Gravitational Lensing Simulations I : Covariance Matrices and Halo
  Catalogues
  Gravitational lensing surveys have now become large and precise enough that
the interpretation of the lensing signal has to take into account an increasing
number of theoretical limitations and observational biases. Since the lensing
signal is the strongest at small angular scales, only numerical simulations can
reproduce faithfully the non-linear dynamics and secondary effects at play.
This work is the first of a series in which all gravitational lensing
corrections known so far will be implemented in the same set of simulations,
using realistic mock catalogues and non-Gaussian statistics. In this first
paper, we present the TCS simulation suite and compute basic statistics such as
the second and third order convergence and shear correlation functions. These
simple tests set the range of validity of our simulations, which are resolving
most of the signals at the sub-arc minute level (or $\ell \sim 10^4$). We also
compute the non-Gaussian covariance matrix of several statistical estimators,
including many that are used in the Canada France Hawaii Telescope Lensing
Survey (CFHTLenS). From the same realizations, we construct halo catalogues,
computing a series of properties that are required by most galaxy population
algorithms. These simulation products are publicly available for download.
