a b s t r a c tMolecular hydrogen is the most abundant molecule in the universe. It is the first one to form and survive photo-dissociation in tenuous environments. Its formation involves catalytic reactions on the surface of interstellar grains. The micro-physics of the formation process has been investigated intensively in the last 20 years, in parallel of new astrophysical observational and modeling progresses. In the perspectives of the probable revolution brought by the future satellite JWST, this article has been written to present what we think we know about the H 2 formation in a variety of interstellar environments.

The Davis–Chandrasekhar–Fermi (DCF) method is widely used to indirectly estimate the magnetic field strength from the plane-of-sky field orientation. In this work, we present a set of 3D MHD simulations and synthetic polarization images using radiative transfer of clustered massive star-forming regions. We apply the DCF method to the synthetic polarization maps to investigate its reliability in high-density molecular clumps and dense cores where self-gravity is significant. We investigate the validity of the assumptions of the DCF method step by step and compare the model and estimated field strength to derive the correction factors for the estimated uniform and total (rms) magnetic field strength at clump and core scales. The correction factors in different situations are cataloged. We find the DCF method works well in strong-field cases. However, the magnetic field strength in weak-field cases could be significantly overestimated by the DCF method when the turbulent magnetic energy is smaller than the turbulent kinetic energy. We investigate the accuracy of the angular dispersion function (ADF; a modified DCF method) method on the effects that may affect the measured angular dispersion and find that the ADF method correctly accounts for the ordered field structure, the beam smoothing, and the interferometric filtering, but may not be applicable to account for the signal integration along the line of sight in most cases. Our results suggest that the DCF methods should be avoided to be applied below ∼0.1 pc scales if the effect of line-of-sight signal integration is not properly addressed.

Context. H 2 is the simplest and the most abundant molecule in the interstellar medium (ISM), and its formation precedes the formation of other molecules. Aims. Understanding the dynamical influence of the environment and the interplay between the thermal processes related to the formation and destruction of H 2 and the structure of the cloud is mandatory to understand correctly the observations of H 2 . Methods. We performed high-resolution magnetohydrodynamical colliding-flow simulations with the adaptive mesh refinement code RAMSES in which the physics of H 2 has been included. We compared the simulation results with various observations of the H 2 molecule, including the column densities of excited rotational levels. Results. As a result of a combination of thermal pressure, ram pressure, and gravity, the clouds produced at the converging point of HI streams are highly inhomogeneous. H 2 molecules quickly form in relatively dense clumps and spread into the diffuse interclump gas. This in particular leads to the existence of significant abundances of H 2 in the diffuse and warm gas that lies in between clumps. Simulations and observations show similar trends, especially for the HI-to-H 2 transition (H 2 fraction vs. total hydrogen column density). Moreover, the abundances of excited rotational levels, calculated at equilibrium in the simulations, turn out to be very similar to the observed abundances inferred from FUSE results. This is a direct consequence of the presence of the H 2 enriched diffuse and warm gas. Conclusions. Our simulations, which self-consistently form molecular clouds out of the diffuse atomic gas, show that H 2 rapidly forms in the dense clumps and, due to the complex structure of molecular clouds, quickly spreads at lower densities. Consequently, a significant fraction of warm H 2 exists in the low-density gas. This warm H 2 leads to column densities of excited rotational levels close to the observed ones and probably reveals the complex intermix between the warm and cold gas in molecular clouds. This suggests that the two-phase structure of molecular clouds is an essential ingredient for fully understanding molecular hydrogen in these objects.

