Explaining the cuspy dark matter halo by Landau-Ginzburg theory

TL;DR

This paper applies Landau-Ginzburg theory to explain the universal cuspy density profile of dark matter halos, proposing a statistical mechanics approach that reproduces the observed NFW profile without additional assumptions.

Contribution

It introduces a novel application of Landau-Ginzburg theory to dark matter halos, linking fluctuations in free energy to the universal density cusp.

Findings

Reproduces the $r^{-1}$ cusp of dark matter halos

Supports the use of statistical mechanics in self-gravitating systems

Aligns with observed power spectrum behavior near cluster scales

Abstract

Twenty three years ago, cosmological N-body simulations revealed quasi-universal NFW dark matter halos, whose physical origin is still unclear. This work tries to solve this issue by Landau-Ginzburg (LG) theory in equilibrium statistical mechanics. We replace the order parameter in LG theory by density and consider the dark matter halos as fluctuations from the equilibrium state of the background, which can be the main halos for the subhalos, or the homogeneous and isotropic Universe for the galaxy cluster halos. With the assumption that the fluctuations of Helmholtz free energy depend mainly on the density and its gradient, which is shown to be consistent with the behavior of the power spectrum near the cluster scale, we can easily obtain the universal $r^{-1}$ cusp of the equilibrium dark matte halo without other requirements. This work strongly suggests that more studies should be done for the self-gravitating systems by statistical mechanics.