ALMAGAL VI. The spatial distribution of dense cores during the evolution of cluster-forming massive clumps

Context. High-mass stars and star clusters form from the fragmentation of massive dense clumps driven by gravity, turbulence and magnetic field. The extent to which each of these agents impacts the fragmentation depending on the clump mass, density and evolutionary stage is still largely unknown. Aims. The ALMAGAL project, with∼1000 clumps observed at∼1000 au resolution, allows a statistically significant characterization of the fragmentation process over a large range of clump physical parameters and evolutionary stages. Our goal is to characterize where and how the dense cores revealed by ALMA are distributed in massive potentially cluster-forming clumps to trace how fragmentation is initially set and how it proceeds before gas dispersal due to stellar feedback. Methods. We characterized the spatial distribution of dense cores in the 514 ALMAGAL clumps that host at least 4 cores, using a set of quantitative descriptors that we evaluated against the clump L/M ratio, which we adopted as an indicator of the evolution of the system. We measured the separations between cores with the minimum spanning tree method (MST), which we compared with the predictions of gravitational fragmentation from Jeans theory. We investigated whether cores have specific arrangements using the Q-parameter or variations due to their masses with the mass segregation ratio, ΛMS R. Results. The ALMAGAL cores are distributed throughout the entire area of the clump, usually arranged in elliptical groups with an axis ratio e∼2.2, although high values with e ≥5 are also observed. We found a single characteristic core separation per clump in∼76% of the cases, suggesting that multiple fragmentation lengths may be frequently present. Typical cores separations are compatible with clump-averaged thermal Jeans length, λth J . However, we found an additional population of cores, typical of low-fragmented and young clumps, which are on average more widely separated with l ≈3 ×λth J . By stacking the distributions of the core separations in clumps of similar evolutionary stage, we also found that separation decreases on average from l∼22000 au in younger systems to l∼7000 au in more evolved ones. The ALMAGAL cores are typically distributed in fractal-type subclusters, while centrally concentrated patterns appear only at later stages, but we do not observe a progressive transition between these configurations with evolution. Finally, we also found 101 ALMAGAL systems with a signature of mass segregation, with an occurrence that increases with evolution.