Nowhere To Hide: Radio-Faint Agn In The Goods-N Field: Ii. Multi-Wavelength Agn Selection Techniques And Host Galaxy Properties

Context. Obtaining a census of active galactic nuclei (AGN) activity across cosmic time is critical to our understanding of galaxy evolution and formation. Many AGN classification techniques are compromised by dust obscuration. However, very long baseline interferometry (VLBI) can be used to identify high brightness temperature compact radio emission (> 10(5) K) in distant galaxies that can only be reliably attributed to AGN activity.Aims. We present the second in a series of papers dealing with the compact radio population in the GOODS-N field. This paper reviews the various multi-wavelength data and AGN classification techniques in the context of a VLBI-detected sample and use these to investigate the nature of the AGN as well as their host galaxies.Methods. Multi-wavelength data from radio to X-ray were compiled for the GOODS-N AGN sample, and fourteen widely used multi-wavelength AGN classification schemes were tested. We discuss and compare the various biases that affect multi-wavelength and VLBI selection. We use the physical interpretation to imply the nature of VLBI-selected AGN and their hosts.Results. Firstly, we find that no single identification technique can identify all VLBI objects as AGN. Infrared colour-colour selection is most notably incomplete. However, the usage of multiple classification schemes can identify all VLBI-selected AGN, independently verifying similar approaches used in other deep field surveys. In the era of large area surveys with instruments such as the SKA and ngVLA, multi-wavelength coverage, which relies heavily upon observations from space, is often unavailable. Therefore, VLBI remains an integral component in detecting AGN of the jetted efficient and inefficient accretion types. Secondly, a substantial fraction (46%) of the VLBI AGN have no X-ray counterpart, which is most likely due to lack of sensitivity in the X-ray band. Thirdly, a high fraction of the VLBI AGN reside in low or intermediate redshift dust-poor early-type galaxies. These most likely exhibit inefficient accretion. Fourthly, A significant fraction of the VLBI AGN reside in symbiotic dusty starburst - AGN systems. Finally, in the appendix, we present an extensive compilation of the multi-wavelength properties of all the VLBI AGN in GOODS-N.