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

TL;DR

This paper presents a toy model explaining the X-ray spectral variability in active galactic nuclei through fluctuations in the transition radius between an ADAF and a thin disc, successfully reproducing observed correlations.

Contribution

It introduces a simplified model linking transition radius fluctuations to spectral variability, aligning with observed index-flux and index-Eddington ratio correlations in AGN.

Findings

Model reproduces observed spectral index-flux correlation.

Transition radius fluctuations explain spectral variability.

Average spectral index correlates with Eddington ratio.

Abstract

The long term X-ray spectral variability of ten active galactic nuclei (AGN) shows a positive spectral index-flux correlation for each object (Sobolewska & Papadakis 2009). An inner advection dominated accretion flow (ADAF) may connect to a thin disc/corona at a certain transition radius, which are responsible for hard X-ray emission in AGN. 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. The increase of the transition radius may lead to decreases of the spectral index (i.e., a hard spectrum) and the X-ray luminosity even if the accretion rate is fixed, and vice versa. We propose that such X-ray variability is caused by the change of 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 {\guillemotright} 5 per cent of that for a thin disc. The average spectral index-Eddington ratio correlation in the AGN sample can also be reproduced by our model calculations, if the equilibrium transition radius increases with decreasing mass accretion rate.