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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. 

Context. The study of molecular line emission is crucial to unveil the kinematics and the physical conditions of gas in star-forming regions. We use data from the ALMAGAL survey, which provides an unprecedentedly large statistical sample of high-mass star-forming clumps that helps us to remove bias and reduce noise (e.g., due to source peculiarities, selection, or environmental effects) to determine how well individual molecular species trace continuum emission. Aims. Our aim is to quantify whether individual molecular transitions can be used reliably to derive the physical properties of the bulk of the H₂gas, by considering morphological correlations in their overall integrated molecular line emission with the cold dust. We selected transitions of H₂CO, CH₃OH, DCN, HC₃N, CH₃CN, CH₃OCHO, SO, and SiO and compared them with the 1.38 mm dust continuum emission at different spatial scales in the ALMAGAL sample. We included two transitions of H₂CO to understand whether the validity of the results depends on the excitation condition of the selected transition of a molecular species. The ALMAGAL project observed more than 1000 candidate high-mass star-forming clumps in ALMA band 6 at a spatial resolution down to 1000 au. We analyzed a total of 1013 targets that cover all evolutionary stages of the high-mass star formation process and different conditions of clump fragmentation. Methods. For the first time, we used the method called histogram of oriented gradients (HOG) as implemented in the toolastroHOGon a large statistical sample to compare the morphology of integrated line emission with maps of the 1.38 mm dust continuum emission. For each clump, we defined two masks: the first mask covered the extended more diffuse continuum emission, and the second smaller mask that only contained the compact sources. We selected these two masks to study whether and how the correlation among the selected molecules changes with the spatial scale of the emission, from extended more diffuse gas in the clumps to denser gas in compact fragments (cores). Moreover, we calculated the Spearman correlation coefficient and compared it with our astroHOG results. Results. Only H₂CO, CH₃OH, and SO of the molecular species we analyzed show emission on spatial scales that are comparable with the diffuse 1.38 mm dust continuum emission. However, according the HOG method, the median correlation of the emission of each of these species with the continuum is only ~24–29%. In comparison with the dusty dense fragments, these molecular species still have low correlation values that are below 45% on average. The weak morphological correlation suggests that these molecular lines likely trace the clump medium or outer layers around dense fragments on average (in some cases, this might be due to optical depth effects) or also trace the inner parts of outflows at this scale. On the other hand DCN, HC₃N, CH₃CN₃and CH₃OCHO are well correlated with the dense dust fragments at above 60%. The lowest correlation is seen with SiO for the extended continuum emission and for compact sources. Moreover, unlike other outflow tracers, in a large fraction of the sources, SiO does not cover the area of the extended continuum emission well. This and the results of the astroHOG analysis reveal that SiO and SO do not trace the same gas, in contrast to what was previously thought. From the comparison of the results of the HOG method and the Spearman correlation coefficient, the HOG method gives much more reliable results than the intensity-based coefficient when the level of similarity of the emission morphology is estimated. 

