Accretion disc coronae as magnetic reservoirs

Most astrophysical sources powered by accretion on to 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 obs erved temperatures and optical depths lying in a narrow range (0.1 less tha n or similar to tau less than or similar to 1 and 1 x 10(9) K less than or similar to T less than or similar to 3 x 10(9) K). Here we argue that these facts constitute strong supporting evidence for a magnetically dominated c orona. We show that the inferred thermal energy content of the corona, in a ll 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 generate d by a sheared rotator (probably the accretion disc). We briefly outline th e main reasons why the former possibility is to be discarded, and the latte r preferred.