Influence of plasma instabilities on the propagation of electromagnetic cascades from distant blazars

Abstract: The propagation of very-high-energy gamma-rays (VHEGRs) in the extragalactic space offers the opportunity to study astrophysical phenomena not reproducible in laboratories. In particular, the deviation from predictions of the observed photon flux from distant sources at the GeV energy scale still represents an open problem. Commonly, this deviation is interpreted as the result of the deflection out of the line of sight of the source of the cascade-produced charged leptons by weak magnetic fields present in the intergalactic medium (IGM). However, plasma instabilities could have an effect on the energy- and momentum-distribution of the secondary electrons and positrons, modifying the development of electromagnetic cascades. In this work, we study the influence of plasma instabilities on the energy spectrum of electromagnetic cascades through a parametric study, performed with the Monte Carlo code CRPropa. We parameterize plasma instabilities with an energy loss length normalisation $\lambda_0$ and a power law index $\alpha$ of its electron/positron energy dependence. We simulate photon spectra at Earth for different blazar scenarios and find that plasma instabilities can reproduce the suppression in the GeV-photon flux of real astrophysical sources, such as 1ES 0229+200, when the energy loss length of electrons/positrons at 1.0 TeV is $\lambda_0 \simeq 100\,\text{kpc}$ and $\alpha\simeq0$. The energy fraction lost by the secondary electron pairs due to the instability is estimated to be about $1\%$ over the typical interaction length of Inverse Compton scattering for these parameter values.