Angular Velocity Perturbations Inducing the Papaloizou-Pringle Instability and QPOs in the Torus around the Black Hole

A numerical study of the dynamic of the nonselfgravitating, unmagnetized, nonaxisymmetric, and rotating the torus around the non-rotating black hole is presented. We investigate the instability of the rotating torus subject to perturbations presented by increasing or decreasing the angular velocity of the stable torus. We have done, for the first time, an extensive analysis of the torus dynamic response to the perturbation of the angular velocity of the stable torus. We show how the high, moderate, and low values of the perturbations affect the torus dynamic and help us to understand the properties of the instability and Quasi-Periodic Oscillation (QPO). Our numerical simulations indicate the presence of Papaloizou-Pringle instability (PPI) with global m=1 mode and QPOs for the moderate and lower values of the perturbations on the angular velocity of the stable torus. Furthermore, with the lower values of the perturbations, the torus can lead to a wiggling initially and then PPI is produced in it. Finally, the matter of the torus would be dissipated due to the presence of a strong torque.