Looking for intermediate mass black holes in globular clusters using action-based dynamical models

The aim of this project is to study the structural and kinematic properties of globular clusters (GCs) by means of novel dynamical models based on analytic distribution functions (DFs) depending on the action integrals. In particular, we focus on the open question of presence of intermediate mass black holes (IMBHs) at the center of these systems. The existence of IMBHs is still controversial, due to many observational issues and to dynamical processes resembling the observable effects of an IMBH. In this Thesis, we use action-based DFs f(J) to produce dynamical models of simulated observations of GCs (mocks) by the 5-th Gaia Challenge. The analytic f(J) DF we use is the one introduced by Pascale et al. (2018). Dealing with mocks rather than real GCs allows us to test the efficiency of our models in constraining the existence of an IMBH in an ideal GC of known parameters. We selected 4 mock GCs, which differ in the number of stars and in the mass of the IMBH. For each mock we compute the stellar projected number density and line-of-sight velocity dispersion profiles. We compare them with the ones derived from the DF-based models using the software package AGAMA (Vasiliev, 2019) and we infer best fit values and confidence intervals of the free parameters, including the BH-to-stellar mass fraction muBH, to be compared to the known input values of the mock. Our results show that the true value of muBH falls within the 1s (=1sigma) confidence level for the mocks with a total number of stars N=1d3 and within the 2s for N=1d4. In the case of the studied mocks, except for the mock with N=1d4 and muBH=0.01, the models without IMBH are within such confidence levels, thus we can only put upper limits on the muBH of such mocks. The isotropic velocity distribution of the mocks is reproduced within 1s in the case of muBH=0.001 and within 3s when muBH=0.01. The true total mass of the system M_true=1d6 Msun falls within 1s in case of N=1d4 and within 2s for the mocks with N=1d3.