Three-dimensional shapelets and an automated classification scheme for dark matter haloes

TL;DR

This paper extends shapelet formalism to three dimensions, enabling detailed analysis and automated classification of dark matter halo structures in cosmological simulations.

Contribution

It develops 3D shapelet equations for halo properties and introduces an automated classification scheme for dark matter halo shapes.

Findings

Shapelet decomposition effectively captures complex halo sub-structures

The method facilitates automated classification of halo morphologies

Potential for GPU acceleration of computations

Abstract

We extend the two-dimensional Cartesian shapelet formalism to d-dimensions. Concentrating on the three-dimensional case, we derive shapelet-based equations for the mass, centroid, root-mean-square radius, and components of the quadrupole moment and moment of inertia tensors. Using cosmological N-body simulations as an application domain, we show that three-dimensional shapelets can be used to replicate the complex sub-structure of dark matter halos and demonstrate the basis of an automated classification scheme for halo shapes. We investigate the shapelet decomposition process from an algorithmic viewpoint, and consider opportunities for accelerating the computation of shapelet-based representations using graphics processing units (GPUs).