Smoothing Algorithms and High‐Order Singularities in Gravitational Lensing

We propose a new smoothing method for obtaining surface densities fromdiscrete particle positions from numerical simulations. This is an essentialstep for many applications in gravitational lensing. This method is based onthe ``scatter'' interpretation of the discrete density field in the SmoothedParticle Hydrodynamics. We use Monte Carlo simulations of uniform densityfields and one isothermal ellipsoid to empirically derive the noise properties,and best smoothing parameters (such as the number of nearest neighbors used). Acluster from high-resolution simulations is then used to assess the reality ofhigh-order singularities such as swallowtails and butterflies in caustics,which are important for the interpretation of substructures in gravitationallenses. We also compare our method with the Delaunay tesselation fieldestimator using the galaxy studied by Bradac et al. (2004), and find goodagreements. We show that higher order singularities are not only connected withbound subhaloes but also with the satellite streams. However, the presence ofhigh-order singularities are sensitive to not only the fluctuation amplitude ofthe surface density, but also the detailed form of the underlying smoothlensing potential (such as ellipticity and external shear).