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This work revisits the electrostatic instability for blazar-induced pair beams propagating through the intergalactic medium (IGM) using linear analysis and PIC simulations. We study the impact of the realistic distribution function of pairs resulting from the 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 the 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 the fastest growth for wave vectors quasi-parallel to the beam direction and a growth rate at oblique directions that is only a factor of 2-4 smaller compared to the maximum. To study the nonlinear 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% of its energy, and we analytically estimate that the beam would lose its total energy over about 100 simulation times. An analytical scaling is then used to extrapolate 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.
The flat spectrum radio quasar 3C 279 is known to exhibit pronounced variability in the high-energy (100MeV < E < 100 GeV) gamma-ray band, which is continuously monitored with Fermi-LAT. During two periods of high activity in April 2014 and June 2015 target-of-opportunity observations were undertaken with the High Energy Stereoscopic System (H.E.S.S.) in the very-high-energy (VHE, E > 100 GeV) gamma-ray domain. While the observation in 2014 provides an upper limit, the observation in 2015 results in a signal with 8 : 7 sigma significance above an energy threshold of 66 GeV. No VHE variability was detected during the 2015 observations. The VHE photon spectrum is soft and described by a power-law index of 4.2 +/- 0.3. The H.E.S.S. data along with a detailed and contemporaneous multiwavelength data set provide constraints on the physical parameters of the emission region. The minimum distance of the emission region from the central black hole was estimated using two plausible geometries of the broad-line region and three potential intrinsic spectra. The emission region is confidently placed at r greater than or similar to 1 : 7 X 1017 cm from the black hole, that is beyond the assumed distance of the broad-line region. Time-dependent leptonic and lepto-hadronic one-zone models were used to describe the evolution of the 2015 flare. Neither model can fully reproduce the observations, despite testing various parameter sets. Furthermore, the H.E.S.S. data were used to derive constraints on Lorentz invariance violation given the large redshift of 3C 279.