Keplerian Ringed-Disk Viscous-Diffusive Evolution and Combined Independent General Relativistic Evolutions

We investigate the evolution of a set of viscous rings, solving a diffusion-like evolution equation in the (Keplerian disk) Newtonian regime. The Lynden-Bell and Pringle approach for a single disk regime is applied to a disk with a ring profile mimicking a set of orbiting viscous rings. We discuss the time evolution of the disk, adopting different initial wavy (ringed) density profiles. Four different stages of the ring-cluster evolution are distinguished. In the second part of this analysis, we also explore the general relativistic framework by investigating the time evolution of composed systems of general relativistic co-rotating and counter-rotating equatorial disks orbiting a central Kerr black hole for faster spinning and slowly spinning black holes. In the sideline of this analysis, we consider a modified viscosity prescription mimicking an effective viscosity in the general relativistic ring interspace acting in the early phases of the rings’ evolutions, exploring the double system dynamics. Each ring of the separate sequence spreads inside the cluster modifying its inner structure following the rings merging. As the original ringed structure disappears, a single disk appears. The final configuration has a (well-defined) density peak, and its evolution turns in the final stages are dominated by its activity at the inner edge.