On the collapse and violent relaxation of protoglobular clusters

During the formation of stellar systems such as globular clusters, low-mass subcondensations which eventually form stars must retain a geometric size throughout the collapse process that is small compared to the characteristic distance separating them. If the local velocity dispersion of the subcondensations is small, the overall dimension of the system can decrease substantially before reaching a dynamical equilibrium state. The maximum collapse factor is deduced by examining the growth of the velocity dispersion and the spread in arrival times at the origin caused by local and global fluctuations. It is shown, analytically as well as in a series of N-body simulations, that the maximum reduction in the characteristic dimension of a system of N fragments with an initial homogeneous distribution subject to N exp 1/2 fluctuations is proportional to N exp 1/3. Direct physical collisions between low-mass subcondensations are therefore unlikely to occur in protoglobular clusters. The results are discussed in the context of fragmentation and violent relaxation.