The impact of plasma instability cooling on intergalactic magnetic field constraints in GeV cascades for optimized instability cooling parameters
Electromagnetic cascades are initiated by TeV gamma rays propagating through the intergalactic medium (IGM), and they can be used to constrain the weak intergalactic magnetic field (IGMF) in cosmic voids. Primary TeV photons produce electrons and positrons through electromagnetic pair production, which can be deflected out of the line-of-sight to the observer by IGMF. In addition, electron-positron pairs can perturb the IGM, triggering plasma instabilities that can cool down the pairs before they upscatter cosmic background photons to GeV energies via inverse Compton (IC) scattering. In this work, we investigate the influence of plasma instabilities on the cascade spectrum by introducing a parameterized instability model within the publicly available Monte Carlo framework CRPropa 3.2 in the presence of IGMF. We first determine the instability parameters that best reproduce the Fermi-LAT observations in the absence of any IGMF. We then use extended-emission observations within the observer's field of view, including the effects of the IGMF, to constrain the IGMF strength in the presence of the corresponding best-fit instability-cooling parameters, based on the Fermi-LAT spectral observations of the blazar 1ES 0229+200. We find that plasma instabilities with a characteristic length scale of $120$ kpc and a spectral index of $\alpha=-0.5$ are consistent with the observed photon spectra. We also find that the fit of the observed data is improved by the presence of an IGMF: we obtain an IGMF lower limit of $B \gtrsim 2.7 \times 10^{-17}$ G for an observer field of view $1.0^\circ$.