Self-Similar Spherical Collapse with Tidal Torque

TL;DR

This paper extends the self-similar spherical collapse model by incorporating tidal torque to better understand dark matter halo structures, aligning analytical results with empirical N-body simulation profiles.

Contribution

It introduces a generalized analytic model including tidal torque effects, providing insights into halo density profiles across different scales.

Findings

Angular momentum influences small-scale density profiles.

Small-scale density profile depends on angular momentum change rate.

Intermediate and outer density profiles follow specific power laws.

Abstract

N-body simulations have revealed a wealth of information about dark matter halos however their results are largely empirical. Using analytic means, we attempt to shed light on simulation results by generalizing the self-similar secondary infall model to include tidal torque. In this first of two papers, we describe our halo formation model and compare our results to empirical mass profiles inspired by N-body simulations. Each halo is determined by four parameters. One parameter sets the mass scale and the other three define how particles within a mass shell are torqued throughout evolution. We choose torque parameters motivated by tidal torque theory and N-body simulations and analytically calculate the structure of the halo in different radial regimes. We find that angular momentum plays an important role in determining the density profile at small radii. For cosmological initial conditions, the density profile on small scales is set by the time rate of change of the angular momentum of particles as well as the halo mass. On intermediate scales, however, $\rho\propto r^{-2}$, while $\rho\propto r^{-3}$ close to the virial radius.