ALMAGAL V. Relations between the core populations and the parent clump physical properties

Context. The fragmentation of massive molecular clumps into smaller, potentially star-forming cores plays a key role in the processes of high-mass star formation. The ALMAGAL project offers high-resolution data to investigate these processes across various evolutionary stages in the Galactic plane. Aims. This study aims at correlating the fragmentation properties of massive clumps, obtained from ALMA observations, with their global physical parameters (e.g., mass, surface density, and temperature) and evolutionary indicators (such as luminosity-to-mass ratio and bolometric temperature) obtained from Herschel observations. It seeks to assess whether the cores evolve in number and mass in tandem with their host clumps, and to determine the possible factors influencing the formation of massive cores (M > 24M_\odot). Methods. We analyzed the masses of 6348 fragments, estimated from 1.4 mm continuum data for 1007 ALMAGAL clumps. Leveraging this unprecedentedly large data set, we evaluated statistical relationships between clump parameters, estimated over about 0.1 pc scales, and fragment properties, corresponding to scales of a few 1000 au, while accounting for potential biases related to distance and observational resolution. Our results were further compared with predictions from numerical simulations. Results. The fragmentation level correlates preferentially with clump surface density, supporting a scenario of density-driven fragmentation, whereas it does not show any clear dependence on total clump mass. Both the mass of the most massive core and the core formation efficiency show a broad range and increase on average by an order of magnitude in the intervals spanned by evolutionary indicators such as clump dust temperature and the luminosity-to-mass ratio. This suggests that core growth continues throughout the clump evolution, favoring clump-fed over core-fed theoretical scenarios.