A fundamental plane of black hole activity

We examine the disc--jet connection in stellar mass and supermassive black holes by investigating the properties of their compact emission in the X-ray and radio bands. We compile a sample of ~100 active galactic nuclei with measured mass, 5 GHz core emission, and 2-10 keV luminosity, together with 8 galactic black holes with a total of ~50 simultaneous observations in the radio and X-ray bands. Using this sample, we study the correlations between the radio (L_{R}) and the X-ray (L_{X}) luminosity and the black hole mass (M). We find that the radio luminosity is correlated with {\em both} M and L_{X}, at a highly significant level. In particular, we show that the sources define a ``fundamental plane'' in the three-dimensional (log L_{R},log L_{X},log M) space, given by log L_{R}=(0.60^{+0.11}_{-0.11}) log L_{X} +(0.78^{+0.11}_{-0.09}) log M + 7.33^{+4.05}_{-4.07}, with a substantial scatter of \sigma_{R}=0.88. We compare our results to the theoretical relations between radio flux, black hole mass, and accretion rate derived by Heinz and Sunyaev (2003). Such relations depend only on the assumed accretion model and on the observed radio spectral index. Therefore, we are able to show that the X-ray emission from black holes accreting at less than a few per cent of the Eddington rate is unlikely to be produced by radiatively efficient accretion, and is marginally consistent with optically thin synchrotron emission from the jet. On the other hand, models for radiatively inefficient accretion flows seem to agree well with the data.