Correlation between the photon index and X-ray luminosity of black hole X-ray binaries and active galactic nuclei: observations and interpretation

Abstract

We investigate the observed correlation between the 2--10 keV X-ray luminosity (in unit of the Eddington luminosity; $l_X\equiv L_X/L_{Edd}$) and the photon index ($\hat{I}“$) of the X-ray spectrum for both black hole X-ray binaries (BHBs) and active galactic nuclei (AGNs). We construct a large sample, with $10^{-9}<l_X<10^{-1}$. We find that $\hat{I}“$ is positively and negatively correlated with $l_X$ when $l_X>10^{-3}$ and $10^{-6.5}<l_X<10^{-3}$ respectively, while $\hat{I}“$ is nearly a constant when $l_X<10^{-6.5}$. We explain the above correlation in the framework of a coupled hot accretion flow -- jet model. The radio emission always come from the jet while the X-ray emission comes from the accretion flow and jet when $l_X$ is above and below $10^{-6.5}$, respectively. More specifically, we assume that with the increase of mass accretion rate, the hot accretion flow develops into a clumpy and further a disc -- corona two-phase structure because of thermal instability. We argue that such kind of two-phase accretion flow can explain the observed positive correlation.

13 pages, 8 figures, accepted for publication in MNRAS