A toy model for the X-ray spectral variability of active galactic nuclei

Abstract

Abstract Investigations into the long-term X-ray spectral variability of 10 active galactic nuclei (AGNs) revealed a positive spectral index–flux correlation for each object. An inner advection-dominated accretion flow (ADAF) may connect to a thin disc/corona at a certain transition radius. Both these structures are responsible for the hard X-ray emission in AGNs. The ADAF is hot and its X-ray spectrum is hard, while the corona above the disc is relatively cold and its X-ray spectrum is therefore soft. The radiation efficiency of the ADAF is usually much lower than that of the thin disc. An increase in the transition radius may lead to a decrease in the spectral index (i.e. a hard spectrum) and the X-ray luminosity even if the accretion rate is fixed, and a decrease of transition radius leads to an increase in spectral index. We propose that such X-ray variability is caused by a change in the transition radius. Our model calculations can reproduce the observed index–flux correlations, if the transition radius fluctuates around an equilibrium position and the radiation efficiency of ADAFs is ∼5 per cent of that for a thin disc. The average spectral index–Eddington ratio correlation for these ten AGNs sample can also be reproduced by our model calculations, if the equilibrium transition radius increases with decreasing mass accretion rate.