A consistent radio to sub-mm pc-scale study of the nucleus of NGC 1068

The origin of radio emission in radio-quiet (RQ) AGN remains a long-standing mystery. We present a detailed study of the cm to sub-mm emission from the nucleus of the nearby prototypical RQ Seyfert 2 galaxy, NGC 1068. We analyse observations between 4.5-706 GHz using $e$-MERLIN, VLA and ALMA. We restricted all data used for imaging to a matching $uv-$range of 15$-$3300 k$\lambda$, to ensure that all data sampled the same spatial scales. All images were restored with a $\sim$ 0.06$''$ beam. To derive the spectral energy distribution (SED), we fit synchrotron, free-free, dust and coronal component models to these data. We report that the sub-mm excess between $\sim$ 200-700 GHz is consistent with synchrotron emission from a compact and optically thick corona with a radius $R_\mathrm{c}\approx 70\pm5 \,R_\mathrm{g}$, a fraction of $\sim$\,$10\pm2$% of the energy density in the form of non-thermal electrons, and a magnetic field strength $B\approx 148$ G. The luminosity of the corona is roughly consistent with -- though higher than -- the expected from mm--X-ray correlations derived in recent studies of RQ AGN. This difference is likely due to the corona SED peaking at ($\approx$550 GHz). Between 10 and $\sim$ 200 GHz, the SED is dominated by free-free emission. High angular resolution observations at frequencies below 5 GHz are needed to constrain a putative optically thin synchrotron component and the amount of free-free absorption.