Aims. We present a new three-dimensional radiation hydrodynamics code called HERACLES that uses an original moment method to solve the radiative transfer. Methods. The radiation transfer is modelled using a two-moment model and a closure relation that allows large angular anisotropies in the radiation field to be preserved and reproduced. The radiative equations thus obtained are solved by a second-order Godunov-type method and integrated implicitly by using iterative solvers. HERACLES has been parallelized with the MPI library and implemented in Cartesian, cylindrical, and spherical coordinates. To characterize the accuracy of HERACLES and to compare it with other codes, we performed a series of tests including purely radiative tests and radiation-hydrodynamics ones.Results. The results show that the physical model used in HERACLES for the transfer is fairly accurate in both the diffusion and transport limit, but also for semi-transparent regions.Conclusions. This makes HERACLES very well-suited to studying many astrophysical problems such as radiative shocks, molecular jets of young stars, fragmentation and formation of dense cores in the interstellar medium, and protoplanetary discs.

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 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 ∼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 pre-requisite 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.