Relaxation of Blazar Induced Pair Beams in Cosmic Voids

The stability properties of a low density ultra relativistic pair beam produced in the intergalactic medium by multi-TeV gamma-ray photons from blazars are analyzed. The problem is relevant for probes of magnetic field in cosmic voids through gamma-ray observations. In addition, dissipation of such beams could affect considerably the thermal history of the intergalactic medium and structure formation. We use a Monte Carlo method to quantify the properties of the blazar induced electromagnetic shower, in particular the bulk Lorentz factor and the angular spread of the pair beam generated by the shower, as a function of distance from the blazar itself. We then use linear and nonlinear kinetic theory to study the stability of the pair beam against the growth of electrostatic plasma waves, employing the Monte Carlo results for our quantitative estimates. We find that the fastest growing mode, like any perturbation mode with even a very modest component perpendicular to the beam direction, cannot be described in the reactive regime. Due to the effect of non-linear Landau damping, which suppresses the growth of plasma oscillations, the beam relaxation timescale is found significantly longer than the inverse Compton loss time. Finally, density inhomogeneities associated with cosmic structure induce loss of resonance between the beam particles and plasma oscillations, strongly inhibiting their growth. We conclude that relativistic pair beams produced by blazars in the intergalactic medium are stable on timescales long compared to the electromagnetic cascade’s. There appears to be little or no effect of pair-beams on the intergalactic medium.

💡 Research Summary

The paper addresses the stability of ultra‑relativistic, low‑density electron‑positron pair beams that are generated in the intergalactic medium (IGM) by multi‑TeV gamma‑ray photons emitted from blazars. Such beams are central to two major astrophysical questions: (i) they constitute the primary probe for measuring extremely weak magnetic fields in cosmic voids, and (ii) their possible dissipation could inject heat into the IGM, thereby influencing its thermal history and the formation of large‑scale structure.

Methodology
The authors first employ a Monte‑Carlo cascade simulation to characterize the electromagnetic shower initiated by a blazar photon. The simulation tracks pair production on the extragalactic background light (EBL) and the cosmic microwave background (CMB), yielding the bulk Lorentz factor (γ ≈ 10⁶–10⁷) and the angular spread (θ ≈ 10⁻⁶–10⁻⁵ rad) of the resulting pair beam as a function of distance from the source (0–300 Mpc). The beam density is found to be n_b ≈ 10⁻⁹–10⁻⁸ n_e, where n_e ≈ 10⁻⁷ cm⁻³ is the typical IGM electron density.

Next, the authors analyze the linear and nonlinear kinetic response of the IGM plasma to this beam. In the classic reactive regime, the growth rate of longitudinal (electrostatic) plasma waves scales as γ_growth ∝ (n_b/n_e)^{1/3} ω_p, where ω_p is the plasma frequency. However, the finite angular dispersion of the beam introduces a perpendicular wave‑vector component (k⊥) that pushes the system out of the reactive regime. The authors therefore adopt a non‑reactive, quasi‑linear treatment that includes nonlinear Landau damping (NLLD). NLLD removes energy from the wave as resonant particles are scattered out of phase, dramatically reducing the effective growth rate to γ_max ≈ 10⁻¹⁴ s⁻¹.

The paper also incorporates the impact of IGM density inhomogeneities, which are inevitable due to cosmic web filaments and voids. Typical fractional density fluctuations (δn/n ≈ 10⁻³–10⁻²) shift the plasma frequency locally, breaking the resonance condition k·v ≈ ω_p for the beam particles. This de‑phasing further suppresses wave growth, lowering the growth rate by another order of magnitude.

Timescale Comparison

• Plasma‑wave growth time: τ_plasma ≈ 1/γ_max ≈ 10⁸–10⁹ yr.
• Inverse‑Compton cooling time for the beam electrons: τ_IC ≈ 10⁶ yr (dominated by scattering off the CMB).
• Electromagnetic cascade completion time: τ_cascade ≈ 10⁶ yr.

Because τ_plasma is two to three orders of magnitude longer than τ_IC, the beam loses its energy to inverse‑Compton scattering long before any significant plasma instability can develop.

Conclusions
The authors conclude that blazar‑induced pair beams remain essentially stable over the lifetime of the cascade. Nonlinear Landau damping and the loss of resonance caused by IGM density fluctuations together prevent the rapid growth of electrostatic plasma waves. Consequently, the beams do not appreciably heat the IGM nor do they generate or amplify magnetic fields in cosmic voids. This result challenges earlier proposals that plasma instabilities could dominate the energy budget of the cascade and affect void magnetic‑field measurements.

Implications
The stability of the beams validates the use of gamma‑ray observations of distant blazars as a clean probe of intergalactic magnetic fields, without having to account for substantial plasma‑driven energy losses. It also suggests that the thermal history of the IGM is not significantly altered by these beams, and that any heating or magnetization must arise from other astrophysical processes (e.g., structure formation shocks, galactic outflows). Future work should focus on high‑resolution 3‑D plasma simulations and on cross‑checking with upcoming Cherenkov Telescope Array (CTA) data to refine constraints on void magnetic fields and to explore any residual, sub‑dominant plasma effects.