New electron - proton Bremsstrahlung rates for a hot plasma where the electron temperature is much smaller than the proton temperature

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.