A physical model for the spectral-timing properties of accreting black holes

We develop new techniques to deconvolve the radial structure of the X-ray emission region in the bright low/hard state of the black hole Cygnus X-1 using both spectral and timing data in the 3-35 keV range. The spectrum at these energies is dominated by Comptonization rather than the disc, but there is a complex pattern in the time lags between different energy bands and differences in the normalization and shape in the power spectra of these bands, which clearly shows that the Comptonization is not produced from a single, homogeneous region. We use a physically based model of density fluctuations propagating through a spectrally inhomogeneous flow, setting the spectral components by jointly fitting to the time-averaged and Fourier-resolved spectra. The predicted variability in any band is modelled analytically in Fourier space so it can be fit directly to the observed power spectra and lags. We find that the best-fitting model picks out three distinct radii in the flow, each with a distinct Compton spectrum. The variability and luminosity produced at these radii is enhanced, while propagation of fluctuations from larger radii is suppressed. We associate these radii with the disc truncation, the inner edge of the flow, and (more speculatively) the jet launch radius. These distinct radii are most evident where the source is close to a transition between the low/hard and high/soft states. We suggest that the smoother power spectra seen at lower luminosities imply that the source structure is simpler away from the transition.