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

TL;DR

This study explores the relationship between X-ray spectral slope and luminosity in black hole systems and AGNs, proposing a coupled accretion-jet model to explain observed correlations across different luminosity regimes.

Contribution

It introduces a comprehensive analysis of the $ ext{Γ}$-$l_X$ correlation in BHBs and AGNs, and proposes a coupled hot accretion flow and jet model to interpret the observations.

Findings

$ ext{Γ}$ correlates positively with $l_X$ above $10^{-3}$

$ ext{Γ}$ correlates negatively with $l_X$ between $10^{-6.5}$ and $10^{-3}$

$ ext{Γ}$ remains nearly constant below $10^{-6.5}$

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 ($\Gamma$) of the X-ray spectrum for both black hole X-ray binaries (BHBs) and active galactic nuclei (AGNs). We construct a large sample, with $10^{-9} < l_X < 10^{-1}$. We find that $\Gamma$ is positively and negatively correlated with $l_X$ when $l_X > 10^{-3}$ and $10^{-6.5} < l_X < 10^{-3}$ respectively, while $\Gamma$ 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.