In this paper we introduce the concept of Lateral Trigger Probability (LTP)
function, i.e., the probability for an extensive air shower (EAS) to trigger an
individual detector of a ground based array as a function of distance to the
shower axis, taking into account energy, mass and direction of the primary
cosmic ray. We apply this concept to the surface array of the Pierre Auger
Observatory consisting of a 1.5 km spaced grid of about 1600 water Cherenkov
stations. Using Monte Carlo simulations of ultra-high energy showers the LTP
functions are derived for energies in the range between 10^{17} and 10^{19} eV
and zenith angles up to 65 degs. A parametrization combining a step function
with an exponential is found to reproduce them very well in the considered
range of energies and zenith angles. The LTP functions can also be obtained
from data using events simultaneously observed by the fluorescence and the
surface detector of the Pierre Auger Observatory (hybrid events). We validate
the Monte-Carlo results showing how LTP functions from data are in good
agreement with simulations.
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