  There are now two dominant models of how stars form: gravitational collapse
theory holds that star-forming molecular clumps, typically hundreds to
thousands of solar masses in mass, fragment into gaseous cores that
subsequently collapse to make individual stars or small multiple systems. In
contrast, competitive accretion theory suggests that at birth all stars are
much smaller than the typical stellar mass (~0.5 solar masses), and that final
stellar masses are determined by the subsequent accretion of unbound gas from
the clump. Competitive accretion models explain brown dwarfs and free-floating
planets as protostars ejected from star-forming clumps before accreting much
mass, predicting that they should lack disks, have high velocity dispersions,
and form more frequently in denser clumps. They also predict that mean stellar
mass should vary within the Galaxy. Here we derive a simple estimate for the
rate of competitive accretion as a function of the star-forming environment,
based partly on simulations, and determine in what types of environments
competitive accretion can occur. We show that no observed star-forming region
produces significant competitive accretion, and that simulations that show
competitive accretion do so because their properties differ from those
determined by observation. Our result shows that stars form by gravitational
collapse, and explains why observations have failed to confirm predictions of
the competitive accretion scenario.
