Star formation through gravitational collapse and competitive accretion

Competitive accretion, a process to explain the origin of the IMF, occurs when stars in a common gravitational potential accrete from a distributed gaseous component. Stars located near the centre of the potential benefit from the gravitational attraction of the full potential and accrete at much higher rates than do isolated stars. We show that concerns recently raised on the efficiency of competitive accretion are incorrect as they use globally averaged properties which are inappropriate for the detailed physics of a forming stellar cluster. A full treatment requires a realistic treatment of the cluster potential, the distribution of turbulent velocities and gas densities. Accreting gas does not travel at the global virial velocity of the system due to the velocity-sizescale relation inherent in turbulent gas and due to the lower velocity dispersion of small-N clusters in which much of the accretion occurs. Accretion occurs due to the effect of the local potential in funneling gas down to the centre. Stars located in the gas-rich centres of such systems initially accrete from low relative velocity gas attaining larger masses before needing to accrete the higher velocity gas. Stars not in the centres of such potentials, or that enter the cluster later when the velocity dispersion is higher, do not accrete significantly and thus retain their low-masses. In competitive accretion, most stars do not continue to accrete significantly such that their masses are set from the fragmentation process. It is the few stars which continue to accrete that become higher-mass stars. Competitive accretion is therefore likely to be responsible for the formation of higher-mass stars and can explain the mass distribution, mass segregation and binary frequency of these stars. Global kinematics of competitive accretion models include large-scale mass infall, with mean inflow velocities of order ≈ 0.5 km/s at scales of 0.5 pc, but infall signatures are likely to be confused by the large tangential velocities and the velocity dispersion present. Finally, we discuss potential limitations of competitive accretion and conclude that competitive accretion is currently the most likely model for the origin of the high-mass end of the IMF.