• 47 Tucanae
• action integrals
• globular cluster
• intermediate mass black hole
• stellar kinematics

This thesis addresses the question of the presence of an intermediate mass black hole (IMBH) at the center of the galactic globular cluster (GC) 47 Tucanae. IMBHs are defined as those black holes (BHs) with mass in the range between stellar BHs and super-massive BHs, and a firm evidence for their existence is so far lacking. GCs have been proposed as promising hosts for IMBHs formation, however, despite the numerous studies that tackled this problem, it is still challenging to confirm or definitely rule out whether IMBHs reside at the center of GCs or not. In this work I tackle, for the first time, the problem by means of dynamical models based on analytical distribution functions which depend on the action integrals. I used a set of proper motion measurements within the innermost 100 arcsecond from the center, obtained with the Hubble Space Telescope, supplemented with a stellar number density profile to constrain the external regions.
I implemented a star-by-star analysis that allowed us to constrain the full shape of the velocity distribution. We found that the model reproduces remarkably well both the kinematics and the density distribution of cluster stars, do not requiring an IMBH in its center. We put an upper limit, at the 99.8% level, on the BH mass of 1000 solar masses, which, up to date, is the tightest that has been ever put by a dynamical study.