Cross-spectral modelling of the black hole X-ray binary XTE J1550-564 challenges to the propagating fluctuations paradigm

Timing properties of black hole X-ray binaries in outburst can be modelled with mass accretion rate fluctuations propagating towards the black hole. Such models predict time lags between energy bands due to propagation delays. First application of a propagating fluctuations model to black hole power spectra showed good agreement with the data. Indeed, hard lags observed from these systems appear to be in agreement with this generic prediction. Our propfluc code allows us to simultaneously predict power spectra, time lags and coherence of the variability as a function of energy. This was successfully applied to the Swift data on the black hole MAXI J1659-152, fitting jointly the power spectra in two energy bands and the cross-spectrum between these two bands. In this work, we attempt to model two high signal-to-noise Rossi X-ray Timing Explorer (RXTE) observations of the black hole XTE J1550-564. We find that neither observation can be adequately explained by the model even when considering, additionally to previous propfluc versions, different propagation speeds of the fluctuations. After extensive exploration of model extensions, we tentatively conclude that the quantitative and qualitative discrepancy between model predictions and data is generic to the propagating fluctuations paradigm. This result encourages further investigation of the fundamental hypotheses of the propagating fluctuations model. We discuss some of these hypotheses with an eye to future works.