On the accuracy of reflection-based supermassive black hole spin measurements in AGN

X-ray emission in active galactic nuclei (AGNs) arises from material located in the close vicinity of the supermassive black hole (SMBH). Thus, they are being used as unique laboratories to directly test the effects of general relativity dominating in these regions. In particular, the detection of a strong relativistic reflection component, in X-ray spectra, is potentially the most powerful method to measure SMBH spins. In this paper, we present an attempt to test the reliability of reflection-based SMBH spin measurements that can be currently achieved. This test is achieved through blind-fitting a set of simulated high-quality XMM-Newton and NuSTAR spectra, considering the most generic configuration of an AGN. Our main results show that at the high signal-to-noise ratio assumed in our simulations, neither the complexity of the spectra, nor the input value of the spin are the major drivers of our results. The height of the X-ray source instead plays a crucial role in recovering the spin. In particular, a high success rate in recovering the spin values is found among the accurate fits for a dimensionless spin parameter larger than 0.8 and a lamp-post height lower than five gravitational radii. We discuss the implications of our results and how some of the limitations faced in spin determination can be overcome. We focus on the possible impact of ATHENA in this field.