A unified accretion-ejection paradigm for black hole X-ray binaries. VI. Radiative efficiency and radio-X-ray correlation during four outbursts from GX339-4

The spectral evolution of transient X-ray binaries can be reproduced by an interplay between two flows separated at a radius $R_J$: a standard accretion disk (SAD) in the outer parts and a jet-emitting disk (JED) in the inner parts. In the previous papers of this series, we recover the spectral evolution in both X-rays and radio for four outbursts of GX339-4 by playing independently with the two parameters: $R_J$ and the accretion rate $\dot{M}_{in}$. In this paper, we compare the time evolution of $R_J$ and $\dot{M}_{in}$ for the four outbursts. We show that despite the undeniable differences between the time evolution of each outburst, a unique pattern in the $\dot{M}_{in}-R_J$ plane seems to be followed by all cycles within the JED-SAD model. We call this pattern a fingerprint, and show that even the 'failed' outburst considered follows it. We also compute the radiative efficiency in X-rays during the cycles and consider its impact on the radio--X-ray correlation. Within the JED-SAD paradigm, we find that the accretion flow is always radiatively efficient in the hard states, with between $15\%$ and $40\%$ of the accretion power being radiated away at any given time. Moreover, we show that the radiative efficiency evolves with the accretion rate because of key changes in the JED thermal structure. These changes give birth to two different regimes with different radiative efficiencies: the thick disk and the slim disk. While the existence of these two regimes is intrinsically linked to the JED-SAD model, we show direct observational evidence of the presence of two different regimes using the evolution of the X-ray power-law spectral index, a model-independent estimate. We then argue that these two regimes could be the origin of the gap in X-ray luminosity in the hard state, the wiggles and different slopes seen in the radio--X-ray correlation, and even the existence of outliers.