Context. Theoretical studies of collapsing clouds have found that even a relatively weak magnetic field may prevent the formation of disks and their fragmentation. However, most previous studies have been limited to cases where the magnetic field and the rotation axis of the cloud are aligned. Aims. We study the transport of angular momentum, and its effects on disk formation, for non-aligned initial configurations and a range of magnetic intensities. Methods. We perform three-dimensional, adaptive mesh, numerical simulations of magnetically supercritical collapsing dense cores using the magneto-hydrodynamic code Ramses. We compute the contributions of all the relevant processes transporting angular momentum, in both the envelope and the region of the disk. We clearly define centrifugally supported disks and thoroughly study their properties. Results. At variance with earlier analyses, we show that the transport of angular momentum acts less efficiently in collapsing cores with non-aligned rotation and magnetic field. Analytically, this result can be understood by taking into account the bending of field lines occurring during the gravitational collapse. For the transport of angular momentum, we conclude that magnetic braking in the mean direction of the magnetic field tends to dominate over both the gravitational and outflow transport of angular momentum. We find that massive disks, containing at least 10% of the initial core mass, can form during the earliest stages of star formation even for mass-to-flux ratios as small as three to five times the critical value. At higher field intensities, the early formation of massive disks is prevented. Conclusions. Given the ubiquity of Class I disks, and because the early formation of massive disks can take place at moderate magnetic intensities, we speculate that for stronger fields, disks will form later, when most of the envelope will have been accreted. In addition, we speculate that some observed early massive disks may actually be outflow cavities, mistaken for disks by projection effects.

Context. Stars, and more particularly massive stars, have a drastic impact on galaxy evolution. Yet the conditions in which they form and collapse are still not fully understood. Aims. In particular, the influence of the magnetic field on the collapse of massive clumps is relatively unexplored, it is therefore of great relevance in the context of the formation of massive stars to investigate its impact. Methods. We perform high resolution, MHD simulations of the collapse of one hundred solar masses, turbulent and magnetized clouds, with the adaptive mesh refinement code RAMSES. We compute various quantities such as mass distribution, magnetic field, and angular momentum within the collapsing core and study the episodic outflows and the fragmentation that occurs during the collapse. Results. The magnetic field has a drastic impact on the cloud evolution. We find that magnetic braking is able to substantially reduce the angular momentum in the inner part of the collapsing cloud. Fast and episodic outflows are being launched with typical velocities of the order of 1−3 km s −1 , although the highest velocities can be as high as 20−40 km s −1 . The fragmentation in several objects is reduced in substantially magnetized clouds with respect to hydrodynamical ones by a factor of the order of 1.5−2. Conclusions. We conclude that magnetic fields have a significant impact on the evolution of massive clumps. In combination with radiation, magnetic fields largely determine the outcome of massive core collapse. We stress that numerical convergence of MHD collapse is a challenging issue. In particular, numerical diffusion appears to be important at high density and therefore could possibly lead to an overestimation of the number of fragments.

Context. Theoretical and numerical studies of star formation have shown that a magnetic field can greatly influence both disk formation and its fragmentation, with even relatively low magnetic field strengths being able to prevent these processes. However, very few studies have investigated the combined effects of magnetic field and turbulence. Aims. We study the collapse of turbulent, magnetized prestellar cores, focusing on the effects of magnetic diffusion, and misalignment between rotation axis and magnetic field, on the formation of disks, fragmentation, and the generation of outflows. Methods. We performed three-dimensional, adaptive-mesh, numerical simulations of magnetically super-critical collapsing dense cores of 5 M using the magneto-hydrodynamic code Ramses. A turbulent velocity field is imposed as initial conditions, characterized by a Kolmogorov power spectrum. Different levels of turbulence (a laminar case, as well as subsonic and supersonic cases) and magnetization (from weak to strong magnetization) are investigated, as are three realizations for the turbulent velocity field. Results. The turbulent velocity field imposed as initial conditions contains a non-zero angular momentum, which is responsible for a misalignment of the rotation axis with respect to the initial magnetic field, and an effective turbulent diffusivity in the vicinity of the core. Both effects are responsible for a significant decrease in the magnetic braking, and they facilitate the formation of early massive disks. These disks can fragment even with μ ∼ 5 at late times, in contrast to simulations of 1 M cores, where fragmentation is prevented for these values of μ. Slow asymmetric outflows are always launched, and they carry a mass comparable to that of the adiabatic first core. Conclusions. Because of turbulence-induced misalignment and magnetic diffusivity, massive disk formation is possible; nevertheless, their mass and size are much more reduced than for disks formed in unmagnetized collapsing cores. We find that for μ ≥ 5 fragmentation can occur.

