Context. Whether or not magnetic fields play a key role in dynamically shaping the products of the star formation process is still largely debated. For example, in magnetized protostellar formation models, magnetic braking plays a major role in the regulation of the angular momentum transported from large envelope scales to the inner envelope, and is expected to be responsible for the resulting protostellar disk sizes. However, non-ideal magnetohydrodynamic effects that rule the coupling of the magnetic field to the gas also depend heavily on the local physical conditions, such as the ionization fraction of the gas. Aims. The purpose of this work is to observationally characterize the level of ionization of the gas at small envelope radii and to investigate its relation to the efficiency of the coupling between the star-forming gas and the magnetic field in the Class 0 protostar B335. Methods. We obtained molecular line emission maps of B335 with ALMA, which we use to measure the deuteration fraction of the gas, R D , its ionization fraction, χ e , and the cosmic-ray ionization rate, ζ CR , at envelope radii ≲1000 au. Results. We find large fractions of ionized gas, χ e ≃ 1 − 8 × 10 −6 . Our observations also reveal an enhanced ionization that increases at small envelope radii, reaching values up to ζ CR ≃ 10 −14 s −1 at a few hundred astronomical units (au) from the central protostellar object. We show that this extreme ζ CR can be attributed to the presence of cosmic rays accelerated close to the protostar. Conclusions. We report the first resolved map of ζ CR at scales ≲ 1000 au in a solar-type Class 0 protostar, finding remarkably high values. Our observations suggest that local acceleration of cosmic rays, and not the penetration of interstellar Galactic cosmic rays, may be responsible for the gas ionization in the inner envelope, potentially down to disk-forming scales. If confirmed, our findings imply that protostellar disk properties may also be determined by local processes that set the coupling between the gas and the magnetic field, and not only by the amount of angular momentum available at large envelope scales and the magnetic field strength in protostellar cores. We stress that the gas ionization we find in B335 significantly stands out from the typical values routinely used in state-of-the-art models of protostellar formation and evolution. If the local processes of ionization uncovered in B335 are prototypical to low-mass protostars, our results call for a revision of the treatment of ionizing processes in magnetized models for star and disk formation.

We present ALMA dust polarization and molecular line observations toward 4 clumps (I(N), I, IV, and V) in the massive star-forming region NGC 6334. In conjunction with large-scale dust polarization and molecular line data from JCMT, Planck, and NANTEN2, we make a synergistic analysis of relative orientations between magnetic fields (θ B ), column density gradients (θ NG ), local gravity (θ LG ), and velocity gradients (θ VG ) to investigate the multi-scale (from ∼30 pc to 0.003 pc) physical properties in NGC 6334. We find that the relative orientation between θ B and θ NG changes from statistically more perpendicular to parallel as column density (N H2 ) increases, which is a signature of trans-tosub-Alfvénic turbulence at complex/cloud scales as revealed by previous numerical studies. Because θ NG and θ LG are preferentially aligned within the NGC 6334 cloud, we suggest that the more parallel alignment between θ B and θ NG at higher N H2 is because the magnetic field line is dragged by gravity. At even higher N H2 , the angle between θ B and θ NG or θ LG transits back to having no preferred orientation or statistically slightly more perpendicular, suggesting that the magnetic field structure is impacted by star formation activities. A statistically more perpendicular alignment is found between θ B and θ VG throughout our studied N H2 range, which indicates a trans-to-sub-Alfvénic state at small scales as well and signifies an important role of magnetic field in the star formation process in NGC 6334. The normalised mass-to-flux ratio derived from the polarization-intensity gradient (KTH) method increases with N H2 , but the KTH method may fail at high N H2 due to the impact of star formation feedback.

In this review article, we aim at providing a global outlook on the progresses made in the recent years to characterize the role of magnetic fields during the embedded phases of the star formation process. Thanks to the development of observational capabilities and the parallel progress in numerical models, capturing most of the important physics at work during star formation; it has recently become possible to confront detailed predictions of magnetized models to observational properties of the youngest protostars. We provide an overview of the most important consequences when adding magnetic fields to state-of-the-art models of protostellar formation, emphasizing their role to shape the resulting star(s) and their disk(s). We discuss the importance of magnetic field coupling to set the efficiency of magnetic processes and provide a review of observational works putting constraints on the two main agents responsible for the coupling in star-forming cores: dust grains and ionized gas. We recall the physical processes and observational methods, which allow to trace the magnetic field topology and its intensity in embedded protostars and review the main steps, success, and limitations in comparing real observations to synthetic observations from the non-ideal MHD models. Finally, we discuss the main threads of observational evidence that suggest a key role of magnetic fields for star and disk formation, and propose a scenario solving the angular momentum for star formation, also highlighting the remaining tensions that exist between models and observations.

Context. It is still largely debated whether magnetic fields play a key role in dynamically shaping the products of the star formation process. For example, in magnetized protostellar formation models, magnetic braking plays a major role in the regulation of the angular momentum transported from large envelope scales to the inner envelope, and is expected to be responsible for the resulting protostellar disk sizes. However, non-ideal magnetohydrodynamic effects that rule the coupling of the magnetic field to the gas also depend heavily on the local physical conditions, such as the ionization fraction of the gas. Aims. The purpose of this work is to observationally characterize the level of ionization of the gas at small envelope radii and investigate its relation to the efficiency of the coupling between the star-forming gas and the magnetic field in the Class 0 protostar B335. Methods. We have obtained molecular line emission maps of B335 with ALMA, which we use to measure the deuteration fraction of the gas, R D , its ionization fraction, χ e , and the cosmic-ray ionization rate, ζ, at envelope radii 1000 au. Results. We find large fractions of ionized gas, χ e 1 − 8 × 10 −6 . Our observations also reveal an enhanced ionization that increases at small envelope radii, reaching values up to ζ 10 −14 s −1 at a few hundred au from the central protostellar object. We show that this extreme ionization rate can be attributed to the presence of cosmic rays accelerated close to the protostar. Conclusions. We report the first resolved map of the cosmic-ray ionization rate at scales 1000 au in a solar-type Class 0 protostar, finding remarkably high values. Our observations suggest that local acceleration of cosmic rays, and not the penetration of interstellar Galactic cosmic rays, may be responsible for the gas ionization in the inner envelope, potentially down to disk forming scales. If confirmed, our findings imply that protostellar disk properties may also be determined by local processes setting the coupling between the gas and the magnetic field, and not only by the amount of angular momentum available at large envelope scales and the magnetic field strength in protostellar cores. We stress that the gas ionization we find in B335 significantly stands out from the typical values routinely used in state-of-the-art models of protostellar formation and evolution. If the local processes of ionization uncovered in B335 are prototypical to low-mass protostars, our results are calling for revising the treatment of ionizing processes in magnetized models for star and disk formation.