Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M∗≳0.5 M ⊙ . The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal‐lobe radius. This occurs as the cluster collapses towards a ρ ∝ R −2 distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ=−3/2 (where Salpeter is γ=−2.35) . Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ=−2 with slightly steeper slopes (γ≈−2.5) if the stars are already mass‐segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low‐mass stars accumulate the majority of their masses during the gas‐dominated phase whereas the high‐mass stars accumulate the majority of their masses during the stellar‐dominated phase. This results in a mass spectrum with a relatively shallow γ≈3/2 power law for low‐mass stars and a steeper power law for high‐mass stars −2.5≲γ≤−2 . This competitive accretion model also results in a mass‐segregated cluster.