  Star formation generally proceeds inside-out, with overdense regions inside
protostellar cores collapsing rapidly and progressively less dense regions
following later. Consequently, a small protostar will form early in the
evolution of a core, and collapsing material will fall to the protostellar
surface and radiate away its gravitational potential energy. The resulting
accretion luminosity will heat the core and may substantially affect the
process of fragmentation. This is of particular interest for massive cores
that, at their initial temperatures, have masses much greater than a thermal
Jeans mass and thus might be expected to fragment into many stars during
collapse. Here I show that accretion luminosity can heat the inner parts of a
core to >100 K very early in the star formation process, and that this in turn
strongly suppresses fragmentation. This has implications for a number of
outstanding problems in star formation, including the mechanism of massive star
formation, the origin of the stellar initial mass function and its relationship
to the core mass function, the demographics of massive binaries, and the
equation of state in star-forming gas.
