Interpreting the radio/X-ray correlation of black hole sources based on the accretion-jet model

Two types of correlations between the radio and X-ray luminosities ($L_R$ and $L_X$) have been found in black hole X-ray binaries. For some sources, they follow the original' type of correlation which is described by a single power-law. Later it was found that some other sources follow a different correlation consisting of three power-law branches, with each branch having different power-law indexes. In this work, we explain these two types of correlation under the coupled accretion--jet model. We attribute the difference between these two types of sources to the different value of viscosity parameter $\alpha$. One possible reason for different $\alpha$ is the different configuration of magnetic field in the accretion material coming from the companion stars. For the single power-law’ sources, their $\alpha$ is high; so their accretion is always in the mode of advection-dominated accretion flow (ADAF) for the whole range of X-ray luminosity. For those `hybrid power-law’ sources, the value of $\alpha$ is small so their accretion mode changes from an ADAF to a luminous hot accretion flow, and eventually to two-phase accretion as the accretion rate increases. Because the dependence of radiative efficiency on the mass accretion rate is different for these three accretion modes, different power-law indexes in the $L_R--L_X$ correlation are expected. Constraints on the ratio of the mass loss rate into the jet and the mass accretion rate in the accretion flow are obtained, which can be tested in future by radiative magnetohydrodynamic numerical simulations of jet formation.