Stochastical variability in accretion discs

The short-term variability of active galactic nuclei is often being linked with a presence of hot spots residing on the surface of an accretion disc. We apply the theory of random point processes to model the observed signal from an ensemble of randomly generated spots and to reproduce typical features that are found by fourier-analysing X-ray lightcurves from galactic centres.

Theory of random processes provides a mathematical tool to describe the fluctuating signal from accreting sources, such as active galactic nuclei and Galactic black holes observed in X-rays. These objects exhibit featureless variability, which appears on different timescales and is thought to originate from an accretion disc.

In our research, we study a general framework with the focus on statistical approach, which permits semi-analytical determination of the expected power spectral density (PSD) of the resulting lightcurves. Fluctuations of the signal are assumed to be governed by the Poisson or by the Hawkes processes. The latter one represents an avalanche mechanism and seems to be suggested by the observed form of the power spectrum. We thus investigate how the local  processes generating the spots and flares on the disc affect the power spectrum of the outgoing radiation. We include general relativity effects shaping the signal on its propagation to a distant observer.

As a case study, we analyse a `spotted' accretion disc lightcurves for a range of parameters. The asymptotic slopes of PSD are 0 at low frequencies and they tend to -2 at high frequencies, usually with a  single frequency break. More complex, two-peak solutions also occur; for example, a doubly-broken power law profile. The amplitude of the peaks and their frequency difference depend on the inherent timescales of the model.