Investigating the Star Formation Rates of Active Galactic Nucleus Hosts Relative to the Star-forming Main Sequence

A fundamental question in galaxy and black hole evolution remains how galaxies and their supermassive black holes have evolved together over cosmic time. Specifically, it is still unclear how the position of X-ray active galactic nucleus (AGN) host galaxies with respect to the star-forming main sequence (MS) may change with the X-ray luminosity (L _X) of the AGN or the stellar mass (M _⋆) of the host galaxy. We use data from the XMM-Spitzer Extragalactic Representative Volume Survey (XMM-SERVS) to probe this issue. XMM-SERVS is covered by the largest medium-depth X-ray survey (with superb supporting multiwavelength data) and thus contains the largest sample to date for study. To ensure consistency, we locally derive the MS from a large reference galaxy sample. In our analysis, we demonstrate that the turnover of the galaxy MS does not allow reliable conclusions to be drawn for high-mass AGNs, and we establish a robust safe regime where the results do not depend upon the choice of MS definition. Under this framework, our results indicate that less massive AGN host galaxies ( $\mathrm{log}{M}_{\star }\sim 9.5\mbox{--}10.5\,{M}_{\odot }$ ) generally possess enhanced star formation rates compared to their normal-galaxy counterparts while the more massive AGN host galaxies ( $\mathrm{log}{M}_{\star }\sim 10.5\mbox{--}11.5\,{M}_{\odot }$ ) lie on or below the star-forming MS. Further, we propose an empirical model for how the placement of an AGN with respect to the MS (SFR_norm) evolves as a function of both M _⋆ and L _X.