X-ray fluctuations from advection-dominated accretion disks with a critical behavior

A new hydrodynamic model for aperiodic X-ray fluctuations from black hole objects is presented. X-ray fluctuation is thought to originate from instabilities of the accretion disk around a black hole. We previously proposed the cellular automaton model based on the notion of self-organized criticality to describe the open, dissipative nature of a disk undergoing instabilities. Assuming that an avalanche was triggered when the mass density exceeded some critical value, we could reproduce the basic statistical features of X-ray variability with this model. As an independent inquiry, we also calculated the response of an axisymmetric, advection-dominated disk to thermal perturbations, demonstrating that it can easily produce an X-ray shot as is observed in X-ray fluctuations. In this paper, we couple these two different lines of study and calculate the time evolution of an advection-dominated disk with a critical behavior, namely, if surface density exceeds some critical value, we let viscosity increase. As a result, we succeed in producing 1/f-like fluctuations. We also find that the fluctuation properties depend upon the prescription of the critical condition. The present model predicts a constant slope in the decline part of the power spectral density (PSD), while f(break), the frequency separating the flat and decline parts of the PSD, changes according to variations in the size of the advection-dominated portions of the disk.