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

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.

arXiv comment17 pages, 10 figures, accepted for publication in EPJC

References in corpus (18)

• The flux-dependent amplitude of broadband noise variability in X-ray binaries and active galaxies
• Relativistic Brownian Motion
• A Bayesian test for periodic signals in red noise
• The optical microvariability and spectral changes of the BL Lacertae object S5 0716+714
• Theory of the Relativistic Brownian Motion. The (1+1)-Dimensional Case
• Theory of Relativistic Brownian Motion: The (1+3)-Dimensional Case
• Enhanced activity of massive black holes by stellar capture assisted by a self-gravitating accretion disc
• Axisymmetric General Relativistic Simulations of the Accretion-Induced Collapse of White Dwarfs
• The Global-Normal Disk Oscillations and the Persistent Low Frequency QPO in X-ray Binaries
• Tidal Capture of Stars by Intermediate-Mass Black Holes
• Intraday Variability in Northern Hemisphere Radio Sources
• Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: Dynamical equivalence and consequences
• Stochastic oscillations of general relativistic disks
• Periastron shift in Weyl class spacetimes
• Modeling the IDV emissions of the BL Lac Objects with a Langevin type stochastic differential equation
• Power Spectral Distribution of the BL Lacertae Object S5 0716+714
• Fractal dimension and thermodynamic fluctuation properties of IDV light curves
• Rms-flux relation in the optical fast variability data of BL Lacertae object S5 0716+714

Cited by in corpus (5)

• Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect
• Bose-Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials
• Electromagnetic radiation of charged particles in stochastic motion
• Spacetime geometry fluctuations and geodesic deviation
• The Stochastic-Dissipative Störmer Problem-Trajectories and Radiation Patterns