Context. Analyzing the properties of dust and its evolution in the early phases of star formation is crucial to put constraints on the collapse and accretion processes as well as on the pristine properties of planet-forming seeds. Aims. In this paper, we aim to investigate the variations of the dust grain size in the envelopes of the youngest protostars. Methods. We analyzed Plateau de Bure interferometric observations at 1.3 mm and 3.2 mm for 12 Class 0 protostars obtained as part of the CALYPSO survey. We performed our analysis in the visibility domain and derived dust emissivity index (β 1−3mm ) profiles as a function of the envelope radius at 200-2000 au scales.Results. Most of the protostellar envelopes show low dust emissivity indices decreasing toward the central regions. The decreasing trend remains after correction of the (potentially optically thick) central region emission, with surprisingly low β 1−3mm < 1 values across most of the envelope radii of NGC1333-IRAS4A, NGC1333-IRAS4B, SVS13B, and Serpens-SMM4. Conclusions. We discuss the various processes that could explain such low and varying dust emissivity indices at envelope radii 200-2000 au. Our observations of extremely low dust emissivity indices could trace the presence of large (millimeter-size) grains in Class 0 envelopes, in which case our results would point to a radial increase of the dust grain size toward the inner envelope regions. While it is expected that large grains in young protostellar envelopes could be built via grain growth and coagulation, we stress that the typical timescales required to build millimeter grains in current coagulation models are at odds with the youth of our Class 0 protostars. Additional variations in the dust composition could also partly contribute to the low β 1−3mm we observe. We find that the steepness of the β 1−3mm radial gradient depends strongly on the envelope mass, which might favor a scenario in which large grains are built in high-density protostellar disks and transported to the intermediate envelope radii, for example with the help of outflows and winds.

Aims. Although from a theoretical point of view magnetic fields are believed to play a significant role during the early stages of star formation, especially during the main accretion phase, the magnetic field strength and topology is poorly constrained in the youngest accreting Class 0 protostars that lead to the formation of solar-type stars. Methods. We carried out observations of the polarized dust continuum emission with the SMA interferometer at 0.87 mm to probe the structure of the magnetic field in a sample of 12 low-mass Class 0 envelopes in nearby clouds, including both single protostars and multiple systems. Our SMA observations probed the envelope emission at scales ∼600 − 5000 au with a spatial resolution ranging from 600 to 1500 au depending on the source distance. Results. We report the detection of linearly polarized dust continuum emission in all of our targets with average polarization fractions ranging from 2% to 10% in these protostellar envelopes. The polarization fraction decreases with the continuum flux density, which translates into a decrease with the H 2 column density within an individual envelope. Our analysis show that the envelope-scale magnetic field is preferentially observed either aligned or perpendicular to the outflow direction. Interestingly, our results suggest for the first time a relation between the orientation of the magnetic field and the rotational energy of envelopes, with a larger occurrence of misalignment in sources in which strong rotational motions are detected at hundreds to thousands of au scales. We also show that the best agreement between the magnetic field and outflow orientation is found in sources showing no small-scale multiplicity and no large disks at ∼100 au scales.

Context. Molecular clouds are known to be magnetised and to display a turbulent and complex structure where warm and cold phases are interwoven. The turbulent motions within molecular clouds transport molecules, and the presence of magnetic fields induces a relative velocity between neutrals and ions known as the ion-neutral drift (v d ). These effects all together can influence the chemical evolution of the clouds. Aims. This paper assesses the roles of two physical phenomena which have previously been invoked to boost the production of CH + under realistic physical conditions: the presence of warm H 2 and the increased formation rate due to the ion-neutral drift. Methods. We performed ideal magnetohydrodynamical (MHD) simulations that include the heating and cooling of the multiphase interstellar medium (ISM), and where we treat dynamically the formation of the H 2 molecule. In a post-processing step we compute the abundances of species at chemical equilibrium using a solver that we developed. The solver uses the physical conditions of the gas as input parameters, and can also prescribe the H 2 fraction if needed. We validate our approach by showing that the H 2 molecule generally has a much longer chemical evolution timescale compared to the other species. Results. We show that CH + is efficiently formed at the edge of clumps, in regions where the H 2 fraction is low (0.3 − 30%) but nevertheless higher than its equilibrium value, and where the gas temperature is high ( 300 K). We show that warm and out of equilibrium H 2 increases the integrated column densities of CH + by one order of magnitude up to values still ∼ 3 − 10 times lower than those observed in the diffuse ISM. We balance the Lorentz force with the ion-neutral drag to estimate the ion-drift velocities from our ideal MHD simulations. We find that the ion-neutral drift velocity distribution peaks around ∼ 0.04 km s −1 , and that high drift velocities are too rare to have a significant statistical impact on the abundances of CH + . Compared to previous works, our multiphase simulations reduce the spread in v d , and our self-consistent treatment of the ionisation leads to much reduced v d . Nevertheless, our resolution study shows that this velocity distribution is not converged: the ion-neutral drift has a higher impact on CH + at higher resolution. On the other hand, our ideal MHD simulations do not include ambipolar diffusion, which would yield lower drift velocities. Conclusions. Within these limitations, we conclude that warm H 2 is a key ingredient in the efficient formation of CH + and that the ambipolar diffusion has very little influence on the abundance of CH + , mainly due to the small drift velocities obtained. However, we point out that small-scale processes and other non-thermal processes not included in our MHD simulation may be of crucial importance, and higher resolution studies with better controlled dissipation processes are needed.

