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; lX ≡ LX/LEdd) and the photon index (G{cyrillic}) 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 ≲ lX ≲ 10-1. We find that G{cyrillic} is positively and negatively correlated with lX when lX ≳ 10-3 and 10-6.5 ≲ lX ≲ 10-3, respectively, while G{cyrillic} is nearly a constant when lX ≲ 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 lX 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.