A binning-free method reveals a continuous relationship between galaxies AGN power and offset from main sequence

Studies investigating the relationship between AGN power and the star formation rates (SFRs) of their host galaxies often rely on averaging techniques -- such as stacking -- to incorporate information from non-detections. However, averages, and especially means, can be strongly affected by outliers and can therefore give a misleading indication of the typical case. Recently, a number of studies have taken a step further by binning their sample in terms of AGN power (approximated by the 2-10keV luminosity of the AGN), and investigating how the SFR distribution differs between these bins. These bin thresholds are often weakly motivated, and binning implicitly assumes that sources within the same bin have similar (or even identical) properties. In this paper, we investigate whether the distribution of host SFRs -- relative to the locus of the star-forming main sequence (i.e., $R_{rm MS}$) -- changes continuously as a function of AGN power. We achieve this by using a hierarchical Bayesian model that completely removes the need to bin in AGN power. In doing so, we find strong evidence that the $R_{rm MS}$ distribution changes with 2-10keV X-ray luminosity. The results suggest that higher X_ray luminosity AGNs have a tighter physical connection to the star-forming process than lower X-ray luminosity AGNs, at least within the $0.8 < z < 1.2$ redshift range considered here.