Context. The spin of supermassive black holes (SMBH) in active galactic nuclei (AGN) can be determined from spectral signature(s) of relativistic reflection such as the X-ray iron Kα line profile, but this can be rather uncertain when the line of sight intersects the so-called warm absorber and/or other wind components as these distort the continuum shape. Therefore, AGN showing no (or very weak) intrinsic absorption along the line-of-sight such as Ark 120, a so-called bare AGN, are the ideal targets for SMBH spin measurements. However, in our previous work on Ark 120, we found that its 2014 X-ray spectrum is dominated by Comptonisation, while the relativistic reflection emission only originates at tens of gravitational radii from the SMBH. As a result, we could not constrain the SMBH spin from disc reflection alone. Aims. Our aim is to determine the SMBH spin in Ark 120 from an alternative technique based on the global energetics of the disc-corona system. Indeed, the mass accretion rate (M) through the outer disc can be measured from the optical-UV emission, while the bolometric luminosity (Lbol) can be fairly well constrained from the optical to hard X-rays spectral energy distribution, giving access to the accretion efficiency η = Lbol/(M c2) which depends on the SMBH spin. Methods. The spectral analysis uses simultaneous XMM-Newton (OM and pn) and NuSTAR observations on 2014 March 22 and 2013 February 18. We applied the OPTXCONV model (based on OPTXAGNF) to self consistently reproduce the emission from the inner corona (warm and hot thermal Comptonisation) and the outer disc (colour temperature corrected black body), taking into account both the disc inclination angle and relativistic effects. For self-consistency, we modelled the mild relativistic reflection of the incident Comptonisation components using the XILCONV convolution model. Results. We infer a SMBH spin of 0.83+0.05-0.03, adopting the SMBH reverberation mass of 1.50 × 108 M·. In addition, we find that the coronal radius decreases with increasing flux (by about a factor of two), from 85+13-10Rg in 2013 to 14 ± 3 Rg in 2014. Conclusions. This is the first time that such a constraint is obtained for a SMBH spin from this technique, thanks to the bare properties of Ark 120, its well determined SMBH reverberation mass, and the presence of a mild relativistic reflection component in 2014 which allows us to constrain the disc inclination angle. We caution that these results depend on the detailed disc-corona structure, which is not yet fully established. However, the realistic parameter values (e.g. Lbol/LEdd, disc inclination angle) found suggest that this is a promising method to determine spin in moderate-M AGN.
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