Tracing the reverberation lag in the hard state of black hole X-ray binaries

We report results obtained from a systematic analysis of X-ray lags in a sample of black hole X-ray binaries, with the aim of assessing the presence of reverberation lags and studying their evolution during outburst. We used XMM-Newton and simultaneous RXTE observations to obtain broad-band energy coverage of both the disc and the hard X-ray Comptonization components. In most cases the detection of reverberation lags is hampered by low levels of variability signal-to-noise ratio (e.g. typically when the source is in a soft state) and/or short exposure times. The most detailed study was possible for GX 339-4 in the hard state, which allowed us to characterize the evolution of X-ray lags as a function of luminosity in a single source. Over all the sampled frequencies (~0.05-9 Hz) we observe the hard lags intrinsic to the power law component, already well-known from previous RXTE studies. The XMM-Newton soft X-ray response allows us to detail the disc variability. At low-frequencies (long time scales) the disc component always leads the power law component. On the other hand, a soft reverberation lag (ascribable to thermal reprocessing) is always detected at high-frequencies (short time scales). The intrinsic amplitude of the reverberation lag decreases as the source luminosity and the disc-fraction increase. This suggests that the distance between the X-ray source and the region of the optically-thick disc where reprocessing occurs, gradually decreases as GX 339-4 rises in luminosity through the hard state, possibly as a consequence of reduced disc truncation.