Heavily Obscured AGN detection: a Radio vs X-ray challenge

In this work, we study the AGN radio detection effectiveness in the major deep extragalactic surveys, considering different AGN obscuration levels, redshift, and AGN bolometric luminosities. We particularly focus on comparing their radio and X-ray detectability, making predictions for present and future radio surveys. We extrapolate the predictions of AGN population synthesis model of cosmic X-ray background (CXB) to the radio band, by deriving the 1.4 GHz luminosity functions of unobscured (i.e. with hydrogen column densities $\log N_{H} <22$), obscured ($22<\log N_{H}<24$) and Compton-thick (CTK, $\log N_{H} >24$) AGN. We then use these functions to forecast the number of detectable AGN based on the area, flux limit, and completeness of a given radio survey and compare it with the AGN number resulting from X-ray predictions. When applied to deep extragalactic fields covered both by radio and X-ray observations, we show that, while X-ray selection is generally more effective in detecting unobscured AGN, the surface density of CTK AGN radio detected is on average $\sim 10$ times larger than the X-ray one, and even greater at high redshifts, considering the current surveys and facilities. Our results suggest that thousands of CTK AGN are already present in current radio catalogs, but most of them escaped any detection in the corresponding X-ray observations. We also present expectations for the number of AGN to be detected by the Square Kilometer Array Observatory (SKAO) in its future deep and wide radio continuum surveys, finding that it will be able to detect more than 2000 AGN at $z>6$ and some tens at $z>10$, more than half of which are expected to be CTK.