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We discuss the origin of the very different hard X‐ray spectral shapes observed in the low hard state (LHS) and high soft state (HSS) of accreting black holes. We study the effects of synchrotron self‐absorption on the Comptonizing electron distribution in the magnetized corona of accreting black holes. We solve the kinetic equations assuming that power is supplied to the coronal electrons through Coulomb collisions with a population of hot protons and/or through the injection of non‐thermal energetic electrons by some unspecified acceleration process. We compute numerically the steady state particle distributions and escaping photon spectra. These numerical simulations confirm that synchrotron self‐absorption, together with e–e Coulomb collision constitute an efficient thermalizing mechanism for the coronal electrons. When compared to the data they allow us to constrain the magnetic field and temperature of the hot protons in the corona independently of any dynamical accretion flow model or geometry. A preliminary comparison with the LHS spectrum of Cygnus X‐1 indicates a magnetic field below equipartition with radiation, suggesting that the corona is not powered through magnetic field dissipation (as assumed in most accretion disc corona models). However, in the LHS of Cygnus X‐1 and other sources, our results also point towards proton temperatures lower than  3 × 10 10  K , i.e. substantially lower than typical temperatures of the ADAF‐like models. In contrast, in the HSS both the proton temperature and magnetic field could be much higher. We also show that in both spectral states the magnetized corona could be powered essentially through acceleration of non‐thermal particles. Therefore, contrary to current beliefs, energy dissipation processes in the corona of the HSS and that of the LHS could be of very similar nature. The main differences between the LHS and HSS coronal emission can then be understood as the consequence of the much stronger radiative cooling in the HSS caused by the soft thermal radiation coming from the geometrically thin accretion disc. In the LHS the soft cooling photon flux is much weaker because the accretion disc is either truncated at large distances from the black hole, or much colder than in the HSS.

The synchrotron boiler and the spectral states of black hole binaries