The physical mechanisms behind the fragmentation of high-mass dense clumps into compact star-forming cores and the properties of these cores are fundamental topics that are heavily investigated in current astrophysical research. The ALMAGAL survey provides the opportunity to study this process at an unprecedented level of detail and statistical significance, featuring high-angular resolution 1.38 mm ALMA observations of 1013 massive dense clumps at various Galactic locations. These clumps cover a wide range of distances (~2–8 kpc), masses (~10²–10⁴M_⊙), surface densities (0.1–10 g cm⁻²), and evolutionary stages (luminosity over mass ratio indicator of ~0.05 <L/M <450L_⊙/M_⊙). Here, we present the catalog of compact sources obtained with theCuTExalgorithm from continuum images of the full ALMAGAL clump sample combining ACA-7 m and 12 m ALMA arrays, reaching a uniform high median spatial resolution of ~1400 au (down to ~800 au). We characterize and discuss the revealed fragmentation properties and the photometric and estimated physical parameters of the core population. The ALMAGAL compact source catalog includes 6348 cores detected in 844 clumps (83% of the total), with a number of cores per clump between 1 and 49 (median of 5). The estimated core diameters are mostly within ~800–3000 au (median of 1700 au). We assigned core temperatures based on theL/Mof the hosting clump, and obtained core masses from 0.002 to 345M_⊙(complete above 0.23 M_⊙), exhibiting a good correlation with the core radii (M ∝ R^2.6). We evaluated the variation in the core mass function (CMF) with evolution as traced by the clumpL/M, finding a clear, robust shift and change in slope among CMFs within subsamples at different stages. This finding suggests that the CMF shape is not constant throughout the star formation process, but rather it builds (and flattens) with evolution, with higher core masses reached at later stages. We found that all cores within a clump grow in mass on average with evolution, while a population of possibly newly formed lower-mass cores is present throughout. The number of cores increases with the core masses, at least until the most massive core reaches ~10M_⊙. More generally, our results favor a clump-fed scenario for high-mass star formation, in which cores form as low-mass seeds, and then gain mass while further fragmentation occurs in the clump. 

We present a comparison of the Milky Way’s star formation rate (SFR) surface density (∑_SFR) obtained with two independent state-of-the-art observational methods. The first method infers Σ_SFRfrom observations of the dust thermal emission from interstellar dust grains in far-infrared wavelengths registered in theHerschelinfrared Galactic Plane Survey (Hi-GAL). The second method determines Σ_SFRby modeling the current population of O-, B-, and A-type stars in a 6 kpc × 6 kpc area around the Sun. We find an agreement between the two methods within a factor of two for the mean SFRs and the SFR surface density profiles. Given the broad differences between the observational techniques and the independent assumptions in the methods for computing the SFRs, this agreement constitutes a significant advance in our understanding of the star formation of our Galaxy and implies that the local SFR has been roughly constant over the past 10 Myr. 

The interstellar medium in the Milky Way’s Central Molecular Zone (CMZ) is known to be strongly magnetised, but its large-scale morphology and impact on the gas dynamics are not well understood. We explore the impact and properties of magnetic fields in the CMZ using three-dimensional non-self gravitating magnetohydrodynamical simulations of gas flow in an external Milky Way barred potential. We find that: (1) The magnetic field is conveniently decomposed into a regular time-averaged component and an irregular turbulent component. The regular component aligns well with the velocity vectors of the gas everywhere, including within the bar lanes. (2) The field geometry transitions from parallel to the Galactic plane near ɀ = 0 to poloidal away from the plane. (3) The magneto-rotational instability (MRI) causes an in-plane inflow of matter from the CMZ gas ring towards the central few parsecs of 0.01−0.1 M_⊙yr⁻¹that is absent in the unmagnetised simulations. However, the magnetic fields have no significant effect on the larger-scale bar-driven inflow that brings the gas from the Galactic disc into the CMZ. (4) A combination of bar inflow and MRI-driven turbulence can sustain a turbulent vertical velocity dispersion ofσ_ɀ= 5 km s⁻¹on scales of 20 pc in the CMZ ring. The MRI alone sustains a velocity dispersion ofσ_ɀ≃ 3 km s⁻¹. Both these numbers are lower than the observed velocity dispersion of gas in the CMZ, suggesting that other processes such as stellar feedback are necessary to explain the observations. (5) Dynamo action driven by differential rotation and the MRI amplifies the magnetic fields in the CMZ ring until they saturate at a value that scales with the average local density asB≃ 102 (n/10³cm⁻³)^0.33µG. Finally, we discuss the implications of our results within the observational context in the CMZ. 

