Do stellar-mass and super-massive black holes have similar dining habits?

Through the years numerous attempts have been made to connect the phenomenology and physics of mass accretion onto stellar-mass and super-massive black holes in a scale-invariant fashion. In this paper, we explore this connection at the radiatively-efficient (and non-jetted) end of accretion modes by comparing the relationship between the luminosity of the accretion disk and corona in the two source classes. We analyse 458 RXTE-PCA archival observations of the X-ray binary (XRB) GX339-4 focusing on the soft and soft-intermediate states, which have been suggested to be analogous to radiatively efficient AGN. The observed scatter in the $\log L_{disk}-\log L_{corona}$ relationship of GX339-4 is high ($\sim0.43\,$dex) and significantly larger than in a representative sample of radiatively-efficient, non- or weakly-jetted AGN ($\sim0.30\,$dex). On the face of it, this would appear contrary to the hypothesis that the systems simply scale with mass. On the other hand we also find that GX339-4 and our AGN sample show different $\dot{m}$ and $\Gamma$ distributions, with the latter being broader in GX339-4 (dispersion of $\sim0.16$ cf. $\sim0.08$ for AGN). GX339-4 also shows an overall softer slope, with mean $\sim2.20$ as opposed to $\sim2.07$ for the AGN sample. Remarkably, once similarly broad $\Gamma$ and $\dot{m}$ distributions are selected, the AGN sample overlaps nicely with GX339-4 observations in the mass-normalised $\log L_{disk}-\log L_{corona}$ plane, with a scatter of $\sim0.30-0.33\,$dex. This indicates that a mass-scaling of properties might hold after all, with our results being consistent with the disk-corona systems in AGN and XRBs exhibiting the same physical processes, albeit under different conditions for instance in terms of temperature, optical depth and/or electron energy distribution in the corona, heating-cooling balance, coronal geometry and/or black hole spin.