ALMA-IMF. XXII. Role of core subfragmentation in the IMF origin: Hierarchical mass cascade in W43-MM1

The gravoturbulent fragmentation of the interstellar medium is expected to create a hierarchical cascade of cloud structures, crossing the scales from core to disk. We aim to predict how the currently observed top-heavy core mass function (CMF) in the massive protocluster W43-MM1 evolves due to core subfragmentation. We used the , a graph-theory-based analysis tool, to create and characterize networks of nested sources in W43-MM1. We compared the hierarchical fragmentation cascade of W43-MM1 to those measured in the NGC 2264 protocluster and in synthetic images of an Orion-like protocluster simulated by magneto-hydrodynamical calculations. algorithm to extract sources in five ALMA images of W43-MM1 at 3 mm, with a spatial resolution ranging from 14 kau to 270 au. Then, we applied FAMILY Assuming self-similarity, we measured a small fractality index of mathcal F _ 3̊m D =1.19± 0.10 in W43-MM1, which means that, on average, a cloud structure fragments into only 1.19 fragments each time the physical scale decreases by a factor of two. In line with values measured above the core scale in the NGC 2264 and synthetic protoclusters, the W43-MM1 fractality index increases by about 30% at larger scales. We also estimate an imbalanced mass partition between siblings, with two-thirds of the mass of siblings at a given scale belonging to the dominant sibling. The mass transfer efficiency, computed from one physical scale to another, is high and corresponds to a core formation efficiency (CFE) from 2400 au cores to 200 au seeds of ∼16%. Based on the fractality and efficiency values measured in W43-MM1, the gravoturbulent model by Thomasson predicts that its fragmentation below ∼14 kau is not driven by turbulence but by gravity. Using these parameters and the measured mass partition, we demonstrate that the seed mass function, from which the initial mass function (IMF) emerges, has a high-mass end that remains top-heavy. Therefore, based on our current assumptions, core subfragmentation in W43-MM1, and perhaps more broadly in massive Galactic protoclusters, plays a minimal role in shaping the high-mass slope of the IMF.