tokens: degrees of freedom. The nonrelativistic Model 1 already gives a good fit to the X-ray spectra of Fairall 9. In addition, we do not clearly detect the signature of a broad iron line in Figures 1 and 2 . All these considerations lead us to conclude that the relativistic reflection component in the spectra of Fairall 9, if present, is weak. To constrain possible deviation from Kerr spacetime around the black hole in Fairall 9, we replace the component relxill in Model 3 with its non-Kerr extension relxill _ nk v1.3.2 (Bambi et al. 2017 ; Abdikamalov et al. 2019a ). Similar to the results with relxill , we also find three solutions. The best-fit parameters are shown in Table 5 and the constraints of the deformation parameters in Figure 6 . We only show the results corresponding to solution 1 (Model 3.1) because the deformation parameters are totally unconstrained in the other two solutions. This is easy to understand since both negative spin and truncated disk result in a large distance between the black hole and the inner edge of the accretion disk. In this case, the effect on the reflected spectrum due to deviations from the Kerr background are not strong enough to be detected with current data. When assuming solution 1, we find from Figure 6 that the deformation parameters can recover 0, which means the Kerr solution is recovered. Figure 6. Confidence contour plot for spin parameter and deformation parameters. The red, green, and blue lines correspond to 68%, 90%, and 99% confidence levels respectively. The gray region is not included in our analysis because the spacetime there has pathological properties. Table 5 Best-fit Values with Model relxill_nk Note. Model: Tbabs ∗ (nthComp + relxill _ nk + xillver + zCutoffpl) . The parameters with * are fixed at given values in the fit. Uncertainties are given at the 90% confidence level. 4. Discussion and Conclusions Fairall 9 has a number of interesting properties (listed at the beginning of this paper) that make it a promising source for testing the Kerr black hole hypothesis using X-ray reflection spectroscopy. Unfortunately, the relativistic reflection component, if present, is weak, which makes the selection of the correct astrophysical model with the available data challenging. However, we should stress that the ideal source with all the nice properties for testing general relativity and no bad properties probably does not exist, so we have to try to do our best with the available sources and data. Moreover, in the case of Fairall 9 we can expect (see Section 4.3 below) that future observations with a higher energy resolution near the iron line can solve the degeneracy and be capable of selecting the astrophysical model and the physical best-fit solution. 4.1. General Considerations We studied a simultaneous XMM+NuSTAR observation of Fairall 9. The soft excess in the spectra can be described by a Comptonization component (Model 1) and the fit is already good. When we add a blurred reflection
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