On determining the shape of matter distributions

TL;DR

This paper critically examines methods for determining the shape of matter distributions in cosmological simulations, identifying biases in common techniques and proposing an improved method using ellipsoidal shells without weighting.

Contribution

It introduces a bias-free method for local shape determination of matter distributions using ellipsoidal shells and subhalo removal, improving accuracy over previous techniques.

Findings

Common methods with weighted volumes lead to biased shape measurements.

Using unweighted ellipsoidal shells reduces bias and preserves shape details.

Removing subhalos enhances the accuracy of shape determination.

Abstract

A basic property of objects, like galaxies and halos that form in cosmological structure formation simulations, is their shape. Here, we critically investigate shape determination methods that are commonly used in the literature. It is found that using an enclosed integration volume and weight factors r^{-2} and r_{ell}^{-2} (elliptical radius) for the contribution of each particle or volume element in the shape tensor leads to biased axis ratios and smoothing of details when calculating the local shape as a function of distance from the center. To determine the local shape of matter distributions as a function of distance for well resolved objects (typically more than O(10^4) particles), we advocate a method that (1) uses an ellipsoidal shell (homoeoid) as an integration volume without any weight factors in the shape tensor and (2) removes subhalos.