorganising the field topology, has crucial consequences for magnetic braking processes, allowing the formation of disk structures. Magnetically supported outflows launched in ideal MHD models are weakened or even disappear when using non-ideal MHD. In contrast to ideal MHD calculations, misalignment between the initial rotation axis and the magnetic field direction does not significantly affect the results for a given magnetisation, showing that the physical dissipation processes truly dominate numerical diffusion. We demonstrate severe limits of the ideal MHD formalism; it yields unphysical behaviours in the long-term evolution of the system. This includes counter-rotation inside the outflow or magnetic tower, interchange instabilities, and flux redistribution triggered by numerical diffusion. These effects are not observed in non-ideal MHD. Disks with Keplerian velocity profiles are found to form around the protostar in all our non-ideal MHD simulations, with a final mass and size that strongly depend on the initial magnetisation. This ranges from a few 10(-2) M-2 and similar to 20-30 au for the most magnetised case (mu = 2) to similar to 2 x 10(-1) M-circle dot and similar to 40-80 au for a lower magnetisation (mu = 5). In all cases, these disks remain significantly smaller than disks found in pure hydrodynamical simulations. Ambipolar diffusion thus bears a crucial impact on the regulation of magnetic flux and angular momentum transport during the collapse of a prestellar core and the formation of the resulting protostellar core-disk system, enabling the formation and growth of rotationally supported structures.