Chaotic behavior in the accretion disk

TL;DR

This paper introduces a nonlinear accretion disk model that exhibits chaotic behavior, explaining eccentric luminosity variations in quasars and aligning with observational data.

Contribution

The paper presents a simple nonlinear accretion disk model demonstrating chaos, and establishes relationships between outburst energy, mean luminosity, and black hole mass.

Findings

Chaotic behavior observed in the model under certain conditions.

Outburst energy scales linearly with mean luminosity in the chaotic domain.

Mean luminosity correlates with black hole mass as <F> ~ M^{0.5}.

Abstract

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)].