  Context: Observations of X-Ray sources harbouring a black hole and an
accretion disc show the presence of at least two spectral components. One
component is black-body radiation from an optically thick standard accretion
disc. The other is produced in a optically thin corona and usually shows a
powerlaw behaviour. Electron-proton (ep) bremsstrahlung is one of the
contributing radiation mechanisms in the corona. Soft photons from the
optically thick disc can Compton cool the electrons in the corona and therefore
lead to a two-temperature plasma, where electrons and ions have different
temperatures. Aims: We qualitatively discuss effects on ep-bremsstrahlung in
the presence of such a two-temperature plasma. Methods: We use the classical
dipole approximation allowing for non-relativistic electrons and protons and
apply quantum corrections through high-precision Gaunt factors. Results: In the
two-temperature case (T_e< T_p) the protons cause a significant fraction of the
ep-bremsstrahlung if their speed is high compared to the electrons. We give
accurate values for ep-bremsstrahlung including quantum-mechanical corrections
in the non-relativistic limit and give some approximations in the relativistic
limit. Conclusions: The formulae presented in this paper can be used in models
of black hole accretion discs where an optically thin corona can comprise a
two-temperature plasma. This work could be extended to include the fully
relativistic case if required.
