Radiative efficiency of hot accretion flow and the radio/X-ray correlation in X-ray binaries

Significant progresses have been made since the discovery of hot accretion flow, a theory successfully applied to the low-luminosity active galactic nuclei (LLAGNs) and black hole (BH) X-ray binaries (BHBs) in their hard states. Motivated by these updates, we re-investigate the radiative efficiency of hot accretion flow. We find that, the brightest regime of hot accretion flow shows a distinctive property, i.e. it has a constant efficiency independent of accretion rates, similar to the standard thin disk. For less bright regime, the efficiency has a steep positive correlation with the accretion rate, while for faint regime typical of advection-dominated accretion flow, the correlation is shadower. This result can naturally explain the observed two distinctive correlations between radio and X-ray luminosities in black hole X-ray binaries. The key difference in systems with distinctive correlations could be the viscous parameter, which determines the critical luminosity of different accretion modes.