Chaotic behavior in the accretion disk

The eccentric luminosity variation of quasars is still a mystery. Analytic results of this behavior ranged from multi-periodic behavior to a purely random process. Recently, we have used nonlinear time-series analysis to analyze the light curve of 3C 273 and found its eccentric behavior may be chaos [L. Liu, Chin. J. Astron. Astrophys. \textbf{6}, 663 (2006)]. This result induces us to look for some nonlinear mechanism to explain the eccentric luminosity variation. In this paper, we propose a simple non-linear accretion disk model and find it shows a kind of chaotic behavior under some circumstances. Then we compute the outburst energy $\triangle F$, defined as the difference of the maximum luminosity and the minimum luminosity, and the mean luminosity $<F>$. We find that $\triangle F\sim < F >^{\alpha}$ in the chaotic domain, where $\alpha\approx 1$. In this domain, we also find that $<F > \sim M^{0.5}$, where $M$ is the mass of central black hole. These results are confirmed by or compatible with some results from the observational data analysis [A. J. Pica and A. G. Smith, Astrophys. J. \textbf{272}, 11 (1983); M. Wold, M. S. Brotherton and Z. Shang, Mon. Not. R. Astron. Soc. \textbf{375}, 989 (2007)].