Notes on the general relativistic viscous ringed disk evolution

Abstract

Abstract A ringed accretion disk (RAD) models a cluster of axi-symmetric co-rotating and/or counter-rotating tori orbiting in the equatorial plane of a central Kerr super-massive Black Hole. We discuss the time evolution of such a ringed disk within the general relativity framework. Our analysis presents a study of the evolving RAD properties using a thin-disk scheme and solving a diffusion-like evolution equation for a RAD in the Kerr spacetime. In the first stage of evolution there is the inter–disk interaction where the individual rings spread inwardly and outwardly, levelling the structure and forming a single distribution with maximum density determined by the initial spread of the component rings. Timescales are dependent on viscosity prescriptions. The early time luminosity, dominated by the dynamics of the inner ringed structure, shows a clear mark of the inner ringed structure. The RAD eventually reaches a single disk phase, building accretion to the inner edge regulated by the inner edge boundary conditions. The late–time luminosity associated to the ringed disk follows a power law decline for the final single disk. In the sideline of this analysis we also considered a modified prescription mimicking an effective turbulent viscosity in the early phases of the rings evolutions.