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 K \alpha 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 ( \dot { M } ) through the outer disc can be measured from the optical-UV emission , while the bolometric luminosity ( L _ { bol } ) can be fairly well constrained from the optical to hard X-rays spectral energy distribution , giving access to the accretion efficiency \eta = L _ { bol } / ( \dot { M } c ^ { 2 } ) 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 \times 10 ^ { 8 } M _ { \odot } .
In addition , we find that the coronal radius decreases with increasing flux ( by about a factor of two ) , from 85 ^ { +13 } _ { -10 } R _ { g } in 2013 to 14 \pm 3 R _ { g } 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 . L _ { bol } / L _ { Edd } , disc inclination angle ) found suggest that this is a promising method to determine spin in moderate- \dot { M } AGN .