A closer look at the electromagnetic signatures of Bethe-Heitler pair production process in blazars

Abstract The “twin birth” of a positron and an electron by a photon in the presence of a nucleus, known as Bethe-Heitler pair production, is a key process in astroparticle physics. The Bethe-Heitler process offers a way of channeling energy stored in a population of relativistic protons (or nuclei) to relativistic pairs with extended distributions. Contrary to accelerated leptons, whose maximum energy is limited by radiative losses, the maximal energy of pairs is determined by the kinematics of the process and can be as high as the parent proton energy. We take a closer look at the features of the injected pair distribution, and provide a novel empirical function that describes the spectrum of pairs produced by interactions of single-energy protons with single-energy photons. The function is the kernel of the Bethe-Heitler pair production spectrum that replaces a double numerical integration involving the complex differential cross section of the process, and can be easily implemented in numerical codes. We further examine under which conditions Bethe-Heitler pairs produced in blazar jets can emit γ -ray photons via synchrotron radiation, thus providing an alternative to the inverse Compton scattering process for high-energy emission in jetted active galactic nuclei. For this purpose, we create 36 numerical models using the code ATHE ν A optimized so that the Bethe-Heitler synchrotron emission dominates their γ -ray emission. After taking into consideration the broadband spectral characteristics of the source, the jet energetics, and the properties of radiation fields present in the blazar environment, we conclude that γ -rays in high-synchrotron-peaked blazars are unlikely to be produced by Bethe-Heitler pairs, because the emitting region is found to be opaque in photon-photon pair production at photon energies ≳ 10 GeV. On the contrary, γ -ray spectra of low-synchrotron-peaked blazars may arise from Bethe-Heitler pairs in regions of the jet with typical transverse size ∼ 10 15 – 10 16 cm and co-moving magnetic field 50 – 500 G. For such cases, an external thermal target photon field with temperatures T ∼ 4 · 10 2 – 6 · 10 3 K is needed. The latter values could point to the dusty torus of the AGN. Interestingly, a Bethe-Heitler-dominated high-energy component is mostly found in models of intermediate-synchrotron peaked blazars, for a wide range of magnetic fields and source radii.