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 \la \tau \la 1 and 1 \times 10 ^ { 9 } { K } \la T \la 3 \times 10 ^ { 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 .