Correlation of time lag and photon index in GX 339-4

Context. Black hole transients, as a class, exhibit during their outbursts a correlation between the time lag of hard photons with respect to softer ones and the photon index of the hard X-ray power law. The correlation is not very tight and therefore it is necessary to examine it source by source. Aims. The objective of the present work is to investigate in detail the correlation between the time lag and the photon index in GX 3394, which is the best studied black hole transient. Methods. We have obtained RXTE energy spectra and light curves and have computed the photon index and the time lag of the 9-15 keV photons with respect to the 2-6 keV photons. The observations cover the first stages of the hard state, the pure hard state, and the hard-intermediate state. Results. We have found a tight correlation between time lag and photon index Gamma in the hard and hard-intermediate states. At low Gamma, the correlation is positive; it becomes negative at high Gamma. By assuming that the hard X-ray power-law index Gamma is produced by inverse Compton scattering of soft disk photons in the jet, we have reproduced the entire correlation by varying two parameters in the jet: the radius of the jet at its base R-0 and the Thomson optical depth along the jet tau. We have found that as the luminosity of the source increases, R-0 initially increases and then decreases. This behavior is expected in the context of the Cosmic Battery. Conclusions. Our jet model nicely explains the correlation with reasonable values of the parameters R-0 and tau. These parameters also correlate between themselves. As a further test of our model, we predict the break frequency in the radio spectrum as a function of the photon index during the rising part of an outburst.