Competitive accretion occurs when stars in a cluster accrete from a shared
reservoir of gas. The competition arises due to the relative attraction of
stars as a function of their mass and location in the cluster.
The low relative motions of the stars and gas in young, gas dominated
clusters results in a tidal limit to the accretion whereas in the stellar
dominated cluster cores, the high relative velocities results in Bondi-Hoyle
accretion.
The combination of these two accretion processes produces a two power-law IMF
with γ≈−1.5, for low-mass stars which accrue their mass in the
gas dominated regime, and a steeper, γ≈−2.5, IMF for higher-mass
stars that form in the core of a cluster. Simulations of the fragmentation and
formation of a stellar cluster show that the final stellar masses, and IMF, are
due to competitive accretion. Competitive accretion also naturally results in a
mass segregated cluster and in a direct correlation between the richness of a
cluster and the mass of the most massive star therein. The {\sl knee} where the
IMF slope changes occurs near the Jeans mass of the system.Comment: 6 pages, 5 figures to appear in the IMF@50, eds E. Corbelli, F.
Palla, and H. Zinnecke