Rapid mass segregation in small stellar clusters

Abstract

In this paper we focus our attention on small-to-intermediate $N$-body systems that are, initially, distributed uniformly in space and dynamically ‘cool’ (virial ratios $Q=2T/|\varOmega|$ below $\sim0.3$). In this work, we study the mass segregation that emerges after the initial violent dynamical evolution. At this scope, we ran a set of high precision $N$-body simulations of isolated clusters by means of HiGPUs, our direct summation $N$-body code. After the collapse, the system shows a clear mass segregation. This (quick) mass segregation occurs in two phases: the first shows up in clumps originated by sub-fragmentation before the deep overall collapse; this segregation is partly erased during the deep collapse to re-emerge, abruptly, during the second phase, that follows the first bounce of the system. In this second stage, the proper clock to measure the rate of segregation is the dynamical time after virialization, which (for cold and cool systems) may be significantly different from the crossing time evaluated from initial conditions. This result is obtained for isolated clusters composed of stars of two different masses (in the ratio $m_{h}/m_{l}=2$), at varying their number ratio, and is confirmed also in presence of a massive central object (simulating a black hole of stellar size). Actually, in stellar systems starting their dynamical evolution from cool conditions, the fast mass segregation adds to the following, slow, secular segregation which is collisionally induced. The violent mass segregation is an effect persistent over the whole range of $N$ ($128 \leq N \leq1\mbox{,}024$) investigated, and is an interesting feature on the astronomical-observational side, too. The semi-steady state reached after virialization corresponds to a mass segregated distribution function rather than that of equipartition of kinetic energy per unit mass as it should result from violent relaxation.