Magnetic fields play a key role during the gravitational collapse of dense protostellar cores. In recent years mm and sub-mm observations of dust polarized emission have been used to unveil the morphology of the magnetic field, but this method relies on the assumption that non-spherical dust grains are well aligned with the magnetic field.

Using non-ideal MHD numerical simulations, we study the evolution of the magnetic field during the gravitational collapse. We use the state-of-the-art radiative transfer code POLARIS to compute the Stokes parameters and produce synthetic observations of mm/submm polarized dust emission. We compare the results obtained using the radiative torques (RAT) mechanism to the results obtained by assuming that grains are perfectly aligned to constrain how well polarized dust emission traces the magnetic field orientation.

The complexity of the magnetic field produces a mild depolarization. The depolarization observed in the inner regions is rather caused by a decrease of the dust alignment efficiency and it cannot be reproduced by just scaling down the polarisation degree obtained for a uniform efficiency. We find that the magnetic field orientation is well constrained by the polarized dust emission as long as its 3D topology remains organized.

Molecular clouds are essentially made up of atomic and molecular hydrogen, which in spite of being the simplest molecule in the ISM plays a key role in the chemical evolution of molecular clouds. Since its formation time is very long, the H2 molecules can be transported by the turbulent motions within the cloud toward low density and warm regions, where its enhanced abundance can boost the abundances of molecules with high endothermicities.

We present high resolution simulations where we include the evolution of the molecular gas under the effect of the dynamics, and we analyze its impact on the abundance of CH+.

Discs are a key element in star and planet formation; however, magnetic fields can efficiently transport angular momentum away from the central region of the collapsing core during the dense core collapse, preventing disc formation. We perform numerical simulations of magnetically supercritical collapsing cores with a misalignment between the rotation axis and the magnetic field (Joos et al. 2012) and in a turbulent environment (Joos et al. 2013). The early formation of massive discs can take place at moderate magnetic intensities if the rotation axis is tilted or in a turbulent environment, because of misalignment and turbulent diffusion.

We review the various theories which have been proposed along the years to explain the origin of the stellar initial mass function. We pay particular attention to four models, namely the competitive accretion and the theories based respectively on stopped accretion, MHD shocks and turbulent dispersion. In each case, we derive the main assumptions and calculations that support each theory and stress their respective successes and failures or difficulties.

Radiative feedback and magnetic field are understood to have a strong impact on the protostellar collapse. We present high resolution numerical calculations of the collapse of a 1 M⊙ dense core in solid body rotation, including both radiative transfer and magnetic field. Using typical parameters for low-mass cores, we study thoroughly the effect of radiative transfer and magnetic field on the first core formation and fragmentation. We show that including the two aforementioned physical processes does not correspond to the simple picture of adding them separately. The interplay between the two is extremely strong, via the magnetic braking and the radiation from the accretion shock.

Detailed modelling of individual protostellar condensations is important to test the various theories. Here we present comparisons between strongly induced collapse models with one young class-0 object, IRAS4A, in the Perseus cloud and one prestellar cloud observed in the Coalsack molecular cloud.