The stellar initial mass function (IMF) is critical to our understanding of star formation and the effects of young stars on their environment. On large scales, it enables us to use tracers such as UV or Hα emission to estimate the star formation rate of a system and interpret unresolved star clusters across the Universe. So far, there is little firm evidence of large-scale variations of the IMF, which is thus generally considered “universal”. Stars form from cores, and it is now possible to estimate core masses and compare the core mass function (CMF) with the IMF, which it presumably produces. The goal of the ALMA-IMF large programme is to measure the core mass function at high linear resolution (2700 au) in 15 typical Milky Way protoclusters spanning a mass range of 2.5 × 10³to 32.7 × 10³M_⊙. In this work, we used two different core extraction algorithms to extract ≈680 gravitationally bound cores from these 15 protoclusters. We adopted a per core temperature using the temperature estimate from the point-process mapping Bayesian method (PPMAP). A power-law fit to the CMF of the sub-sample of cores above the 1.64M_⊙completeness limit (330 cores) through the maximum likelihood estimate technique yields a slope of 1.97 ± 0.06, which is significantly flatter than the 2.35 Salpeter slope. Assuming a self-similar mapping between the CMF and the IMF, this result implies that these 15 high-mass protoclusters will generate atypical IMFs. This sample currently is the largest sample that was produced and analysed self-consistently, derived at matched physical resolution, with per core temperature estimates, and cores as massive as 150M_⊙. We provide both the raw source extraction catalogues and the catalogues listing the source size, temperature, mass, spectral indices, and so on in the 15 protoclusters. 

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. 

Context. The degree of coupling between the gas and the magnetic field during the collapse of a core and the subsequent formation of a disk depends on the assumed dust size distribution. Aims. We study the impact of grain–grain coagulation on the evolution of magnetohydrodynamic (MHD) resistivities during the collapse of a prestellar core. Methods. We use a 1D model to follow the evolution of the dust size distribution, out-of-equilibrium ionisation state, and gas chemistry during the collapse of a prestellar core. To compute the grain–grain collisional rate, we consider models for both random and systematic, size-dependent, velocities. We include grain growth through grain–grain coagulation and ice accretion, but ignore grain fragmentation. Results. Starting with a Mathis-Rumpl-Nordsieck (MRN) size distribution (Mathis et al. 1977, ApJ, 217, 425), we find that coagulation in grain–grain collisions generated by hydrodynamical turbulence is not efficient at removing the smallest grains and, as a consequence, does not have a large effect on the evolution of the Hall and ambipolar diffusion MHD resistivities, which still drop significantly during the collapse like in models without coagulation. The inclusion of systematic velocities, possibly induced by the presence of ambipolar diffusion, increases the coagulation rate between small and large grains, removing small grains earlier in the collapse and therefore limiting the drop in the Hall and ambipolar diffusion resistivities. At intermediate densities ( n H ~ 10 8 cm −3 ), the Hall and ambipolar diffusion resistivities are found to be higher by 1 to 2 orders of magnitude in models with coagulation than in models where coagulation is ignored, and also higher than in a toy model without coagulation where all grains smaller than 0.1 μ m would have been removed in the parent cloud before the collapse. Conclusions. When grain drift velocities induced by ambipolar diffusion are included, dust coagulation happening during the collapse of a prestellar core starting from an initial MRN dust size distribution appears to be efficient enough to increase the MHD resistivities to the values necessary to strongly modify the magnetically regulated formation of a planet-forming disk. A consistent treatment of the competition between fragmentation and coagulation is, however, necessary before reaching firm conclusions. 

