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

Topological phase transition based on the attractive Hubbard model

We theoretically investigate the effect of an attractive on-site interaction on the two-band magnetic Dirac fermion model based on a square lattice system. When the attractive fermion interaction is taken into account by the mean-field approximation, a phase diagram is obtained. It is found that a quantum phase transition from a band insulator state to quantum anomalous Hall state occurs with increased attractive interaction. For an existing quantum anomalous Hall state, the attractive interaction enlarges its nontrivial band gap and makes the topological edge states more localized, which protects the transport of linear-dispersive edge states against finite-size and further disorder effects.Comment: 5 pages, 4 figure