We use the XMM–Newton EPIC‐pn instrument in timing mode to extend spectral time‐lag studies of hard state black hole X‐ray binaries into the soft X‐ray band. We show that variations of the disc blackbody emission substantially lead variations in the power‐law emission, by tenths of a second on variability time‐scales of seconds or longer. The large lags cannot be explained by Compton scattering but are consistent with time delays due to viscous propagation of mass accretion fluctuations in the disc. However, on time‐scales less than a second the disc lags the power‐law variations by a few milliseconds, consistent with the disc variations being dominated by X‐ray heating by the power law, with the short lag corresponding to the light traveltime between the power‐law emitting region and the disc. Our results indicate that instabilities in the accretion disc are responsible for continuum variability on time‐scales of seconds or longer and probably also on shorter time‐scales.

Recent XMM-Newton studies of X-ray variability in the hard states of black hole X-ray binaries (BHXRBs) indicate that the variability is generated in the 'standard' optically thick accretion disc that is responsible for the multi-colour blackbody emission. The variability originates in the disc as mass-accretion fluctuations and propagates through the disc to 'light up' inner disc regions, eventually modulating the power-law emission that is produced relatively centrally. Both the covariance spectra and time-lags that cover the soft bands strongly support this scenario.Here, we present a comparative spectral-timing study of XMM-Newton data from the BHXRB SWIFT J1753.5−0127 in a bright 2009 hard state with that from the significantly fainter 2006 hard state to show for the first time the change in disc spectral-timing properties associated with a global increase in both the accretion rate and the relative contribution of the disc emission to the bolometric luminosity.We show that, although there is strong evidence for intrinsic disc variability in the more luminous hard state, the disc variability amplitude is suppressed relative to that of the power-law emission, which contrasts with the behaviour at lower luminosities where the disc variability is slightly enhanced when compared with the power-law variations. Furthermore, in the higher luminosity data the disc variability below 0.6 keV becomes incoherent with the power-law and higher energy disc emission at frequencies below 0.5 Hz, in contrast with the coherent variations seen in the 2006 data. We explain these differences and the associated complex lags in the 2009 data in terms of the fluctuating disc model, where the increase in accretion rate seen in 2009 leads to more pronounced and extended disc emission. If the variable signals are generated at small radii in the disc, the variability of disc emission can be naturally suppressed by the fraction of unmodulated disc emission arising from larger radii. Furthermore, the drop in coherence can be produced by disc accretion fluctuations arising at larger radii which are viscously damped and hence unable to propagate to the inner, power-law emitting region.

The X‐ray variations of hard state black hole X‐ray binaries above 2 keV show ‘hard lags’, in that the variations at harder energies follow variations at softer energies, with a time lag τ depending on frequency ν approximately as τ∝ν−0.7. Several models have so far been proposed to explain this time delay, including fluctuations propagating through an accretion flow, spectral variations during coronal flares, Comptonization in the extended hot corona or a jet, or time delays due to large‐scale reflection from the accretion disc. In principle, these models can be used to predict the shape of the energy spectrum as well as the frequency dependence of the time lags, through the construction of energy‐dependent response functions which map the emission as a function of time delay in the system. Here we use this approach to test a simple reflection model for the frequency‐dependent lags seen in the hard state of GX 339−4, by simultaneously fitting the model to the frequency‐dependent lags and energy spectrum measured by XMM–Newton in 2004 and 2009. Our model cannot simultaneously fit both the lag and spectral data, since the relatively large lags require an extremely flared disc which subtends a large solid angle to the continuum at large radii, in disagreement with the observed Fe Kα emission. Therefore, we consider it more likely that the lags >2 keV are caused by propagation effects in the accretion flow, possibly related to the accretion disc fluctuations which have been observed previously.