Evolution of first-interaction second-harmonic anisotropy in cosmic-ray air showers

RESUMO

The longitudinal evolution of second-harmonic anisotropy inherited from the first interaction in extensive air showers is investigated with CORSIKA simulations. Events with large initial anisotropy are selected. Second-harmonic observables are evaluated separately using the coordinate and momentum azimuths at several atmospheric depths and compared with their corresponding initial harmonic orientations. More than 84% of the initial second-harmonic signal is attenuated within the first 20 g cm$^{-2}$ of shower development. In coordinate space, the second-harmonic correlation with the initial orientation persists to ground level at approximately 0.09% of its initial magnitude. This residual is evaluated against a matched source-isotropized reference, constructed for each selected event by independently randomizing the azimuths of the first-interaction final-state particles and simulating the shower under identical atmospheric conditions. The positive coordinate-space ensemble-mean difference at ground level is statistically resolved, and the two samples show little event-level separation. In momentum space, a weak ensemble-level residual remains at 200 g cm$^{-2}$, and the original and source-isotropized signals become statistically indistinguishable by 300 g cm$^{-2}$ and remain so at ground level.