Dark Matter Angular Momentum Profile from the Jeans Equation

TL;DR

This paper introduces a modified Jeans equation incorporating a rotational term to model dark matter angular momentum profiles, aligning well with simulation data and revealing new relationships with velocity anisotropy.

Contribution

It proposes a perturbed Jeans equation with a rotational term and establishes a novel connection between angular momentum profiles and velocity anisotropy in dark matter structures.

Findings

The rotational term is proportional to the mass distribution.

The radial angular momentum profile matches simulation results.

A new link between angular momentum and velocity anisotropy is found.

Abstract

Cosmological simulations of dark matter structures have shown that the equilibrated dark matter structures have a fairly small angular momentum. It appears from these N-body simulations that the radial profile of the angular momentum has an almost universal behavior, even if the different dark matter structures have experienced very different formation and merger histories. We suggest a perturbed Jeans equation, which includes a rotational term. This is done under a reasonable assumed form of the change in the distribution function. By conjecturing that the (new) subdominant rotation term must be proportional to the (old) dominant mass term, we find a clear connection, which is in rather good agreement with the results of recent high resolution simulations. We also present a new connection between the radial profiles of the angular momentum and the velocity anisotropy, which is also in fair agreement with numerical findings. Finally we show how the spin parameter $\lambda$ increases as a function of radius.