Stellar Density Profile and Central Black Hole Mass in Globular Clusters

One of the most puzzling open issues in modern astrophysics is the paucity of evidence for the existence of intermediate-mass black holes (IMBHs), which lie in the mass range between 100 and 10,000 solar masses. Some of the best candidates for hosting them, the globular clusters (GCs), have been the subjects of many observational studies. Nonetheless, only very debated IMBH detections have been made inside them, so far. This thesis studies spherical, isotropic, one-component models for GCs with central IMBHs. The phase-space consistency of these models can be easily assessed, as the formula to recover their distribution function (DF) from a given density profile is known. As a compelling consequence, one can say which density profiles are incompatible with a central black hole (BH) of a given mass for inconsistency reasons, if the velocity distribution is isotropic. This can help rule out some GCs as possible hosts of IMBHs. I explored several models of this kind, using not only direct computations of the DF, but also some analytic consistency conditions. I show that isotropic γ-models with γ≥1/2 are consistent, while those with γ<1/2 are not, independently of the BH mass, confirming previous findings. In addition, Sérsic models with Sérsic index n<2, Einasto models, Plummer models and King models are found to be inconsistent when they are isotropic and a BH is present. On the contrary, isotropic Sérsic models with n≥2 are consistent for all BH masses. I constructed models with outer King profiles and an inner r^(-7/4) cusp, whose consistency depends on the cusp’s extent and the BH mass. Identifying those with the smallest cusp to prevent inconsistency as a function of the BH-to-stellar mass ratio, I argue that these models may be used to exclude the presence of IMBHs more massive than about 0.5% of the host cluster’s mass in the closest and most massive systems. This work might pave the way for future techniques to exclude the presence of IMBHs in GCs.