The center of lateral iso-density contours for inclined cosmic air showers

The horizontal lateral density of a cosmic air shower with a non-zero zenith angle is asymmetric. The asymmetry consist of a stretching of the iso-density contours to ellipses and to a shift of the center of the elliptic contours with respect to the core of the shower. The shift is caused by atmospheric attenuation. The modeling of the attenuation results in an equation for the shift as a function of zenith angle and the size of the iso-density contours. A more accurate equation is obtained by investigating the shift in lateral densities of simulated showers. It is shown how the shift can be incorporated in an elliptic lateral density function. A linear approximation for the shift allows for an analytical solution for the shifted elliptic density. Its predictions for the polar variations of the density are compared with data of simulated showers.