The flux-dependent amplitude of broadband noise variability in X-ray binaries and active galaxies

Standard shot-noise models, which seek to explain the broadband noise variability that characterizes the X-ray light curves of X-ray binaries and active galaxies, predict that the power spectrum of the X-ray light curve is stationary (i.e. constant amplitude and shape) on short time-scales. We show that the broadband noise power spectra of the black hole candidate Cyg X-1 and the accreting millisecond pulsar SAX J1808.4−3658 are intrinsically non-stationary, in that rms variability scales linearly with flux. Flux-selected power spectra confirm that this effect is due to changes in power-spectral amplitude and not shape. The light curves of three Seyfert galaxies are also consistent with a linear relationship between rms variability and flux, suggesting that it is an intrinsic feature of the broadband noise variability in compact accreting systems over more than six decades of central object mass. The rms variability responds to flux variations on all measured time-scales, raising fundamental difficulties for shot-noise models which seek to explain this result by invoking variations in the shot parameters. We suggest that models should be explored where the longest time-scale variations are fundamental and precede the variations on shorter time-scales. Possible models which can explain the linear rms-flux relation include the fractal break-up of large coronal flares, or the propagation of fluctuations in mass accretion rate through the accretion disc. The linear relationship between rms variability and flux in Cyg X-1 and SAX J1808.4−3658 is offset on the flux axis, suggesting the presence of a second, constant-flux component to the light curve which contributes ∼25 per cent of the total flux. The spectrum of this constant component is similar to the total spectrum, suggesting that it may correspond to quiet, non-varying regions in the X-ray emitting corona.