What Physics Determines the Peak of the IMF? Insights from the Structure
  of Cores in Radiation-Magnetohydrodynamic Simulations
  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 timescale, the opacity limit for fragmentation, at $\sim 0.01$
$M_\odot$. 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, $\sim 0.01$ $M_\odot$, 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 $\sim 0.01$ $M_\odot$ 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 $\sim 0.2$ $M_\odot$, 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 $\sim 0.2$ $M_\odot$.
