Lag-spectrum modeling. Top: Ratio $\frac{L_{\mathrm{diff}}}{L_{\mathrm{inc}}+L_{\mathrm{diff}}}$, calculated from the emissivity profile of BLR clouds centered at log r (cm) = 16.65 from Cloudy, shown as a function of wavelength. Additionally, the dust fraction, $\frac{L_{\mathrm{dust}}}{L_{\mathrm{inc}}+L_{\mathrm{diff}}}$, is overplotted as a dashed brown line. Black and brown points indicate the corresponding values averaged over the response curves of the filters used to measure continuum delays, respectively. Bottom: Lag-spectrum of Fairall 9. Black points indicate the observed data; open red squares show the RPC-model recovered time delays; and solid red squares denote the RPC-model predictions when the contribution from hot torus dust is included in the continuum lags. Solid black and dashed blue lines represent the best-fit results from the KYNXiltr model for spin a *  = 0 and a *  = 0.998, respectively. The corresponding fits obtained after excluding τ_uI from the lag-spectrum are shown by dotted lines. The fit ranges for the full lag-spectrum fitting are indicated by the gray- and blue-shaded regions.