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ABSTRACT The relationship between magnetic field strength B and gas density n in the interstellar medium is of fundamental importance. We present and compare Bayesian analyses of the B–n relation for two comprehensive observational data sets: a Zeeman data set and 700 observations using the Davis–Chandrasekhar–Fermi (DCF) method. Using a hierarchical Bayesian analysis we present a general, multiscale broken power-law relation, $$B=B_0(n/n_0)^{\alpha }$$, with $$\alpha =\alpha _1$$ for $$n< n_0$$ and $$\alpha _2$$ for $$n>n_0$$, and with $$B_0$$ the field strength at $$n_0$$. For the Zeeman data, we find: $$\alpha _1={0.15^{+0.06}_{-0.09}}$$ for diffuse gas and $$\alpha _2 = {0.53^{+0.09}_{-0.07}}$$ for dense gas with $$n_0 = 0.40^{+1.30}_{-0.30}\times 10^4$$ cm$$^{-3}$$. For the DCF data, we find: $$\alpha _1={0.26^{+0.01}_{-0.01}}$$ and $$\alpha _2={0.77_{-0.15}^{+0.14}}$$, with $$n_0=14.00^{+10.00}_{-7.00}\times 10^4$$ cm$$^{-3}$$, where the uncertainties give 68 per cent credible intervals. We perform a similar analysis on nineteen numerical magnetohydrodynamic simulations covering a wide range of physical conditions from protostellar discs to dwarf and Milky Way-like galaxies, computed with the arepo, flash, pencil, and ramses codes. The resulting exponents depend on several physical factors such as dynamo effects and their time-scales, turbulence, and initial seed field strength. We find that the dwarf and Milky Way-like galaxy simulations produce results closest to the observations. 

Dust grains influence many aspects of star formation, including planet formation and the opacities for radiative transfer, chemistry, and the magnetic field via Ohmic, Hall, as well as ambipolar diffusion. The size distribution of the dust grains is the primary characteristic influencing all these aspects. Grain size increases by coagulation throughout the star formation process. In this work, we describe numerical simulations of protostellar collapse using methods described in earlier papers of this series. We compute the evolution of the grain size distribution from coagulation and the non-ideal magnetohydrodynamics effects self-consistently and at low numerical cost. We find that the coagulation efficiency is mostly affected by the time spent in high-density regions. Starting from sub-micron radii, grain sizes reach more than 100 µm in an inner protoplanetary disk that is only 1000 yr old. We also show that the growth of grains significantly affects the resistivities, while also having an indirect effect on the dynamics and angular momentum of the disk. 

Thermal ionization is a critical process at temperatures T  > 10 3 K, particularly during star formation. An increase in ionization leads to a decrease in nonideal magnetohydrodynamics (MHD) resistivities, which has a significant impact on protoplanetary disks and protostar formation. We developed an extension of the fast computational ionization method presented in our recent paper to include thermal ionization. The model can be used to inexpensively calculate the density of ions and electrons and the electric charge of each size of grains for an arbitrary size distribution. This tool should be particularly useful for the self-consistent calculation of nonideal MHD resistivities in multidimensional simulations, especially of protostellar collapse and protoplanetary disks. 

Context. A large fraction of stars form in clusters containing high-mass stars, which subsequently influences the local and galaxy-wide environment. Aims. Fundamental questions about the physics responsible for fragmenting molecular parsec-scale clumps into cores of a few thousand astronomical units (au) are still open, that only a statistically significant investigation with ALMA is able to address; for instance: the identification of the dominant agents that determine the core demographics, mass, and spatial distribution as a function of the physical properties of the hosting clumps, their evolutionary stage and the different Galactic environments in which they reside. The extent to which fragmentation is driven by clumps dynamics or mass transport in filaments also remains elusive. Methods. With the ALMAGAL project, we observed the 1.38 mm continuum and lines toward more than 1000 dense clumps in our Galaxy, withM≥ 500 M_⊙, Σ ≥ 0.1 g cm⁻²andd≤ 7.5 kiloparsec (kpc). Two different combinations of ALMA Compact Array (ACA) and 12-m array setups were used to deliver a minimum resolution of ∼1000 au over the entire sample distance range. The sample covers all evolutionary stages from infrared dark clouds (IRDCs) to H IIregions from the tip of the Galactic bar to the outskirts of the Galaxy. With a continuum sensitivity of 0.1 mJy, ALMAGAL enables a complete study of the clump-to-core fragmentation process down toM∼ 0.3 M_⊙across the Galaxy. The spectral setup includes several molecular lines to trace the multiscale physics and dynamics of gas, notably CH₃CN, H₂CO, SiO, CH₃OH, DCN, HC₃N, and SO, among others. Results. We present an initial overview of the observations and the early science product and results produced in the ALMAGAL Consortium, with a first characterization of the morphological properties of the continuum emission detected above 5σin our fields. We used “perimeter-versus-area” and convex hull-versus-area metrics to classify the different morphologies. We find that more extended and morphologically complex (significantly departing from circular or generally convex) shapes are found toward clumps that are relatively more evolved and have higher surface densities. Conclusions. ALMAGAL is poised to serve as a game-changer for a number of specific issues in star formation: clump-to-core fragmentation processes, demographics of cores, core and clump gas chemistry and dynamics, infall and outflow dynamics, and disk detections. Many of these issues will be covered in the first generation of papers that closely follow on the present publication. 

Dust grains play a major role in many astrophysical contexts. They affect the chemical, magnetic, dynamical, and optical properties of their environment, from galaxies down to the interstellar medium, star-forming regions, and protoplanetary disks. Their coagulation leads to shifts in their size distribution and ultimately to the formation of planets. However, although the coagulation process is reasonably uncomplicated to numerically implement by itself, it is difficult to couple it with multidimensional hydrodynamics numerical simulations because of its high computational cost. We propose here a simple method for tracking the coagulation of grains at far lower cost. Given an initial grain size distribution, the state of the distribution at time t is solely determined by the value of a single variable integrated along the trajectory, independently of the specific path taken by the grains. Although this method cannot account for processes other than coagulation, it is mathematically exact, fast, inexpensive, and can be used to evaluate the effect of grain coagulation in most astrophysical contexts. It is applicable to all coagulation kernels in which local physical conditions and grain properties can be separated. We also describe another method for calculating the average electric charge of grains and the density of ions and electrons in environments that are shielded from radiation fields, given the density and temperature of the gas, the cosmic-ray ionization rate, and the average mass of the ions. The equations we provide are fast to integrate numerically and can be used in multidimensional numerical simulations to self-consistently calculate on the fly the local resistivities that are required to model nonideal magnetohydrodynamics.