  Massive stars influence their surroundings through radiation, winds, and
supernova explosions far out of proportion to their small numbers. However, the
physical processes that initiate and govern the birth of massive stars remain
poorly understood. Two widely discussed models are monolithic collapse of
molecular cloud cores and competitive accretion. To learn more about massive
star formation, we perform simulations of the collapse of rotating, massive,
cloud cores including radiative heating by both non-ionizing and ionizing
radiation using the FLASH adaptive mesh refinement code. These simulations show
fragmentation from gravitational instability in the enormously dense accretion
flows required to build up massive stars. Secondary stars form rapidly in these
flows and accrete mass that would have otherwise been consumed by the massive
star in the center, in a process that we term fragmentation-induced starvation.
This explains why massive stars are usually found as members of high-order
stellar systems that themselves belong to large clusters containing stars of
all masses. The radiative heating does not prevent fragmentation, but does lead
to a higher Jeans mass, resulting in fewer and more massive stars than would
form without the heating. This mechanism reproduces the observed relation
between the total stellar mass in the cluster and the mass of the largest star.
It predicts strong clumping and filamentary structure in the center of
collapsing cores, as has recently been observed. We speculate that a similar
mechanism will act during primordial star formation.
