On the coupled origin of the stellar IMF and multiplicity

TL;DR

The paper investigates whether the stellar IMF can originate from the CMF via hierarchical fragmentation and how such fragmentation shapes multiplicity. It presents a scale-free, multi-level fragmentation model applied to the top-heavy CMF observed in the W43-MM2&MM3 region, linking core fragmentation to the canonical IMF and to multiplicity statistics, and identifies a tension between achieving a universal IMF and observed multiplicity with purely scale-free fragmentation. The authors show that four fragmentation levels are needed to reproduce the cIMF turnover and demonstrate that mass-dependent fragmentation with a specific ratio ($\xi'_M/\phi'_M\approx0.26$) can reproduce a Salpeter-like high-mass slope, though not simultaneously with observed multiplicity. They propose a two-phase fragmentation picture—mass-dependent early fragmentation establishing the high-mass slope and mass-independent late fragmentation setting the turnover—along with the influence of disks, environment, dynamics, and feedback, as necessary ingredients to match both IMF shape and multiplicity; their framework provides a quantitative basis to compare core subfragmentation across regions and simulations.

Abstract

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.

Figures (8)

• Figure 1: Sketch of the hierarchical fragmentation model used. A parental object at spatial scale $R_l$ (red) fragments into a number $n_l$ of children at scale $R_{l+1}$ (blue), here $n_l = 2$. The children are identified by an index $i$ where $i = 1$ represents the primary, (i.e. most massive) child.
• Figure 2: Parameter space for which a fCMF is compatible with the masch2013 cIMF in the sense of the AD test. Top: Parameter space at which a fCMF is compatible with the cIMF at 0.05 confidence level, in the fragmentation rate ($\phi$) vs mass transfer rate ($\xi$) diagram for different fragments mass ratio $q$. Yellow, blue, orange, green, red and magenta patches highlight the solutions at $R_\text{stop} = 741, 494, 329, 219, 146, 98$ AU after $l = 3, 4, 5, 6, 7, 8$ levels of fragmentation, respectively. Crosses at $q = 3.0$ indicate points where the average total number of fragments produced at $R_\text{stop}$ is $\approx$2.5. Bottom: fCMF associated to the coloured-labelled points. Blue, red and black dashed lines represent the fCMF, cIMF and the slope of the initial top-heavy CMF respectively. The AD test is performed from $M = 0.2$ M$_\odot$ to $M = 150$ M$_\odot$ to compare the fCMF with the cIMF.
• Figure 3: Convergence of the local logarithmic slope $\Gamma(R, M)$ under the influence of hierarchical fragmentation with the spatial scales $R$ (solid black line) towards the Salpeter slope (dotted red line) for different initial slopes $\Gamma_0 = -2.0, -1.5, -0.5, 0, 0.5, 1.0$. This convergence is only possible if $\xi'_M > \phi'_M$, with $\xi'_M = \partial \xi / \partial \log M$ and $\phi'_M = \partial \phi / \partial \log M$. The initial distribution can also converge towards other asymptotic values (dotted grey lines) depending on the relationship between $\xi'_M$ and $\phi'_M$ according to Eq. \ref{['eq:alpha_variation_phi_xi']}. The slopes associated with the cases $\xi'_M = 0$ and $\phi'_M = 0$ (dotted blue lines) correspond to the asymptotes determined in Sects.\ref{['sec:Effect of the mass transfer rate']} and \ref{['sec:Effect of the fragmentation rate']} respectively.
• Figure 4: Survival function of the fragmented CMF correlated with the multiplicity of stellar systems formed at different mass interval. Top: We perform $10^4$ random fragmentation draws (black lines) from the sample constituting the W43-MM2&MM3 CMF as presented in pouteau2022 (blue crosses), using parameters $\phi = 1.0$, $\xi = -0.1$, and $q = 2$. Fragmentation covers spatial scales from $R_0 = 2500$ AU down to $R_\text{stop} = 219$ AU. For visibility, only the first 100 Monte Carlo draws are shown. The solid red and dashed blue line represents the canonical IMF and the power-law distribution fit from pouteau2022 respectively. The dashed red line represents the average of the slopes obtained from fitting each Monte Carlo draw, using masses $M > 0.8~$M$_\odot$. Bottom: Distribution of the number of neighbors that a star of mass $M$ possesses in different mass interval indicated above each plot. The mean value is indicated by the horizontal dashed line.
• Figure 5: Multiplicity fraction as a function of the primary masses grouped inside bins, for different fragmentation scenarios. Each Monte-Carlo simulation is carried out using $10^4$ random cores drawn from a top-heavy CMF with $\Gamma = -0.95$pouteau2022, with $\xi = -0.2$, $q = 2$ and 8 levels of fragmentation. Blue and black, green and red dots represent simulations using $\phi = 0.8, \phi = 0.4, \phi'_M = 0.5, \phi'_M = -0.5$.