Self-consistent computation of γ-ray spectra due to proton–proton interactions in black hole systems

In the inner regions of an accretion disc around a black hole, relativistic protons can interact with ambient matter to produce electrons, positrons and γ-rays. The resultant steady-state electron and positron particle distributions are self-consistently computed taking into account Coulomb and Compton cooling,  e⁻ e⁺  pair production (due to γ–γ annihilation) and pair annihilation. While earlier works used the diffusion approximation to obtain the particle distributions, here we solve a more general integro-differential equation that correctly takes into account the large change in particle energy that occurs when the leptons Compton scatter off hard X-rays. Thus this formalism can also be applied to the hard state of black hole systems, where the dominant ambient photons are hard X-rays. The corresponding photon energy spectrum is calculated and compared with broad-band data of black hole binaries in different spectral states. The results indicate that the γ-ray spectra  ( E > 0.8 MeV)  of both the soft and hard spectral states and the entire hard X-ray/γ-ray spectrum of the ultrasoft state could be due to p–p interactions. These results are consistent with the hypothesis that there always exists in these systems a γ-ray spectral component due to p–p interactions that can contribute between 0.5 and 10 per cent of the total bolometric luminosity. The model predicts that GLAST would be able to detect black hole binaries and provide evidence for the presence of non-thermal protons, which in turn would give insight into the energy dissipation process and jet formation in these systems.