XMM–Newton X-ray spectra of the hard state black hole X-ray binaries (BHXRBs) SWIFT J1753.5?0127 and GX 339?4 show evidence for accretion disc blackbody emission, in addition to hard power laws. The soft and hard band power spectral densities (PSDs) of these sources demonstrate variability over a wide range of time-scales. However, on time-scales of tens of seconds, corresponding to the putative low-frequency Lorentzian in the PSD, there is additional power in the soft band. To interpret this behaviour, we introduce a new spectral analysis technique, the 'covariance spectrum', to disentangle the contribution of the X-ray spectral components to variations on different time-scales. We use this technique to show that the disc blackbody component varies on all time-scales, but varies more, relative to the power law, on longer time-scales. This behaviour explains the additional long-term variability seen in the soft band. Comparison of the blackbody and iron line normalizations seen in the covariance spectra in GX 339?4 implies that the short-term blackbody variations are driven by thermal reprocessing of the power-law continuum absorbed by the disc. However, since the amplitude of variable reflection is the same on long and short time-scales, we rule out reprocessing as the cause of the enhanced disc variability on long time-scales. Therefore, we conclude that the long time-scale blackbody variations are caused by instabilities in the disc itself, in contrast to the stable discs seen in BHXRB soft states. Our results provide the first observational evidence that the low-frequency Lorentzian feature present in the PSD is produced by the accretion disc.<br/><br/
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