Competitive Accretion and the IMF

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 $\gamma \approx -1.5$, for low-mass stars which accrue their mass in the gas dominated regime, and a steeper, $\gamma\approx -2.5$, 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.