The most stringent upper limit from dynamical models on the mass of a central black hole in 47 Tucanae

Globular clusters (GCs) were proposed as promising sites for discovering intermediate-mass black holes (IMBHs), possibly providing crucial insights into the formation and evolution of these elusive objects. The Galactic GC 47 Tucanae (also known as NGC 104) has been suggested as a potential IMBH host, but, previous studies have yielded conflicting results. We, therefore, present self-consistent dynamical models based on distribution functions (DFs) that depend on action integrals to assess the presence (or absence) of an IMBH in 47 Tucanae. Leveraging state-of-the-art Multi Unit Spectroscopic Explorer and Hubble Space Telescope data, we analyzed the three-dimensional (3D) kinematics of the cluster's central regions, fitting individual star velocities down to the sub-arcsec scale (approximately $10^{-2}$ pc). According to our analysis, the inner kinematics of 47 Tucanae is incompatible with a central BH more massive than 578 M$_\odot$ (at $3\sigma$). This is the most stringent upper limit on the mass of a putative IMBH in 47 Tucanae that has been put by any dynamical study.