A jet model for Galactic black-hole X-ray sources: The correlation between cutoff energy and phase lag

Context. Galactic black-hole X-ray binaries emit a compact, optically thick, mildy relativistic radio jet when they are in the hard and hard-intermediate states, that is, typically at the beginning and the end of an X-ray outburst. In a series of papers, we have developed a jet model and have shown through Monte Carlo simulations that our model can explain many observational results. Aims. In this work, we investigate one more constraining relationship between the cutoff energy and the phase lag during the early stages of an X-ray outburst of the black-hole X-ray binary GX 339-4: the cutoff energy decreases while the phase lag increases during the brightening of the hard state. Methods. We performed Monte Carlo simulations of the Compton upscattering of soft accretion-disk photons in the jet and computed the phase lag between soft and hard photons and the cutoff energy of the resulting high-energy power law. Results. We demonstrate that our jet model naturally explains the above correlation, with a minor modification consisting of introducing an acceleration zone at the base of the jet. Conclusions. The observed correlation between the cutoff energy and the phase lag in the black-hole binary GX 339-4 suggests that the lags are produced by the hard component. Here we show that this correlation arises naturally if Comptonization in the jet produces these two quantities.