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

We present a comparative study of X-ray and IR selected AGNs at $zapprox2$ to highlight the importance of the AGN selection effects on the distributions of star formation (SF) and morphological properties of the host galaxies. We find that while the median SF of X-ray AGN hosts are similar to non-AGN star forming galaxies (SFGs), the incidence of X-ray AGNs, q$_{rm{AGN}}$, is higher among galaxies with suppressed SF and larger stellar mass surface density within both the half-light radius ($Sigma_e$) and the central 1 kpc ($Sigma_{rm{1kpc}}$), IR AGN hosts are different. They are less massive, have elevated SF and share similar distributions of colors, $Sigma_e$ and $Sigma_{rm{1kpc}}$ with normal SFGs. Given that $Sigma_e$ and $Sigma_{rm{1kpc}}$ strongly correlate with stellar mass (M$_*$), we introduce $frac{M_{rm{1kpc}}}{M_*}$, the fractional mass within central 1 kpc, to quantify galaxy compactness, which is independent on M$_*$. Both AGN populations have similar $frac{M_{rm{1kpc}}}{M_*}$ distributions to normal SFGs. We show that while q$_{rm{AGN}}$ increases with both $Sigma_e$ and $Sigma_{rm{1kpc}}$, it remains constant with $frac{M_{rm{1kpc}}}{M_*}$, indicating that the trend of increasing q$_{rm{AGN}}$ with $Sigma$ is driven by M$_*$. While our findings are not in conflict with the scenario of AGN quenching, they do not directly imply it either, because the incidence of AGNs being hosted by transitional galaxies depends crucially on AGN selections. The additional evidence that no clear correlation is observed between SF and AGN bolometric luminosity, regardless of the selection, calls into question the notion that AGNs are the direct cause of quenching in $zapprox2$ massive galaxies.