Gamma-ray emission from proton-proton interactions in hot accretion flows

We present a model of gamma-ray emission through neutral pion production and decay in two-temperature accretion flows around supermassive black holes. We refine previous studies of such a hadronic gamma-ray emission by taking into account (1) relativistic effects in the photon transfer and (2) absorption of gamma-ray photons in the radiation field of the flow. We use a fully general relativistic description of both the radiative and hydrodynamic processes, which allows us to study the dependence on the black hole spin. The spin value strongly affects the gamma-ray emissivity within ~10 gravitational radii. The central regions of flows with the total luminosities L < 0.001 of the Eddington luminosity are mostly transparent to photons with energies below 10 GeV, permitting investigation of the effects of space-time metric. For such L, an observational upper limit on the gamma-ray (0.1-10 GeV) to X-ray (2-10 keV) luminosity ratio of L_{0.1-10 GeV}/L_{2-10 keV} << 0.1 can rule out rapid rotation of the black hole; on the other hand, a measurement of L_{0.1-10 GeV}/L_{2-10 keV} ~ 0.1 cannot be regarded as the evidence of rapid rotation, as such a ratio can also result from a flat radial profile of gamma-ray emissivity (which would occur for nonthermal acceleration of protons in the whole body of the flow). At L > 0.01 of the Eddington luminosity, the gamma-ray emission from the innermost region is strongly absorbed and the observed gamma-rays do not carry information on the value of the black hole spin. We note that if the X-ray emission observed in Centaurus A comes from an accretion flow, the hadronic gamma-ray emission from the flow should contribute significantly to the MeV/GeV emission observed from the core of this object, unless it contains a slowly rotating black hole and protons in the flow are thermal.