Article

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

(Impact Factor: 0.71). 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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Available from: Tiberiu Harko, Feb 25, 2014
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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.
Full-text · Article · Jan 2012