On the coupled origin of the stellar IMF and multiplicity

In the solar neighborhood, the Initial Mass Function (IMF) follows is canonically described by the Salpeter power-law slope for the high-mass range. The stellar 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. We aim to (i) quantify the influence of hierarchical fragmentation of cores on the resulting IMF, and (ii) determine the consequences of this fragmentation on the multiplicity of the stellar systems. We employed a scale-free, hierarchical fragmentation model to investigate the fragmentation of top-heavy CMF. Hierarchical fragmentation of gas clumps shifts the CMF towards lower mass range and can modify its shape. Starting from the top-heavy power-law CMF observed in W43-MM2&MM3 star forming region, we show that at least four levels of hierarchical fragmentation are required to generate the turn-over peak of the cIMF. Within a radius of 0.2-2.5 kAU, massive stars (M > 10 Msun) have on average 0.9 companions, five times fewer than low-mass stars (M < 0.1 Msun); the latter 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 less fragments compared to lower mass cores and transfer their mass less efficiently to their fragments. Hierarchical fragmentation alone 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 subfragmentation in various star-forming regions and numerical simulations.

💡 Research Summary

This paper investigates how the stellar initial mass function (IMF) can emerge from the core mass function (CMF) through hierarchical fragmentation, and how this process simultaneously shapes the observed mass‑dependent multiplicity of stars. The authors begin by noting that the canonical IMF in the Milky Way exhibits a Salpeter‑like power‑law slope (Γ ≈ –1.35) for masses above ~1 M⊙, a log‑normal turnover around 0.1–0.3 M⊙, and well‑defined low‑ and high‑mass cut‑offs. Recent ALMA‑IMF observations of the massive star‑forming complex W43‑MM2&MM3 reveal a CMF that is “top‑heavy” (Γ ≈ –0.95), i.e., an excess of high‑mass cores relative to the canonical IMF. A simple, constant star‑formation efficiency cannot reconcile this discrepancy, suggesting that additional processing of the cores—most plausibly fragmentation—is required.

To explore this hypothesis, the authors adopt the scale‑free hierarchical fragmentation framework introduced by Thomasson et al. (2024). In this model a parent structure at spatial scale Rℓ fragments into nℓ children at a smaller scale Rℓ+1. The average number of children ⟨nℓ⟩ and the mass‑transfer efficiency ϵℓ are parameterised by spatial rates ϕ and ξ, respectively: ⟨nℓ⟩ = (Rℓ+1 / Rℓ)^(–ϕ), ϵℓ = (Rℓ+1 / Rℓ)^(–ξ). Thus, as the cascade proceeds, more fragments are produced but each receives a smaller share of the parent mass. The mass partition among siblings is controlled by a ratio q ≥ 1: the primary fragment receives a fraction q/(q + nℓ – 1) of the available mass, while each satellite receives 1/(q + nℓ – 1). When q = 1 the distribution is uniform; for q ≫ 1 a dominant fragment co‑exists with many low‑mass satellites.

Using the observed top‑heavy CMF of W43‑MM2&MM3 as the initial condition, the authors run Monte‑Carlo realizations of the fragmentation cascade, varying the number of hierarchical levels L, the rates ϕ and ξ, and the mass‑ratio parameter q. They find that at least four fragmentation levels (L ≥ 4) are required to shift the CMF sufficiently toward lower masses to reproduce both the Salpeter high‑mass slope and the turnover near 0.2 M⊙. With ⟨nℓ⟩ ≈ 2–3 and ϵℓ ≈ 0.3–0.5 per level, the resulting stellar mass distribution matches the canonical IMF within statistical uncertainties.

A key outcome concerns stellar multiplicity. By tracking the number of fragments that survive to become bound stellar systems, the model predicts that massive primaries (M > 10 M⊙) have on average ~0.9 companions, whereas very low‑mass objects (M < 0.1 M⊙) acquire ~4–5 companions. This reproduces the observed trend that high‑mass stars are more frequently found in multiple systems, while low‑mass stars are predominantly single. However, the authors demonstrate that a purely scale‑free fragmentation scheme cannot simultaneously satisfy the IMF shape and the multiplicity statistics across the full mass range.

Consequently, they propose a two‑regime fragmentation picture. In the first, mass‑dependent regime, the fragmentation rates ϕ(M) and ξ(M) vary with core mass: massive cores produce fewer fragments (lower ϕ) and retain a larger fraction of their mass (lower ξ), leading to a small number of relatively massive fragments. Low‑mass cores fragment more vigorously, generating many low‑mass fragments. In the second, mass‑independent regime, the remaining mass is redistributed more uniformly, establishing the log‑normal turnover. By tuning the transition between the two regimes, the model can reproduce both the universal IMF and the observed multiplicity fractions.

The discussion connects the abstract parameters to physical processes: the mass‑dependent regime may be governed by thermal pressure versus turbulent support, variations in the Jeans mass, or feedback‑driven outflows that preferentially limit fragmentation in massive cores. The mass‑independent regime could reflect a regime where turbulence becomes sub‑sonic and fragmentation proceeds in a scale‑free manner down to the first hydrostatic core. The authors also compare their framework to recent numerical simulations (e.g., Bate 2012; Guszejnov et al. 2017) and suggest that future high‑resolution ALMA or JWST observations of core sub‑fragmentation can directly test the predicted values of ϕ, ξ, and q.

In conclusion, the paper provides a quantitative bridge between the CMF and the IMF, showing that hierarchical fragmentation—when allowed to operate in two distinct, mass‑dependent phases—can naturally generate the canonical IMF while also accounting for the mass‑dependent multiplicity of stars. This dual‑phase model offers a testable paradigm for interpreting variations in the IMF across different star‑forming environments and for guiding future observational and simulation efforts.