Generalized Langevin equation description of the stochastic oscillations of general relativistic disks

TL;DR

This paper models the stochastic oscillations of relativistic accretion disks using a generalized Langevin equation, deriving observable luminosity variations and comparing them with astrophysical data.

Contribution

It introduces a novel application of the generalized Langevin equation to relativistic disks, incorporating retarded friction effects and fluctuation-dissipation theorems.

Findings

Derived explicit expressions for disk displacements, velocities, and luminosities.

Obtained the Power Spectral Distribution showing non-standard features.

Compared theoretical luminosity variations with observational data of a blazar.

Abstract

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. 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 of the luminosity it is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.