Context. The amount of data collected by spectrometers from radio to ultraviolet (UV) wavelengths opens a new era where the statistical and chemical information contained in the observations can be used concomitantly to investigate the thermodynamical state and the evolution of the interstellar medium (ISM). Aims. In this paper, we study the statistical properties of the HI-to-H2 transition observed in absorption in the local diffuse and multiphase ISM. Our goal is to identify the physical processes that control the probability of occurrence of any line of sight and the origins of the variations of the integrated molecular fraction from one line of sight to another. Methods. The turbulent diffuse ISM is modeled using the RAMSES code, which includes detailed treatments of the magnetohydrodynamics, the thermal evolution of the gas, and the chemistry of H2. The impacts of the UV radiation field, the mean density, the turbulent forcing, the integral scale, the magnetic field, and the gravity on the molecular content of the gas are explored through a parametric study that covers a wide range of physical conditions. The statistics of the HI-to-H2 transition are interpreted through analytical prescriptions and compared with the observations using a modified and robust version of the Kolmogorov-Smirnov test. Results. The analysis of the observed background sources shows that the lengths of the lines of sight follow a flat distribution in logarithmic scale from ~100 pc to ~3 kpc. Without taking into account any variation of the parameters along a line of sight or from one line of sight to another, the results of one simulation, convolved with the distribution of distances of the observational sample, are able to simultaneously explain the position, the width, the dispersion, and most of the statistical properties of the HI-to-H2 transition observed in the local ISM. The tightest agreement is obtained for a neutral diffuse gas modeled over ~200 pc, with a mean density n̅H̅ = 1−2 cm−3, illuminated by the standard interstellar UV radiation field, and stirred up by a large-scale compressive turbulent forcing. Within this configuration, the 2D probability histogram of the column densities of H and H2, poetically called the kingfisher diagram, is remarkably stable and is almost unaltered by gravity, the strength of the turbulent forcing, the resolution of the simulation, or the strength of the magnetic field Bx, as long as Bx < 4 μG. The weak effect of the resolution and our analytical prescription suggest that the column densities of HI are likely built up in large-scale warm neutral medium and cold neutral medium (CNM) structures correlated in density over ~20 pc and ~10 pc, respectively, while those of H2 are built up in CNM structures between ~3 and ~10 pc. Conclusions. Combining the chemical and statistical information contained in the observations of HI and H2 sheds new light on the study of the diffuse matter. Applying this new tool to several atomic and molecular species is a promising perspective to understanding the effects of turbulence, magnetic field, thermal instability, and gravity on the formation and evolution of molecular clouds.

How and when in the star formation sequence do dust grains start to grow into pebbles is a cornerstone question to both star and planet formation. We compute the polarized radiative transfer from a model solar-type protostellar core, using the POLARIS code, aligning the dust grains with the local magnetic field, following the radiative torques (RATs) theory. We test the dependency of the resulting dust polarized emission with the maximum grain size of the dust size distribution at the envelope scale, from a max = 1 µm to 50 µm. Our work shows that, in the framework of RAT alignment, large dust grains are required to produce polarized dust emission at levels similar to those currently observed in solar-type protostellar envelopes at millimeter wavelengths. Considering the current theoretical difficulties to align a large fraction of small ISM-like grains in the conditions typical of protostellar envelopes, our results suggest that grain growth (typically > 10 µm) might have already significantly progressed at scales 100 − 1000 au in the youngest objects, observed less than 10 5 years after the onset of collapse. Observations of dust polarized emission might open a new avenue to explore dust pristine properties and describe, for example, the initial conditions for the formation of planetesimals.