Gamma-ray opacity of the anisotropic stratified broad-line regions in blazars

Abstract: The GeV-range spectra of blazars are shaped not only by non-thermal emission processes internal to the relativistic jet but also by external pair-production absorption on the thermal emission of the accretion disc and the broad-line region (BLR). For the first time, we compute here the pair-production opacities in the GeV range produced by a realistic BLR accounting for the radial stratification and radiation anisotropy. Using photoionization modelling with the CLOUDY code, we calculate a series of BLR models of different sizes, geometries, cloud densities, column densities and metallicities. The strongest emission features in the model BLR are Ly$\alpha$ and HeII Ly$\alpha$. Contribution of recombination continua is smaller, especially for hydrogen, because Ly continuum is efficiently trapped inside the large optical depth BLR clouds and converted to Lyman emission lines and higher-order recombination continua. The largest effects on the gamma-ray opacity are produced by the BLR geometry and localization of the gamma-ray source. We show that when the gamma-ray source moves further from the central source, all the absorption details move to higher energies and the overall level of absorption drops because of decreasing incidence angles between the gamma-rays and BLR photons. The observed positions of the spectral breaks can be used to measure the geometry and the location of the gamma-ray emitting region relative to the BLR. Strong dependence on geometry means that the soft photons dominating the pair-production opacity may be actually produced by a different population of BLR clouds than the bulk of the observed broad line emission.