Cosmological $\gamma$-$\gamma$ Pair-Production Background

Abstract

The origin of positrons is one of the unsolved puzzles in astrophysics as the majority of sources are still unidentified. The Cosmic Photon Background (CPB) is the isotropic radiation spanning the entire electromagnetic spectrum. Interactions of the CPB with itself may pose a promising source of positrons and secondary emission. We calculate the electron-positron pair production rate from the $\gamma$-$\gamma$ pair-production of the CPB with itself for redshifts $z \leq 10$, and determine the annihilation spectrum, Inverse Compton emission, and bremsstrahlung. The CPB is decomposed into a sum of gray body functions, of which each is being evolved according to source type luminosity functions and redshift. We compute the pair-production rate by integrating the angle- and energy-dependent cross section over the evolving CPB. The pairs produced at each redshift are then propagated towards $z=0$, taking into account a cosmological, intergalactic, energy loss function. The photon emission is calculated per redshift and then line-of-sight integrated towards a contribution of the Cosmic Gamma-Ray Background (CGB) today. The resulting pair-production emissivity increases steeply from $z=0$ of about $2 \times 10^{-36}$ to a peak of $1.8 \times 10^{-31}\,\mathrm{e^\pm\,cm^{-3}\,s^{-1}}$ at $z=2.7$, then declines again. This yields a total cosmic pair-production rate on the order of $10^{54}\,\mathrm{e^\pm\,s^{-1}}$ up to redshift $10$. The secondary emission of pairs experiencing Inverse Compton scattering off the CPB results in a sizable contribution to the CGB. The pairs from cosmological $\gamma$-$\gamma$ absorption provide a minimum level of secondary emission which needs to be taken into account for any CGB study. Especially in the range from 1 MeV to 1 GeV, this background can make up 20% of the total CGB emission and may substantially reduce the gap between MeV observations and models.