Asymmetry of the angular distribution of Cherenkov photons of extensive air showers induced by the geomagnetic field

The angular distribution of Cherenkov light in an air shower is closely linked to that of the shower electrons and positrons. As charged particles in extensive air showers are deflected by the magnetic field of the Earth, a deformation of the angular distribution of the Cherenkov light, that would be approximately symmetric about the shower axis if no magnetic field were present, is expected. In this work we study the variation of the Cherenkov light distribution as a function of the azimuth angle in the plane perpendicular to shower axis. It is found that the asymmetry induced by the geomagnetic field is most significant for early stages of shower evolution and for showers arriving almost perpendicular to the vector of the local geomagnetic field. Furthermore, it is shown that ignoring the azimuthal asymmetry of Cherenkov light might lead to a significant under- or overestimation of the Cherenkov light signal especially at sites where the local geomagnetic field is strong. Based on CORSIKA simulations, the azimuthal distribution of Cherenkov light is parametrized in dependence on the magnetic field component perpendicular to the shower axis and the local air density. This parametrization provides an efficient approximation for estimating the asymmetry of the Cherenkov light distribution for shower simulation and reconstruction in cosmic ray and gamma-ray experiments in which the Cherenkov signal of showers with energies above 1014 eV is observed.