Perturbative Analysis of Adaptive Smoothing Methods in Quantifying Large-Scale Structure

摘要

Smoothing operation to make continuous density field from observed point-likedistribution of galaxies is crucially important for topological ormorphological analysis of the large-scale structure, such as, the genusstatistics or the area statistics (equivalently the level crossing statistics).It has been pointed out that the adaptive smoothing filters are more efficienttools to resolve cosmic structures than the traditional spatially fixedfilters. We study weakly nonlinear effects caused by two representativeadaptive methods often used in smoothed hydrodynamical particle (SPH)simulations. Using framework of second-order perturbation theory, we calculatethe generalized skewness parameters for the adaptive methods in the case ofinitially power-law fluctuations. Then we apply the multidimensional Edgeworth expansion method and investigateweakly nonlinear evolution of the genus statistics and the area statistics.Isodensity contour surfaces are often parameterized by the volume fraction ofthe regions above a given density threshold. We also discuss thisparameterization method in perturbative manner.