Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed st ellar mass spectrum for masses M* greater than or similar to 0.5 M-.. The m odel depends solely on the competitive accretion that occurs in stellar clu sters where each star's accretion rate depends on the local gas density and the square of the accretion radius. Zn a stellar cluster, there are two di fferent regimes depending on whether the gas or the stars dominate the grav itational potential. When the cluster is dominated by cold gas, the accreti on radius is given by a tidal-lobe radius. This occurs as the cluster colla pses towards a rho proportional to R-2 distribution. Accretion in this regi me results in a mass spectrum with an asymptotic Limit of gamma = -3/2 (whe re Salpeter is gamma = -2.35). Once the stars dominate the potential and ar e virialized, which occurs first in the cluster core, the accretion radius is the Bondi-Hoyle radius. The resultant mass spectrum has an asymptotic li mit of gamma = -2 with slightly steeper slopes (gamma approximate to -2.5) if the stars are already mass-segregated. Simulations of accretion on to cl usters containing 1000 stars show that, as expected, the low-mass stars acc umulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the ste llar-dominated phase. This results in a mass spectrum with a relatively sha llow gamma approximate to 3/2 power law for low-mass stars and a steeper po wer law for high-mass stars -2.5 less than or similar to gamma less than or equal to -2. This competitive accretion model also results in a mass-segre gated cluster.