  We report the discovery of the ``mm fundamental plane of black-hole accretion'', which is a tight correlation between the nuclear 1 mm luminosity ($L_{\rm \nu, mm}$), the $2$ -- $10$~keV X-ray luminosity ($L_{\rm X,2-10}$) and the supermassive black hole (SMBH) mass ($M_{\rm BH}$) with an intrinsic scatter ($\sigma_{\rm int}$) of $0.40$ dex. The plane is found for a sample of 48 nearby galaxies, most of which are radiatively-inefficient, low-luminosity active galactic nuclei (LLAGN). Combining these sources with a sample of high-luminosity (quasar-like) nearby AGN, we find that the plane still holds. We also find that $M_{\rm BH}$ correlates with $L_{\rm \nu, mm}$ at a highly significant level, although such correlation is less tight than the mm fundamental plane ($\sigma_{\rm int}=0.51$ dex). Crucially, we show that spectral energy distribution (SED) models for both advection-dominated accretion flows (ADAFs) and compact jets can explain the existence of these relations, which are not reproduced by the standard torus-thin accretion disc models usually associated to quasar-like AGN. The ADAF models reproduces the observed relations somewhat better than those for compact jets, although neither provides a perfect prediction. Our findings thus suggest that radiatively-inefficient accretion processes such as those in ADAFs or compact (and thus likely young) jets may play a key role in both low- and high-luminosity AGN. This mm fundamental plane also offers a new, rapid method to (indirectly) estimate SMBH masses. 
A fundamental plane of black hole accretion at millimetre wavelengths