We use X-ray Active Galactic Nuclei (AGN) observed by the Chandra X-ray Observatory within the 9.3 deg$^2$ Bo$rm ddot{o}$tes field of the NDWFS to study whether there is a correlation between X-ray luminosity (L$_X$) and star formation rate (SFR) of the host galaxy, at $rm 0.5<z<2.0$, with respect to the position of the galaxy to the main sequence (SFR$_{norm}$). About half of the sources in the X-ray sample have spectroscopic redshifts. We also construct a reference galaxy catalogue. For both datasets, we use photometric data from optical to the far infrared, compiled by the HELP project and apply spectral energy distribution (SED) fitting, using the X-CIGALE code. We exclude quiescent sources from both the X-ray and the reference samples. We also account for the mass completeness of our dataset, in different redshifts bins. Our analysis highlights the importance of studying the SFR-L$_X$ relation, in a uniform manner, taking into account the systematics and selection effects. Our results suggest that, in less massive galaxies ($rm log,[M_*(M_odot)] sim 11$), AGN enhances the SFR of the host galaxy by $sim 50%$ compared to non AGN systems. A flat relation is observed for the most massive galaxies. SFR$_{norm}$ does not evolve with redshift. The results, although tentative, are consistent with a scenario in which, in less massive systems, both AGN and star formation (SF) are fed by cold gas, supplied by a merger event. In more massive galaxies, the flat relation could be explained by a different SMBH fuelling mechanism that is decoupled from the star formation of the host galaxy (e.g. hot diffuse gas). Finally, we compare the host galaxy properties of X-ray absorbed and unabsorbed sources. Our results show no difference which suggests that X-ray absorption is not linked with the properties of the galaxy.
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