Modelling the IDV Emissions of the BL Lac Objects with a Langevin Type Stochastic Differential Equation

Journal of Astrophysics and Astronomy (Impact Factor: 0.5). 06/2011; 32(1):189-192. DOI: 10.1007/s12036-011-9026-3
Source: arXiv

ABSTRACT In this paper, we introduce a simplified model for explaining the observations of optical intra-day variability (IDV) of the
BL Lac Objects. We assume that the source of the IDV are the stochastic oscillations of an accretion disk around a supermassive
black hole. The stochastic fluctuations on the vertical direction of the accretion disk are described by using a Langevin
type equation with a damping term and a random, white noise type force. Furthermore, preliminary numerical simulation results
are presented, which are based on the numerical analysis of the Langevin stochastic differential equation.

KeywordsLangevin type stochastic differential equation–BL Lac objects

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    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.
    Journal of Astrophysics and Astronomy 06/2013; · 0.50 Impact Factor
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    ABSTRACT: Based on a generalized Langevin equation, we consider a full general relativistic model to describe the vertical oscillations of particles in accretion disks around compact astrophysical objects, and calculate oscillating luminosity and power spectral density (PSD) of an accretion disk. The influences of the friction parameter ζ, spin parameter a* and mass M of the center compact object on the stochastic resonance (SR) in PSD curves are discussed. The results show that a large spin parameter a* can enhance the SR phenomenon, but the larger the ζ or M is, the weaker the SR phenomenon becomes. In addition, our simulated PSD curves of the output luminosity of stochastically oscillating disk have the same profile as the observed PSD of x-ray binaries, and the resonance peak in the PSD curve can interpret the quasi-periodic oscillations at the same time.
    Chinese Physics Letters 09/2013; 30(9):099801. · 0.92 Impact Factor
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    ABSTRACT: Observational data in the BVRI bands of the variable BL Lacertae Object S5 0716+714 is discussed from the point of view of its Power Spectral Distribution (PSD). A model of the type $P(f) = \beta f^{-1} [1 + (\frac{f} {\delta}) ^{\alpha -1}]^{-1} + \gamma $ is fitted to the data for four null hypothesis and the Bayesian $p$ parameter for the fits is calculated. Spectral slopes with values ranging from 1.083 to 2.65 are obtained, with medium values for each band of $\bar{\alpha}_B =2.028$, $\bar{\alpha}_V = 1.809$, $\bar{\alpha}_R = 1.932$ and $\bar{\alpha}_I = 1.54$ respectively. These values confirm conclusions of previous studies, namely that the source is turbulent. Two disk models, the standard prescription of the Shakura-Sunyaev disk and magnetized disks exhibiting MagnetoRotational Instability, were discussed. We found that it is unlikely that they explain this set of observational data.

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