2025A&A...701A..41D

Context. Active galactic nuclei (AGNs) host accreting supermassive black holes (SMBHs). The accretion process can lead to the formation of a hot, X-ray emitting corona close to the SMBH that can accelerate relativistic electrons. Observations in the millimeter band can probe its synchrotron emission.
Aims. We intend to provide a framework to derive physical information of SMBH coronae by modelling their spectral energy distribution (SED) from radio to far-infrared frequencies. We also explore the possibilities of deriving additional information from millimeter observations, such as the SMBH mass, and studying high-redshift lensed sources.
Methods. We introduce a corona emission model based on a one-zone spherical region with a hybrid thermal and non-thermal plasma. We investigated the dependence of the corona SED on different parameters such as size, opacity, and magnetic field strength. Other galactic emission components from dust, ionised gas, and diffuse relativistic electrons were also included in the SED fitting scheme. We applied our code consistently to a sample of radio-quiet AGNs with strong indications of a coronal component in the millimeter.
Results. The detected millimeter emission from SMBH coronae is consistent with a non-thermal relativistic particle population with an energy density that is ≈0.5-10% of that in the thermal plasma. This requires magnetic energy densities close to equipartition with the thermal gas and corona sizes of 60-250 gravitational radii. The model can also reproduce the observed correlation between millimeter emission and SMBH mass when we accounted for the uncertainties in the corona size.
Conclusions. The millimeter band offers a unique window into the physics of SMBH coronae, enabling the study of highly dust-obscured sources and high-redshift lensed quasars. Gaining a deeper understanding of the relativistic particle population in SMBH coronae can provide key insights into their potential multiwavelength and neutrino emission.