Context. A tight correlation exists between far-infrared and radio emission for star-forming galaxies (SFGs), which seems to hold out to high redshifts (z {ap} 2). Any excess of radio emission... Show moreContext. A tight correlation exists between far-infrared and radio emission for star-forming galaxies (SFGs), which seems to hold out to high redshifts (z {ap} 2). Any excess of radio emission over that expected from star formation processes is most likely produced by an active galactic nucleus (AGN), often hidden by large amounts of dust and gas. Identifying these radio-excess sources will allow us to study a population of AGN unbiased by obscuration and thus find some of the most obscured, Compton-thick AGN, which are in large part unidentified even in the deepest X-ray and infrared (IR) surveys. Aims: We present here a new spectral energy distribution (SED) fitting approach that we adopt to select radio-excess sources amongst distant star-forming galaxies in the GOODS-Herschel (North) field and to reveal the presence of hidden, highly obscured AGN. Methods: Through extensive SED analysis of 458 galaxies with radio 1.4 GHz and mid-IR 24 {$μ$}m detections using some of the deepest Chandra X-ray, Spitzer and Herschel infrared, and VLA radio data available to date, we have robustly identified a sample of 51 radio-excess AGN (~{}1300 deg$^{-2}$) out to redshift z {ap} 3. These radio-excess AGN have a significantly lower far-IR/radio ratio (q {lt} 1.68, 3{$σ$}) than the typical relation observed for star-forming galaxies (q {ap} 2.2). Results: We find that {ap}45% of these radio-excess sources have a dominant AGN component in the mid-IR band, while for the remainders the excess radio emission is the only indicator of AGN activity. The presence of an AGN is also confirmed by the detection of a compact radio core in deep VLBI 1.4 GHz observations for eight of our radio-excess sources ({ap}16%; {ap}66% of the VLBI detected sources in this field), with the excess radio flux measured from our SED analysis agreeing, to within a factor of two, with the radio core emission measured by VLBI. We find that the fraction of radio-excess AGN increases with X-ray luminosity reaching ~{}60% at L$_X$ {ap} 10$^{44}$ - 10$^{45}$ erg s$^{-1}$, making these sources an important part of the total AGN population. However, almost half (24/51) of these radio-excess AGN are not detected in the deep Chandra X-ray data, suggesting that some of these sources might be heavily obscured. Amongst the radio-excess AGN we can distinguish three groups of objects: i) AGN clearly identified in infrared (and often in X-rays), a fraction of which are likely to be distant Compton-thick AGN; ii) moderate luminosity AGN (L$_X$ {lsim} 10$^{43}$ erg s$^{-1}$) hosted in strong star-forming galaxies; and iii) a small fraction of low accretion-rate AGN hosted in passive (i.e. weak or no star-forming) galaxies. We also find that the specific star formation rates (sSFRs) of the radio-excess AGN are on average lower that those observed for X-ray selected AGN hosts, indicating that our sources are forming stars more slowly than typical AGN hosts, and possibly their star formation is progressively quenching. Tables 1, 3 and Appendices are available in electronic form at http://www.aanda.orgShow less
