Probing Intergalactic Magnetic Fields with Simulations of Electromagnetic Cascades

We determine the effect of intergalactic magnetic fields on the distribution of high energy gamma rays by performing three-dimensional Monte Carlo simulations of the development of gamma-ray-induced electromagnetic cascades in the magnetized intergalactic medium. We employ the so-called 'Large Sphere Observer' method to efficiently simulate blazar gamma ray halos. We study magnetic fields with a Batchelor spectrum and with maximal left- and right-handed helicities. We also consider the case of sources whose jets are tilted with respect to the line of sight. We verify the formation of extended gamma ray halos around the source direction, and observe spiral-like patterns if the magnetic field is helical. We apply the $Q$-statistics to the simulated halos to extract their spiral nature and also propose an alternative method, the $S$-statistics. Both methods provide a quantative way to infer the helicity of the intervening magnetic fields from the morphology of individual blazar halos for magnetic field strengths $B \gtrsim 10^{-15}\,{\rm G}$ and magnetic coherence lengths $L_{\rm c} \gtrsim 100\,{\rm Mpc}$. We show that the $S$-statistics has a better performance than the $Q$-statistics when assessing magnetic helicity from the simulated halos.