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tokens: simple power-law component does not achieve a formally acceptable fit to either spectrum. The fit to the lower-sensitivity spectrum from Obs. 1 measured a power-law index of , but only achieved (where ν is the number of degrees of freedom in the fit). The spectrum of Obs. 2 is steeper, with in this simple fit, and a very fit statistic result owing to the improved S/N: . These simple fits are shown in Figure 2 . The data/model ratio from each fit shows residuals that are consistent with disk reflection, including Fe K emission and a Compton back-scattering excess peaking in the 20–30 keV range. The ratio from Obs. 2 is consistent with blurred reflection from an inner disk that extends close to the black hole, similar to the features observed in the low/hard state of GRS 1915+105 (see Miller et al. 2013a ). Figure 2. NuSTAR spectra of GS 1354−645, fit with a fiducial power-law continuum. The FPMA is shown in black, the FPMB is shown in red, and the model for the FPMA is shown in blue. The data in each panel have been rebinned for visual clarity. Left: the spectrum of Obs. 1 is shown. Right: the spectrum of Obs. 2 is shown. This ratio reveals evidence of strong, broadened reflection consistent with illumination of the inner accretion disk. We next considered fits with relxill (version 0.4c; Garcia et al. 2013 ; Dauser et al. 2014 ). This model includes the power law that illuminates the disk and also incorporates a Kerr blurring function to translate from the frame of the accretion disk to the frame of the observer. It is this function that measures the strong Doppler shifts and gravitational redshifts imprinted on the reflection spectrum. Spin is measured directly using relxill , within the bounds . The inclination of the inner disk—not necessarily the same as the binary system—is also measured directly. For these parameters, values obtained in fits to Obs. 2 were assumed in fits to Obs. 1, owing to its lower sensitivity. Relxill also allows the inner disk to deviate from the ISCO for a given spin parameter, so we also allowed the parameter R in to vary (the model has a hard upper limit of ) in fits to both observations. The emissivity of the disk is described as a broken power law in radius (e.g., ), giving three parameters: q in , q out , and R break . Any corona with an energetic profile defined by the underlying potential and linked to the disk is likely to have a time-averaged emissivity that falls with radius, so we require in fits to both observations. The limited sensitivity of Obs. 1 does not permit more detail to be discerned, so we simply fixed , obviating the meaning of R break . For Obs. 2, however, additional constraints can be imposed based on theoretical and observational expectations. Wilkins Fabian ( 2012 ) have calculated the emissivity profiles expected for idealized point source scenarios, including a “lamp-post” geometry. All calculations assume a disk that extends to the ISCO. The predicted profiles are complex and a