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

We investigate the observed correlation between the 2-10 keV X-ray luminosity (in unit of the Eddington luminosity; l(X) L-X/L-Edd) and the photon index (Gamma) 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) less than or similar to l(X) less than or similar to 10(-1). We find that Gamma is positively and negatively correlated with l(X) when l(X) greater than or similar to 10(-3) and 10(-65) less than or similar to l(X) less than or similar to 10(-3), respectively, while Gamma is nearly a constant when l(X) less than or similar to 10(-6.5). We explain the above correlation in the framework of a coupled hot accretion flow-jet model. The radio emission always comes 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.