Accretion disc coronae as magnetic reservoirs

Most astrophysical sources powered by accretion onto a black hole, either of stellar mass or supermassive, when observed with hard X-rays show signs of a hot Comptonizing component in the flow, the so-called corona, with observed temperatures and optical depths lying in a narrow range (0.1 < \tau < 1 and 1x10^9 K < T < 3x10^9 K). Here we argue that these facts constitute strong supporting evidence for a magnetically-dominated corona. We show that the inferred thermal energy content of the corona, in all black hole systems, is far too low to explain their observed hard X-ray luminosities, unless either the size of the corona is at least of the order of 10^3 Schwarzschild radii, or the corona itself is in fact a reservoir, where the energy is mainly stored in the form of a magnetic field generated by a sheared rotator (probably the accretion disc). We briefly outline the main reasons why the former possibility is to be discarded, and the latter preferred.