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 Strings and Quantum Spectral Problems

We consider certain quantum spectral problems appearing in the study of local Calabi-Yau geometries. The quantum spectrum can be computed by the Bohr-Sommerfeld quantization condition for a period integral. For the case of small Planck constant, the periods are computed perturbatively by deformation of the Omega background parameters in the Nekrasov-Shatashvili limit. We compare the calculations with the results from the standard perturbation theory for the quantum Hamiltonian. There have been proposals in the literature for the non-perturbative contributions based on singularity cancellation with the perturbative contributions. We compute the quantum spectrum numerically with some high precisions for many cases of Planck constant. We find that there are also some higher order non-singular non-perturbative contributions, which are not captured by the singularity cancellation mechanism. We fix the first few orders formulas of such corrections for some well known local Calabi-Yau models.Comment: 47 pages, 3 figures. v2: journal version, typos correcte