Can Self Organized Critical Accretion Disks Generate a Log-normal
  Emission Variability in AGN?
  Active Galactic Nuclei (AGN), such as Seyfert galaxies, quasars, etc., show
light variations in all wavelength bands, with various amplitude and in many
time scales. The variations usually look erratic, not periodic nor purely
random. Many of these objects also show lognormal flux distribution and RMS -
flux relation and power law frequency distribution. So far, the lognormal flux
distribution of black hole objects is only observational facts without
satisfactory explanation about the physical mechanism producing such
distribution in the accretion disk. One of the most promising models based on
cellular automaton mechanism has been successful in reproducing PSD (Power
Spectral Density) of the observed objects but could not reproduce lognormal
flux distribution. Such distribution requires the existence of underlying
multiplicative process while the existing SOC models are based on additive
processes. A modified SOC model based on cellular automaton mechanism for
producing lognormal flux distribution is presented in this paper. The idea is
that the energy released in the avalanche and diffusion in the accretion disk
is not entirely emitted instantaneously as in the original cellular automaton
model. Some part of the energy is kept in the disk and thus increase its energy
content so that the next avalanche will be in higher energy condition and will
release more energy. The later an avalanche occurs, the more amount of energy
is emitted to the observers. This can provide multiplicative effects to the
flux and produces lognormal flux distribution.
