Context. In the solar neighbourhood, the initial mass function (IMF) is canonically described by the Salpeter power-law slope for the high-mass range. As stars inherit their mass from their environment, their IMF may directly result from a core mass function (CMF) through accretion, gravitational collapse, and fragmentation. This inheritance implies that the mass of the gaseous fragments may be connected to the properties of clustered and multiple stellar systems. In these systems, mass and multiplicity are related, and this is supported by the fact that more massive primaries are observed more frequently in multiple systems. Aims. We aim to (i) quantify the influence of the hierarchical fragmentation of cores on the resulting IMF and (ii) determine the consequences of this fragmentation on the multiplicity of the stellar systems. Methods. To do so, we employed a scale-free hierarchical fragmentation model to investigate the stochastic fragmentation of the 2.5 kAU cores of the W43-MM2&MM3 molecular cloud, whose CMF is top-heavy. We also used this model to quantify the influence of deterministic mass-dependent fragmentation processes. Results. The hierarchical fragmentation of gas clumps shifts the CMF towards a lower mass range and can modify its shape. The shift is quantified by both the number of fragments produced at each level of fragmentation and the mass the fragments inherit from their parental core. Starting from the top-heavy power-law CMF observed in W43-MM2&MM3, we show that at least four levels of hierarchical fragmentation are required to generate the turn-over peak of the canonical IMF. Within a radius of 0.2–2.5 kAU, massive stars (M > 10 M⊙) have on average 0.9 companions, five times fewer than low-mass stars (M < 0.1 M⊙), which are less dynamically stable and should disperse. We show that a universal IMF can emerge from mass-dependent fragmentation processes provided that more massive cores produce fewer fragments compared to lower mass cores and transfer their mass less efficiently to their fragments. Conclusions. Hierarchical fragmentation alone, however, cannot reconcile a universal IMF with observed stellar multiplicity. We propose that fragmentation is not scale-free but operates in two distinct regimes: a mass-dependent phase establishing the Salpeter slope and a mass-independent phase setting the turn-over. Our framework provides a way to compare core sub-fragmentation in various star-forming regions and numerical simulations.
Thomasson et al. (Tue,) studied this question.