tokens: Also included is the total reflection from the disc, R ( E ), but we do not include the intrinsic or reprocessed disc emission as the energy of this is too low to make a significant contribution to the RXTE data above 3 keV. Figure 1. The assumed geometry. The green region emits the soft spectral shape, S ( E ), and the cyan region emits the hard spectral shape, H ( E ). The direct contribution from the thermal disc (red) is neglected. Fluctuations are generated throughout the flow on the viscous time-scale, t visc ( r ), and propagate down towards the compact object at a local velocity, v ( r ) = rf visc ( r ). Figure 2. The decomposition of Observation 1 (ObsID: 10238-01-08-00) used to augment the standard propagating fluctuations model. Shown are the total energy spectrum (black), the hard Compton component ( H ( E ), cyan), the soft Compton component ( S ( E ), green) and the reflection component ( R ( E ), magenta). Filled circles show the PCA (red) and HEXTE (black) data. The red, green and blue bands denote the Low (3.13–4.98 keV), Mid (9.94–20.09 keV) and High (20.09–34.61 keV) energy ranges, respectively. Table 1. Fit parameters for the spectral model shown in Fig. 2 , with the reflected emission from the sum of the two Comptonization components: tbabs*(nthcomp+nthcomp+kdblur*xilconv*twocomp) . The electron temperatures ( kT e ) of both Comptonization components are tied. The fixed parameters in our fits are the Galactic absorption column density (0.6 × 10 22 cm −2 ), the seed photon temperature (0.2 keV), the kdblur index (3.0), the inclination angle of Cyg X-1 (27 o ), the inner disc radius (10 R g ) and the xilconv iron abundance (1.0). 4.2 Spectral-timing model In all simulations, we assume that Cyg X-1 has a black hole of mass, M BH = 15 M ⊙ , and a dimensionless spin parameter of a * ∼ 0.85 (Kawano et al. 2017 ). The inner radius is set to the approximate ISCO size implied from the spin of Cyg X-1, so that r i = 2.5. The time-averaged spectrum, , emitted from each radius is given by the expression r SH here is the transition radius between the soft and hard Comptonization regions. This is analytically derived from an assumed emissivity, ε( r ) ∝ r −γ b ( r ), where b ( r ) is an inner boundary condition, such that the luminosity ratio between the two components matches that observed, such that The light curves produced by the standard propagating fluctuations model at each radius are then made energy-dependent and renormalized such that their time-average is the flux for that energy bin and radius, yielding The summation limits implied by ‘ region ’ are { r o to r SH } for r n > r SH and { r SH to r i } for r n r SH . This normalization guarantees that if equation ( 6 ) is time averaged and summed over all radii, the observed energy spectrum is reproduced. We match our spectra to the data as closely as possible by converting these fluxes into count rates using the detector effective area A eff ( E ) and Galactic absorption
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