Accretion-driven core collapse and the collisional formation of massive stars

We consider the conditions required for a cluster core to shrink, by adiabatic accretion of gas from the surrounding cluster, to densities such that stellar collisions are a likely outcome. We show that the maximum densities attained, and hence the viability of collisions, depend oil the balance between core shrinkage (driven by accretion) and core puffing up (driven by relaxation effects). The expected number of collisions scales as N-core(5/3) (v) over tilde (2), where N-core is the number of stars in the cluster core and D is the free-fall velocity of the parent Cluster (gas reservoir). Thus, whereas collisions are very unlikely in a relatively low-mass, low-internal-velocity system such as the Orion Nebula Cluster, they become considerably more important at the mass and velocity scales characteristic of globular clusters. Thus, stellar collisions in response to accretion-induced core shrinkage remain a viable prospect in more massive clusters, and may contribute to the production of intermediate-mass black holes ill these systems.