Compton scattering of electrons in the intergalactic medium

This paper investigates the distribution and implications of cosmic ray electrons within the intergalactic medium (IGM). Utilizing a synthesis model of the extragalactic background, we evolve the spectrum of Compton-included cosmic rays. The energy density distribution of cosmic ray electrons peaks at redshift $z \approx2$, and peaks in the $\sim$MeV range. The fractional contribution of cosmic ray pressure to the general IGM pressure progressively increases toward lower redshift. At mean density, the ratio of cosmic ray electron to thermal pressure in the IGM $P_{\rm CRe} / P_{\rm th}$ is 0.3% at $z=2$, rising to 1.0% at $z=1$, and 1.8% at $z=0.1$ (considering only the cosmic rays produced locally by Compton scattering). We compute the linear Landau damping rate of plasma oscillations in the IGM caused by the $\sim$MeV cosmic ray electrons, and find it to be of order $\sim 10^{-6}\,\rm s^{-1}$ for wavenumbers $1.2\lesssim ck/\omega_{\rm p}\lesssim 5$ at $z=2$ and mean density (where $\omega_{\rm p}$ is the plasma frequency). This strongly affects the fate of TeV $e^+e^-$ pair beams produced by blazars, which are potentially unstable to oblique instabilities involving plasma oscillations with wavenumber $ck/\omega_{\rm p}\approx\sec\theta$ ($\theta$ being the angle between the beam and wave vector). Linear Landau damping is at least thousands of times faster than either pair beam instability growth or collisional effects; it thus turns off the pair beam instability except for modes with very small $\theta$ ($ck/\omega_{\rm p}\rightarrow 1$, where linear Landau damping is kinematically suppressed). This leaves open the question of whether the pair beam instability is turned off entirely, or can still proceed via the small-$\theta$ modes.