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

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.Comment: 5 pages, accepted by MNRAS Letter

Error Estimates from Noise Samples for Iterative Algorithm in Shift-Invariant Signal Spaces

We consider error estimates of iterative algorithm in shift-invariant signal spaces. For the classical sampling and reconstruction algorithm, error estimate from its samples corrupted by white noises are widely studied, but the error analysis of noise with time jitter and iterative noise has not been given as much attention. In this paper, three types of error estimates are studied. In detail, we obtain the error estimate for reconstructing a signal from its noise samples, noise samples with time jitter, and iterative noise