2 00 1 Implication of Ω m through the Morphological Analysis of Weak Lensing Fields

We apply the morphological descriptions of two-dimensional contour map, the so-called Minkowski functionals (the area fraction, circumference, and Euler characteristics), to the convergence field κ(θ) of the large-scale structure reconstructed from the shear map produced by the ray-tracing simulations. The perturbation theory of structure formation has suggested that the non-Gaussian features on the Minkowski functionals with respect to the threshold in the weakly nonlinear regime are induced by the three skewness parameters of κ that are sensitive to the density parameter of matter, Ωm. We show that, in the absence of noise due to the intrinsic ellipticities of source galaxies with which the perturbation theory results can be recovered, the accuracy of Ωm determination is improved by ∼ 20% using the Minkowski functionals compared to the conventional method of using the direct measure of skewness. Subject headings: cosmology: theory — cosmology: gravitational lensing — methods: numerical