A robust determination of halo environment in the cosmic field

A number of methods for studying the large-scale cosmic matter distribution exist in the literature. One particularly common method employed to define the cosmic web is to examine the density, velocity or potential field. Such methods are advantageous since a Hessian matrix can be constructed whose eigenvectors (and eigenvalues) indicate the principal directions (and strength) of local collapse or expansion. Technically this is achieved by diagonalizing the Hessian matrix using a fixed finite grid. The resultant large-scale structure quantification is thus inherently limited by the grid's finite resolution. Here, we overcome the obstacle of finite grid resolution by introducing a new method to determine halo environment using an adaptive interpolation which is more robust to resolution than the typical "Nearest Grid Point" (NGP) method. Essentially instead of computing and diagonalizing the Hessian matrix once for the entire grid, we suggest doing so once for each halo or galaxy in question. We examine how the eigenvalues and eigenvector direction's computed using our algorithm and the NGP method converge for different grid resolutions, finding that our new method is convergent faster. Namely changes of resolution have a much smaller effect than in the NGP method. We therefore suggest this method for future use by the community.