We consider stochastic particle acceleration in plasmas around stellar mass black holes to explain the emissions above 1 MeV from Galactic black hole candidates. We show that for certain parameter regimes, electrons can overcome Coulomb losses and be accelerated beyond the thermal distribution to form a new population, whose distribution is broad and usually not a power law; the peak energy of the distribution is determined by the balance between acceleration and cooling, with particles piling up around it. Radiation by inverse Compton scattering off the thermal (from background) and non-thermal (produced by acceleration) particles can in principle explain the hard X-ray to gamma-ray emissions from black hole candidates. We present model fits of Cyg X-1 and GRO J0422 in 50 keV – 5 MeV region observed with OSSE and COMPTEL.

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