The Necessity of Feedback Physics in Setting the Peak of the Initial
  Mass Function
  A popular theory of star formation is gravito-turbulent fragmentation, in
which self-gravitating structures are created by turbulence-driven density
fluctuations. Simple theories of isothermal fragmentation successfully
reproduce the core mass function (CMF) which has a very similar shape to the
initial mass function (IMF) of stars. However, numerical simulations of
isothermal turbulent fragmentation thus far have not succeeded in identifying a
fragment mass scale that is independent of the simulation resolution. Moreover,
the fluid equations for magnetized, self-gravitating, isothermal turbulence are
scale-free, and do not predict any characteristic mass. In this paper we show
that, although an isothermal self-gravitating flow does produce a CMF with a
mass scale imposed by the initial conditions, this scale changes as the parent
cloud evolves. In addition, the cores that form undergo further fragmentation
and after sufficient time forget about their initial conditions, yielding a
scale-free pure power-law distribution $\mathrm{d} N/\mathrm{d} M\propto
M^{-2}$ for the stellar IMF. We show that this problem can be alleviated by
introducing additional physics that provides a termination scale for the
cascade. Our candidate for such physics is a simple model for stellar radiation
feedback. Radiative heating, powered by accretion onto forming stars, arrests
the fragmentation cascade and imposes a characteristic mass scale that is
nearly independent of the time-evolution or initial conditions in the
star-forming cloud, and that agrees well with the peak of the observed IMF. In
contrast, models that introduce a stiff equation of state for denser clouds but
that do not explicitly include the effects of feedback do not yield an
invariant IMF.
