Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

TL;DR

This paper models the stochastic oscillations of relativistic accretion disks using a generalized Langevin equation with colored noise, revealing how memory effects influence disk dynamics and variability, with potential implications for understanding AGN variability.

Contribution

It introduces a novel approach using a generalized Langevin equation with colored noise to describe accretion disk oscillations, incorporating memory effects and analyzing their impact on disk behavior.

Findings

Memory effects alter disk response to external perturbations.

Vertical displacements and luminosities are explicitly computed for Schwarzschild and Kerr black holes.

The model suggests stochastic disk instabilities could explain AGN variability features.

Abstract

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise, which accounts for the general memory and retarded effects of the frictional force, and on the fluctuation-dissipation theorem. The presence of the memory effects influences the response of the disk to external random interactions, and modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution (PSD) of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the Intra Day Variability (IDV) of the Active Galactic Nuclei (AGN) may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.