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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 finite-difference time-domain (FDTD) method is a widespread numerical tool for full-wave analysis of electromagnetic fields in complex media and for detailed geometries. Applications of the FDTD method cover a range of time and spatial scales, extending from subatomic to galactic lengths and from classical to quantum physics. Technology areas that benefit from the FDTD method include biomedicine — bioimaging, biophotonics, bioelectronics and biosensors; geophysics — remote sensing, communications, space weather hazards and geolocation; metamaterials — sub-wavelength focusing lenses, electromagnetic cloaks and continuously scanning leaky-wave antennas; optics — diffractive optical elements, photonic bandgap structures, photonic crystal waveguides and ring-resonator devices; plasmonics — plasmonic waveguides and antennas; and quantum applications — quantum devices and quantum radar. This Primer summarizes the main features of the FDTD method, along with key extensions that enable accurate solutions to be obtained for different research questions. Additionally, hardware considerations are discussed, plus examples of how to extract magnitude and phase data, Brillouin diagrams and scattering parameters from the output of an FDTD model. The Primer ends with a discussion of ongoing challenges and opportunities to further enhance the FDTD method for current and future applications. 

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. 

Context.Stars form preferentially in clusters embedded inside massive molecular clouds, many of which contain high-mass stars. Thus, a comprehensive understanding of star formation requires a robust and statistically well-constrained characterization of the formation and early evolution of these high-mass star clusters. To achieve this, we designed the ALMAGAL Large Program that observed 1017 high-mass star-forming regions distributed throughout the Galaxy, sampling different evolutionary stages and environmental conditions. Aims.In this work, we present the acquisition and processing of the ALMAGAL data. The main goal is to set up a robust pipeline that generates science-ready products, that is, continuum and spectral cubes for each ALMAGAL field, with a good and uniform quality across the whole sample. Methods.ALMAGAL observations were performed with the Atacama Large Millimeter/submillimeter Array (ALMA). Each field was observed in three different telescope arrays, being sensitive to spatial scales ranging from ≈1000 au up to ≈0.1 pc. The spectral setup allows sensitive (≈0.1 mJy beam⁻¹) imaging of the continuum emission at 219 GHz (or 1.38 mm), and it covers multiple molecular spectral lines observed in four different spectral windows that span about ≈4 GHz in frequency coverage. We have designed a Python-based processing workflow to calibrate and image these observational data. This ALMAGAL pipeline includes an improved continuum determination, suited for line-rich sources; an automatic self-calibration process that reduces phase-noise fluctuations and improves the dynamical range by up to a factor ≈5 in about 15% of the fields; and the combination of data from different telescope arrays to produce science-ready, fully combined images. Results.The final products are a set of uniformly generated continuum images and spectral cubes for each ALMAGAL field, including individual-array and combined-array products. The fully combined products have spatial resolutions in the range 800–2000 au, and mass sensitivities in the range 0.02–0.07M_⊙. We also present a first analysis of the spectral line information included in the ALMAGAL setup, and its potential for future scientific studies. As an example, specific spectral lines (e.g., SiO and CH₃CN) at ≈1000 au scales resolve the presence of multiple outflows in clusters and will help us to search for disk candidates around massive protostars. Moreover, the broad frequency bands provide information on the chemical richness of the different cluster members, which can be used to study the chemical evolution during the formation process of star clusters.