We present the application of a 2D broadband homodecoupled proton NMR experiment to the visualization of enantiomers. In a chiral environment, the existence of diastereoisomeric intermolecular interactions can yield-generally slight-variations of proton chemical shifts from one enantiomer to another. We show that this approach, which relies on a spatial encoding of the NMR sample, is particularly well suited to the analysis of enantiomeric mixtures, since it allows, within one single 2D experiment, to detect subtle chemical shift differences between enantiomers, even in the presence of several couplings. This sequence, which uses semiselective radio-frequency (rf) pulses combined to a z-field gradient pulse, produces different selective echoes in various parts of the sample. The resulting homonuclear decoupling provides an original delta-resolved spectrum along the diagonal of the 2D map where it becomes possible to probe the chiral differentiation process through every proton site where the resulting variation in the chemical shift is detectable. We discuss the advantages and drawbacks of this approach, regarding other experiments which provide homodecoupled proton spectra. This methodology is applied to the observation of enantiomers of (1) ( +/- )2-methyl-isoborneol coordinated to europium (III) tris[3-(trifluoromethyl-hydroxymethylene)-(+)-camphorate] in isotropic solution, and (2) ( +/- )3-butyn-2-ol dissolved in a chiral liquid-crystal solvent, in order to show the robustness of this pulse sequence for a wide range of chiral samples.

Context. The formation of protostellar discs is severely hampered by magnetic braking, as long as magnetic fields remain frozen in the gas. The latter condition depends on the levels of ionisation that characterise the innermost regions of a collapsing cloud. Aims. The chemistry of dense cloud cores and, in particular, the ionisation fraction is largely controlled by cosmic rays. The aim of this paper is to evaluate whether the attenuation of the flux of cosmic rays expected in the regions around a forming protostar is sufficient to decouple the field from the gas, thereby influencing the formation of centrifugally supported disc. Methods. We adopted the method developed in a former study to compute the attenuation of the cosmic-ray flux as a function of the column density and the field strength in clouds threaded by poloidal and toroidal magnetic fields. We applied this formalism to models of low-and high-mass star formation extracted from numerical simulations of gravitational collapse that include rotation and turbulence.Results. For each model we determine the size of the magnetic decoupling zone, where collapse or rotation motion becomes unaffected by the local magnetic field. In general, we find that decoupling only occurs when the attenuation of cosmic rays is taken into account with respect to a calculation in which the cosmic-ray ionisation rate is kept constant. The extent of the decoupling zone also depends on the dust grain size distribution and is larger if large grains (of radius ∼10 −5 cm) are formed by compression and coagulation during cloud collapse. The decoupling region disappears for the high-mass case. This is due to magnetic field diffusion caused by turbulence that is not included in the low-mass models. Conclusions. We conclude that a realistic treatment of cosmic-ray propagation and attenuation during cloud collapse may lead to a value of the resistivity of the gas in the innermost few hundred AU around a forming protostar that is higher than generally assumed. Forthcoming self-consistent calculations should investigate whether this effect is strong enough to effectively decouple the gas from the field and to compute the amount of angular momentum lost by infalling fluid particles when they enter the decoupling zone.

Context. Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability (MRI). Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behaviour in the Ohmic diffusion regime has not been clearly established. Aims. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the most common subgrid scale models for this problem. Methods. Unstratified shearing box simulations are performed both in the compressible and incompressible limits, with a resolution up to 800 cells per disc scale height. This is the highest resolution ever attained for a simulation of MRI turbulence. Different magnetic field geometry and a wide range of dimensionless dissipative coefficients are considered. We also systematically investigate the relevance of using large eddy simulations (LES) in place of direct numerical simulations. Results. In the presence of a mean magnetic field threading the domain, angular momentum transport converges to a finite value in the small Pm limit. When the mean vertical field amplitude is such that β (the ratio between the thermal and magnetic pressure) equals 10 3 , we find α ∼ 3.2 × 10 −2 when Pm approaches zero. In the case of a mean toroidal field for which β = 100, we find α ∼ 1.8 × 10 −2 in the same limit. Implicit LES and the Chollet-Lesieur closure model both reproduce these results for the α parameter and the power spectra. A reduction in computational cost by a factor of at least 16 (and up to 256) is achieved when using such methods. Conclusions. MRI turbulence operates efficiently in the small Pm limit provided there is a mean magnetic field. Implicit LES offers a practical and efficient means of investigation of this regime but should be used with care, particularly in the case of a vertical field. The Chollet-Lesieur closure model is perfectly suited for simulations done with a spectral code.

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.

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