Context. Among the most central open questions regarding the initial mass function (IMF) of stars is the impact of environment on the shape of the core mass function (CMF) and thus potentially on the IMF. Aims. The ALMA-IMF Large Program aims to investigate the variations in the core distributions (CMF and mass segregation) with cloud characteristics, such as the density and kinematic of the gas, as diagnostic observables of the formation process and evolution of clouds. The present study focuses on the W43-MM2&MM3 mini-starburst, whose CMF has recently been found to be top-heavy with respect to the Salpeter slope of the canonical IMF. Methods. W43-MM2&MM3 is a useful test case for environmental studies because it harbors a rich cluster that contains a statistically significant number of cores (specifically, 205 cores), which was previously characterized in Paper III. We applied a multi-scale decomposition technique to the ALMA 1.3 mm and 3 mm continuum images of W43-MM2&MM3 to define six subregions, each 0.5–1 pc in size. For each subregion we characterized the probability distribution function of the high column density gas, η -PDF, using the 1.3 mm images. Using the core catalog, we investigate correlations between the CMF and cloud and core properties, such as the η -PDF and the core mass segregation. Results. We classify the W43-MM2&MM3 subregions into different stages of evolution, from quiescent to burst to post-burst, based on the surface number density of cores, number of outflows, and ultra-compact HII presence. The high-mass end (>1 M ⊙ ) of the subregion CMFs varies from close to the Salpeter slope (quiescent) to top-heavy (burst and post-burst). Moreover, the second tail of the η -PDF varies from steep (quiescent) to flat (burst and post-burst), as observed for high-mass star-forming clouds. We find that subregions with flat second η -PDF tails display top-heavy CMFs. Conclusions. In dynamical environments such as W43-MM2&MM3, the high-mass end of the CMF appears to be rooted in the cloud structure, which is at high column density and surrounds cores. This connection stems from the fact that cores and their immediate surroundings are both determined and shaped by the cloud formation process, the current evolutionary state of the cloud, and, more broadly, the star formation history. The CMF may evolve from Salpeter to top-heavy throughout the star formation process from the quiescent to the burst phase. This scenario raises the question of if the CMF might revert again to Salpeter as the cloud approaches the end of its star formation stage, a hypothesis that remains to be tested. 

Aims.The processes that determine the stellar initial mass function (IMF) and its origin are critical unsolved problems, with profound implications for many areas of astrophysics. The W43-MM2&MM3 mini-starburst ridge hosts a rich young protocluster, from which it is possible to test the current paradigm on the IMF origin. Methods.The ALMA-IMF Large Program observed the W43-MM2&MM3 ridge, whose 1.3 mm and 3 mm ALMA 12 m array continuum images reach a ~2500 au spatial resolution. We used both the best-sensitivity and the line-free ALMA-IMF images, reduced the noise with the multi-resolution segmentation techniqueMnGSeg, and derived the most complete and most robust core catalog possible. Using two different extraction software packages,getsfandGExt2D, we identified ~200 compact sources, whose ~100 common sources have, on average, fluxes consistent to within 30%. We filtered sources with non-negligible free-free contamination and corrected fluxes from line contamination, resulting in a W43-MM2&MM3 catalog of 205getsfcores. With a median deconvolved FWHM size of 3400 au, core masses range from ~0.1M_⊙to ~70M_⊙and thegetsfcatalog is 90% complete down to 0.8M_⊙.Results.The high-mass end of the core mass function (CMF) of W43-MM2&MM3 is top-heavy compared to the canonical IMF. Fitting the cumulative CMF with a single power-law of the formN(> logM) ∝M^α, we measuredα= −0.95 ± 0.04, compared to the canonicalα= −1.35 Salpeter IMF slope. The slope of the CMF is robust with respect to map processing, extraction software packages, and reasonable variations in the assumptions taken to estimate core masses. We explore several assumptions on how cores transfer their mass to stars (assuming a mass conversion efficiency) and subfragment (defining a core fragment mass function) to predict the IMF resulting from the W43-MM2&MM3 CMF. While core mass growth should flatten the high-mass end of the resulting IMF, core fragmentation could steepen it. Conclusions.In stark contrast to the commonly accepted paradigm, our result argues against the universality of the CMF shape. More robust functions of the star formation efficiency and core subfragmentation are required to better predict the resulting IMF, here suggested to remain top-heavy at the end of the star formation phase. If confirmed, the IMFs emerging from starburst events could inherit their top-heavy shape from their parental CMFs, challenging the IMF universality.