Different X-ray spectral evolution for black hole X-ray binaries in dual tracks of radio-X-ray correlation

Recently an `outliers' track of radio-X-ray correlation was found, which is much steeper than the former universal correlation, where dual tracks were speculated to be triggered by different accretion processes. In this work, we test this issue by exploring hard X-ray spectral evolution in four black-hole X-ray binaries (XRBs) with multiple, quasi-simultaneous radio and X-ray observations. Firstly, we find that hard X-ray photon indices, $\Gamma$, are anti- and positively correlated to X-ray fluxes when the X-ray flux, $F_{\rm 3-9keV}$, is below and above a critical flux, $F_{\rm X,crit}$, which are consistent with prediction of advection dominated accretion flow (ADAF) and disk-corona model respectively. Secondly and most importantly, we find that the radio-X-ray correlations are also clearly different when the X-ray fluxes are higher and lower than the critical flux that defined by X-ray spectral evolution. The data points with $F_{\rm 3-9keV}\gtrsim F_{\rm X,crit}$ have a steeper radio-X-ray correlation ($F_{\rm X}\propto F_{\rm R}^{b}$ and $b\sim 1.1-1.4$), which roughly form the `outliers' track. However, the data points with anti-correlation of $\Gamma-F_{\rm 3-9keV}$ either stay in the universal track with $b\sim0.61$ or stay in transition track (from the universal to `outliers' tracks or vice versa). Therefore, our results support that the universal and `outliers' tracks of radio-X-ray correlations are regulated by radiatively inefficient and radiatively efficient accretion model respectively.