Modelling the cross-spectral variability of the black hole binary MAXI J1659-152 with propagating accretion rate fluctuations

The power spectrum of the X-ray fluctuations of accreting black holes often consists of two broad humps. We quantitatively investigate the hypothesis that the lower frequency hump originates from variability in a truncated thin accretion disc, propagating into a large scaleheight inner hot flow which, in turn, itself is the origin of the higher frequency hump. We extend the propagating mass accretion rate fluctuations model PROPFLUC to accommodate double-hump power spectra in this way. Furthermore, we extend the model to predict the cross-spectrum between two energy bands in addition to their power spectra, allowing us to constrain the model using the observed time lags, which in the model result from both propagation of fluctuations from the disc to the hot flow, and inside the hot flow. We jointly fit soft and hard power spectrum, and the cross-spectrum between the two bands using this model for five Swift X-ray Telescope observations of MAXI J1659-152. The new double-hump model provides a better fit to the data than the old single-hump model for most of our observations. The data show only a small phase lag associated with the low-frequency hump. We demonstrate quantitatively that this is consistent with the model. We compare the truncation radius measured from our fits with that measured purely by spectral fitting and find agreement within a factor of two. This analysis encompasses the first joint fits of stellar-mass black hole cross-spectra and power spectra with a single self-consistent physical model.