Stochastic oscillations of general relativistic disks

TL;DR

This paper models the stochastic oscillations of relativistic accretion disks around compact objects using Langevin equations, incorporating external medium interactions, and analyzes their vertical oscillations in Schwarzschild and Kerr geometries.

Contribution

It introduces a relativistic Langevin framework for disk oscillations, including stochastic forces and viscous effects, and provides numerical analysis of vertical oscillations in black hole spacetimes.

Findings

Vertical displacements and luminosities are explicitly computed for Schwarzschild and Kerr disks.

Stochastic forces significantly influence disk oscillation dynamics.

The model captures the effects of external medium interactions on relativistic accretion disks.

Abstract

We analyze the general relativistic oscillations of thin accretion disks around compact astrophysical objects interacting with the surrounding medium through non-gravitational forces. The interaction with the external medium (a thermal bath) is modeled via a friction force, and a random force, respectively. The general equations describing the stochastically perturbed disks are derived by considering the perturbations of trajectories of the test particles in equatorial orbits, assumed to move along the geodesic lines. By taking into account the presence of a viscous dissipation and of a stochastic force we show that the dynamics of the stochastically perturbed disks can be formulated in terms of a general relativistic Langevin equation. The stochastic energy transport equation is also obtained. The vertical oscillations of the disks in the Schwarzschild and Kerr geometries are considered in detail, and they are analyzed by numerically integrating the corresponding Langevin equations. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases.