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Observations have indicated that the pre-stellar core mass function (CMF) is similar to the stellar initial mass function (IMF), except for an offset towards larger masses. This has led to the idea that there is a one-to-one relation between cores and stars, such that the whole stellar mass reservoir is contained in a gravitationally bound pre-stellar core, as postulated by the core-collapse model, and assumed in recent theoretical models of the stellar IMF. We test the validity of this assumption by comparing the final mass of stars with the mass of their progenitor cores in a high-resolution star formation simulation that generates a realistic IMF under physical condition characteristic of observed molecular clouds. Using a definition of bound cores similar to previous works we obtain a CMF that converges with increasing numerical resolution. We find that the CMF and the IMF are closely related in a statistical sense only; for any individual star there is only a weak correlation between the progenitor core mass and the final stellar mass. In particular, for high-mass stars only a small fraction of the final stellar mass comes from the progenitor core, and even for low-mass stars the fraction is highly variable, with a median fraction of only about 50 per cent. We conclude that the core-collapse scenario and related models for the origin of the IMF are incomplete. We also show that competitive accretion is not a viable alternative., We are grateful to the anonymous referee for a detailed and useful report. PP and VMP acknowledge support by the Spanish MINECO under project AYA2017-88754-P, and financial support from the State Agency for Research of the Spanish Ministry of Science and Innovation through the ‘Unit of Excellence María de Maeztu 2020-2023’ award to the Institute of Cosmos Sciences (CEX2019-000918-M). The research leading to these results has received funding from the Independent Research Fund Denmark through grant No. DFF 8021-00350B (TH). We acknowledge PRACE for awarding us access to Curie at GENCI@CEA, France. Storage and computing resources at the University of Copenhagen HPC centre, funded in part by Villum Fonden (VKR023406), were used to carry out part of the data analysis.

We introduce a new dual power law (DPL) probability distribution function for the mass distribution of stellar and substellar objects at birth, otherwise known as the initial mass function (IMF). The model contains both deterministic and stochastic elements, and provides a unified framework within which to view the formation of brown dwarfs and stars resulting from an accretion process that starts from extremely low mass seeds. It does not depend upon a top down scenario of collapsing (Jeans) masses or an initial lognormal or otherwise IMF-like distribution of seed masses. Like the modified lognormal power law (MLP) distribution, the DPL distribution has a power law at the high mass end, as a result of exponential growth of mass coupled with equally likely stopping of accretion at any time interval. Unlike the MLP, a power law decay also appears at the low mass end of the IMF. This feature is closely connected to the accretion stopping probability rising from an initially low value up to a high value. This might be associated with physical effects of ejections sometimes (i.e., rarely) stopping accretion at early times followed by outflow driven accretion stopping at later times, with the transition happening at a critical time (therefore mass). Comparing the DPL to empirical data, the critical mass is close to the substellar mass limit, suggesting that the onset of nuclear fusion plays an important role in the subsequent accretion history of a young stellar object., Comment: 6 pages, 2 figures, to appear in MNRAS

Linear analysis of the formation of protostellar cores in planar magnetic interstellar clouds shows that molecular clouds exhibit a preferred length scale for collapse that depends on the mass-to-flux ratio and neutral-ion collision time within the cloud. This linear analysis can be used to investigate the formation of star forming clusters and the distribution of mass within star forming regions. By combining the results of the linear analysis with a realistic ionization profile for the cloud, we find that a molecular cloud may evolve through two fragmentation events in the evolution toward the formation of stars. Our model suggests that the initial fragmentation into clumps occurs for a transcritical cloud on parsec scales while the second fragmentation can occur for transcritical and supercritical cores on subparsec scales. Comparison of our results with several star forming regions (Perseus, Taurus, Pipe Nebula) shows support for a two-stage fragmentation model. Simulations of the thin-disk magnetohydrodynamic equations show that the two-stage fragmentation model is valid for a small region of parameter space assuming some form of recurrent density fluctuations within the region. In addition, applying Monte Carlo methods to these fragmentation length scales and distributions of other environmental variables (e.g., column density and mass-to-flux ratio) allow us to produce synthetic core mass functions (CMFs) for various environmental conditions. Our analysis shows that the shape of the CMF is directly dependent on the physical conditions of the cloud. Specifically, magnetic fields act to broaden the mass function and develop a high-mass tail while ambipolar diffusion will truncate this high-mass tail. We also analyze the effect of small number statistics on the shape and high-mass slope of the synthetic CMFs. We find that observed core mass functions are severely statistically limited, which has a profound effect on the derived slope for the high-mass tail.