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Comparison of the star formation of X-ray selected active galactic nuclei in eFEDS with star-forming galaxies

We use $\sim 1800$ X-ray Active Galactic Nuclei (AGN) in the eROSITA Final Equatorial-Depth Survey (eFEDS), that span over two orders of magnitude in X-ray luminosity, $\rm L_{X,2-10keV} \approx 10^{43-45}\,ergs^{-1}$, and compare their star-formation rate (SFR) relative to that of non-AGN star-forming systems, at $\rm 0.5<z<1.5$. For that purpose, we compile a reference galaxy catalogue with $\sim 17000$ sources. Both samples have the same photometric coverage, from optical to far-infrared. We construct the spectral energy distributions (SEDs) of all sources and fit them using the CIGALE code, utilizing the same templates and parametric grid for both samples. We account for the mass incompleteness and exclude quiescent systems from both datasets. These allow us to compare the SFR of the two populations in a uniform manner, minimising systematic effects. Based on our analysis, AGN at low and moderate L$_X$ ($\rm L_{X,2-10keV} < 10^{44}\,ergs^{-1}$), have SFR that is lower, or at most, equal to that of star-forming galaxies, in agreement with previous studies. The large number of luminous X-ray AGN available in the eFEDS dataset, enable us to expand our investigations at higher L$_X$ to test previous, tentative results. At $\rm L_{X,2-10keV} > 10^{44.2}\,ergs^{-1}$, the SFR of AGN appears enhanced, by $\sim 30\%$, compared to that of star-forming sources, for systems with stellar mass, $\rm 10.5 < log\,[M_*(M_\odot)] < 11.5$, confirming indications found in previous studies. The most massive sources $\rm log\,[M_*(M_\odot)] > 11.5$, present a flat SFR$_{norm}$-L$_X$ relation up to $\rm L_{X,2-10keV} \sim 10^{44.5}\,ergs^{-1}$, with SFR similar to that of star-forming galaxies. However, at higher L$_X$ ($\rm L_{X,2-10keV} \sim 10^{45}\,ergs^{-1}$), we find indications that the SFR of these massive AGN hosts may be enhanced compared to that of non-AGN systems.