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A popular theory of star formation is gravito-turbulent fragmentation, inwhich self-gravitating structures are created by turbulence-driven densityfluctuations. Simple theories of isothermal fragmentation successfullyreproduce the core mass function (CMF) which has a very similar shape to theinitial mass function (IMF) of stars. However, numerical simulations ofisothermal turbulent fragmentation thus far have not succeeded in identifying afragment mass scale that is independent of the simulation resolution. Moreover,the fluid equations for magnetized, self-gravitating, isothermal turbulence arescale-free, and do not predict any characteristic mass. In this paper we showthat, although an isothermal self-gravitating flow does produce a CMF with amass scale imposed by the initial conditions, this scale changes as the parentcloud evolves. In addition, the cores that form undergo further fragmentationand after sufficient time forget about their initial conditions, yielding ascale-free pure power-law distribution $\mathrm{d} N/\mathrm{d} M\proptoM^{-2}$ for the stellar IMF. We show that this problem can be alleviated byintroducing additional physics that provides a termination scale for thecascade. Our candidate for such physics is a simple model for stellar radiationfeedback. Radiative heating, powered by accretion onto forming stars, arreststhe fragmentation cascade and imposes a characteristic mass scale that isnearly independent of the time-evolution or initial conditions in thestar-forming cloud, and that agrees well with the peak of the observed IMF. Incontrast, models that introduce a stiff equation of state for denser clouds butthat do not explicitly include the effects of feedback do not yield aninvariant IMF.

The Necessity of Feedback Physics in Setting the Peak of the Initial Mass Function