“…where ξ e is the fraction of the kinetic energy dissipated at the shock front channeled into the acceleration of supra-thermal electrons, A is the surface area of the relic, n e, d is the downstream electron density, T d is the downstream electron temperature, B is the magnetic field strength, B CMB is the field strength equivalent to the Cosmic Microwave Background energy density, B CMB = 3.24 (1 + z) 2 µG, and Ψ(M, T d ) comprises all Mach number dependencies. For the relic, we adopt n e, d = 1 × 10 −3 cm −3 and T d = 8 keV (Trasatti et al 2015;Ge et al 2020). The other measured values are A = 0.8 Mpc 2 , α = −1.07, and Ψ(M) = 0.76 (assuming a shock of M = 5.4).…”