Zenith angle dependence of the cosmic ray rate as measured with Imaging air-Cherenkov Telescopes

The rate of extensive air-showers observed with imaging air-Cherenkov telescopes is zenith angle dependent. This effect originates from the increasing geometrical distance of the observed shower to the telescope with increasing zenith distance. This paper investigates how this alters the observed image and how this affects the trigger rate as a function of zenith angle. The discussed effects include the change of Cherenkov light yield, of absorption in the atmosphere, of photon density at the aperture and of the image size at the focal plane of the telescope. Based on a simple model for the atmosphere and well-known first principles on the development of extensive air-showers, the zenith angle dependence is expressed analytically. The assumption that most light is emitted from the shower core and mathematical approximations allow to derive an analytical expression describing the zenith angle dependence well with only three free parameters which are directly linked with the underlying physics. This suggests further investigations about how these fit parameters are linked to the properties of the atmosphere and the instrument. Using data published by the First G-APD Cherenkov Telescope, a good match of the fit functions with the data is obtained. For the trigger rate of cosmic rays, the obtained parameters are consistent with the naive expectation.