The electrostatic instability for realistic pair distributions in blazar/EBL cascades

TL;DR

This study investigates the electrostatic instability in blazar-induced pair beams in the intergalactic medium, showing that realistic pair distributions affect growth rates and energy dissipation, with implications for gamma-ray observations.

Contribution

It provides a combined analytical and PIC simulation analysis of electrostatic instability considering realistic pair distributions, revealing their impact on beam energy loss.

Findings

Finite angular spread reduces growth rate at oblique angles

Beam loses about 1% of energy in simulations

Electrostatic instability may dissipate beam energy faster than inverse-Compton scattering

Abstract

This work revisits the electrostatic instability for blazar-induced pair beams propagating through IGM with the methods of linear analysis and PIC simulations. We study the impact of the realistic distribution function of pairs resulting from interaction of high-energy gamma-rays with the extragalactic background light. We present analytical and numerical calculations of the linear growth rate of the instability for arbitrary orientation of wave vectors. Our results explicitly demonstrate that the finite angular spread of the beam dramatically affects the growth rate of the waves, leading to fastest growth for wave vectors quasi-parallel to the beam direction and a growth rate at oblique directions that is only by a factor of 2-4 smaller compared to the maximum. To study the non-linear beam relaxation, we performed PIC simulations that take into account a realistic wide-energy distribution of beam particles. The parameters of the simulated beam-plasma system provide an adequate physical picture that can be extrapolated to realistic blazar-induced pairs. In our simulations the beam looses only 1\% percent of its energy, and we analytically estimate that the beam would lose its total energy over about $100$ simulation times. Analytical scaling is then used to extrapolate to the parameters of realistic blazar-induced pair beams. We find that they can dissipate their energy slightly faster by the electrostatic instability than through inverse-Compton scattering. The uncertainties arising from, e.g., details of the primary gamma-ray spectrum are too large to make firm statements for individual blazars, and an analysis based on their specific properties is required.