The ATESP 5 GHz radio survey IV. 19, 38, and 94 GHz observations and radio spectral energy distributions

It is now established that the faint radio population is a mixture of star-forming galaxies and faint active galactic nuclei (AGNs), with the former dominating below S(1.4GHz) \sim 100 muJy and the latter at larger flux densities. The faint radio AGN component can itself be separated into two main classes, mainly based on the host-galaxy properties: sources associated with red/early-type galaxies (like radio galaxies) are the dominant class down to \sim 100 muJy; quasar/Seyfert--like sources contribute an additional 10-20\%. One of the major open questions regarding faint radio AGNs is the physical process responsible for their radio emission. This work aims at investigating this issue, with particular respect to the AGN component associated with red/early-type galaxies. Such AGNs show, on average, flatter radio spectra than radio galaxies and are mostly compact (<= 30 kpc in size). Various scenarios have been proposed to explain their radio emission. For instance they could be core/core-jet dominated radio galaxies, low-power BL LACs, or advection-dominated accretion flow (ADAF) systems. We used the Australia Telescope Compact Array (ATCA) to extend a previous follow-up multi-frequency campaign to 38 and 94 GHz. (abridged)