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As star-forming clouds collapse, the gas within them fragments to ever-smaller masses. Naively one might expect this process to continue down to the smallest mass that is able to radiate away its binding energy on a dynamical time-scale, the opacity limit for fragmentation, at ~0.01 M⊙. However, the observed peak of the initial mass function (IMF) lies a factor of 20-30 higher in mass, suggesting that some other mechanism halts fragmentation before the opacity limit is reached. In this paper we analyse radiation-magnetohydrodynamic simulations of star cluster formation in typical Milky Way environments in order to determine what physical process limits fragmentation in them. We examine the regions in the vicinity of stars that form in the simulations to determine the amounts of mass that are prevented from fragmenting by thermal and magnetic pressure. We show that, on small scales, thermal pressure enhanced by stellar radiation heating is the dominant mechanism limiting the ability of the gas to further fragment. In the brown dwarf mass regime, ~0.01 M⊙, the typical object that forms in the simulations is surrounded by gas whose mass is several times its own that is unable to escape or fragment, and instead is likely to accrete. This mechanism explains why ~0.01 M⊙ objects are rare: unless an outside agent intervenes (e.g. a shock strips away the gas around them), they will grow by accreting the warmed gas around them. In contrast, by the time stars grow to masses of ~0.2 M⊙, the mass of heated gas is only tens of percent of the central star mass, too small to alter its final mass by a large factor. This naturally explains why the IMF peak is at ~0.2 M⊙.

As star-forming clouds collapse, the gas within them fragments to ever-smaller masses. Naively one might expect this process to continue down to the smallest mass that is able to radiate away its binding energy on a dynamical time-scale, the opacity limit for fragmentation, at ~0.01 M⊙. However, the observed peak of the initial mass function (IMF) lies a factor of 20-30 higher in mass, suggesting that some other mechanism halts fragmentation before the opacity limit is reached. In this paper we analyse radiation-magnetohydrodynamic simulations of star cluster formation in typical Milky Way environments in order to determine what physical process limits fragmentation in them. We examine the regions in the vicinity of stars that form in the simulations to determine the amounts of mass that are prevented from fragmenting by thermal and magnetic pressure. We show that, on small scales, thermal pressure enhanced by stellar radiation heating is the dominant mechanism limiting the ability of the gas to further fragment. In the brown dwarf mass regime, ~0.01 M⊙, the typical object that forms in the simulations is surrounded by gas whose mass is several times its own that is unable to escape or fragment, and instead is likely to accrete. This mechanism explains why ~0.01 M⊙ objects are rare: unless an outside agent intervenes (e.g. a shock strips away the gas around them), they will grow by accreting the warmed gas around them. In contrast, by the time stars grow to masses of ~0.2 M⊙, the mass of heated gas is only tens of percent of the central star mass, too small to alter its final mass by a large factor. This naturally explains why the IMF peak is at ~0.2 M⊙.