AGN Selection Methods Have Profound Impacts on the Distributions of Host Galaxy Properties

We present a comparative study of X-ray and IR AGNs at $z\approx2$ to highlight the important AGN selection effects on the distributions of host galaxy properties. Compared with non-AGN star-forming galaxies (SFGs) on the main sequence, X-ray AGNs have similar median star formation (SF) properties, but their incidence (q$_{\rm{AGN}}$) is higher among galaxies with either enhanced or suppressed SF, and among galaxies with larger stellar mass surface density, regardless if it is measured within half-light radius ($\Sigma_e$) or central 1kpc ($\Sigma_{\rm{1kpc}}$). Unlike X-ray AGNs, IR AGNs are less massive, and have enhanced SF and similar distributions of colors, $\Sigma_e$ and $\Sigma_{\rm{1kpc}}$ relative to non-AGN SFGs. Given that $\Sigma_e$ and $\Sigma_{\rm{1kpc}}$ strongly correlate with M$_*$, we introduce the fractional mass within central 1kpc ($\rm{\frac{M_{1kpc}}{M_*}}$), which only weakly depends on M$_*$, to quantify galaxy compactness. Both AGN populations have similar $\rm{\frac{M_{1kpc}}{M_*}}$ distributions compared to non-AGN SFGs'. While q$_{\rm{AGN}}$ increases with $\Sigma_e$ and $\Sigma_{\rm{1kpc}}$, it remains constant with $\rm{\frac{M_{1kpc}}{M_*}}$, indicating that the trend of increasing q$_{\rm{AGN}}$ with $\rm{\Sigma}$ is driven by M$_*$ more than morphology. While our findings are not in conflict with the scenario of AGN quenching, they do not imply it either, because the incidence of AGNs hosted in transitional galaxies depends crucially on AGN selections. Additionally, despite the relatively large uncertainty of AGN bolometric luminosities, their very weak correlation, if any, with SF activities, regardless of AGN selections, also argues against a direct causal link between the presences of AGNs and the quenching of massive galaxies at $z\sim2$.