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We use $\sim 1,000$ X-ray sources in the COSMOS-Legacy survey and study theposition of the AGN relative to the star forming main sequence (MS). We alsoconstruct a galaxy (non-AGN) reference sample that includes $\sim 90,000$sources. We apply the same photometric selection criteria on both datasets andconstruct their spectral energy distributions (SEDs) using optical tofar-infrared photometry compiled by the HELP project. We perform SED fitting,using the X-CIGALE algorithm and the same parametric grid for both datasets, tomeasure the star formation rate (SFR) and stellar mass of the sources. The masscompleteness of the data is calculated at different redshift intervals and isapplied on both samples. We define our own main sequence, based on thedistributions of the specific SFR at different redshift ranges and excludequiescent galaxies from our analysis. These allow us to compare the SFR of thetwo populations in a uniform manner, minimizing systematics and selectioneffects. Our results show that at low to moderate X-ray luminosities, AGN tendto have lower or, at most, equal star formation rates compared to non-AGNsystems with similar stellar mass and redshift. At higher ($\rm L_{X,2-10keV} >2-3\times 10^{44}\,erg\,s^{-1}$), we observe an increase of the SFR of AGN, forsystems that have $\rm 10.5 < log\,[M_*(M_\odot)] < 11.5$.

Star formation of X-ray AGN in COSMOS: The role of AGN activity and galaxy stellar mass