The wavefront of the radio signal emitted by cosmic ray air showers

Analyzing measurements of the LOPESantenna array together with corresponding CoREAS simulations for more than 300 measured events with energy above 1017 eV and zenith angles smaller than 45o, we find that the radio wavefrontof cosmic-ray air showersis of approximately hyperbolic shape. The simulations predict a slightly steeper wavefronttowards East than towards West, but this asymmetry is negligible against the measurement uncertaintiesof LOPES. At axis distances ?50 m, the wavefrontcan be approximated by a simple cone. According to the simulations, the cone angle is clearly correlated with the showermaximum. Thus, we confirm earlier predictions that arrival time measurements can be used to study the longitudinal showerdevelopment, but now using a realistic wavefront. Moreover, we show that the hyperbolic wavefrontis compatible with our measurement, and we present several experimental indications that the cone angle is indeed sensitive to the showerdevelopment. Consequently, the wavefrontcan be used to statistically study the primary composition of ultra-high energy cosmic rays. At LOPES, the experimentally achieved precision for the showermaximum is limited by measurement uncertaintiesto approximately 140 g/c 2. But the simulations indicate that under better conditions this method might yield an accuracy for the atmospheric depth of the showermaximum, Xmax, better than 30 g/c 2. This would be competitive with the established air-fluorescence and air-Cherenkov techniques, where the radio technique offers the advantage of a significantly higher duty-cycle. Finally, the hyperbolic wavefrontcan be used to reconstruct the showergeometry more accurately, which potentially allows a better reconstruction of all other showerparameters, too.