On the formation of compact, massive subsystems in stellar clusters and its relation with intermediate-mass black holes

During their evolution, star clusters undergo mass segregation, by which the orbits of the most massive stars shrink, while the lighter stars move outwards from the cluster centre. In this context, recent observations and dynamical modelling of several galactic and extragalactic globular clusters (GCs) suggest that most of them show, close to their centre, an overabundance of mass whose nature is still matter of debate. For instance, many works show that orbitally segregated stars may collide with each other in a runaway fashion, leading to the formation of a very massive star or an intermediate-mass black hole (IMBH) with a mass comparable to the observed mass excess. On the other hand, segregated stars can form a dense system if the IMBH formation fails. In this paper we study the early formation phase of a dense, massive subsystem (MSS) in several GCs models using a recently developed semi-analytical treatment of the mass segregation process. In order to investigate how the MSS properties depend on the host cluster properties, we varied initial mass function (IMF), total mass, spatial distribution and metallicity of our models. Our results show how the IMF contributes to determine the final mass of the MSS, while the metallicity and the spatial distribution play a minor role. The method presented in this paper allowed us to provide scaling relations that connect the MSS mass and the host cluster mass in agreement with the observed correlation. In order to follow the early formation stage of the MSSs and improve our statistical results, we performed several N-body simulations of stellar clusters with masses between 103 and 2 × 105 M☉....