The Tidal Torque Theory Revisited. I. Protohalo Angular Momentum

TL;DR

This paper revisits the tidal torque theory for dark matter halo angular momentum, providing a new analytic derivation that aligns well with simulations and sets the stage for future analysis of halo rotation.

Contribution

The paper introduces a fully analytic, simplified expression for protohalo angular momentum within the peak model, improving interpretability and applicability over previous numerical methods.

Findings

Analytic expression for protohalo angular momentum derived.

Model predictions agree with cosmological simulation results.

Lays groundwork for analyzing halo rotational properties in future work.

Abstract

In the tidal-torque theory, the angular momentum (AM) of dark matter halos arises from the tidal torque suffered by aspherical collapsing patches due to surrounding mass fluctuations. This theory was implemented in the peak model where protohalos are ellipsoidal. However, the adopted delimitation of these objects was doubtful and the protohalo AM was calculated numerically, which complicated the interpretation of the result and compromised its applicability. In addition, the AM of final halos was derived without taking into account non-linear effects. Here, we re-derive the protohalo AM in the peak model, delimiting ellipsoids in the usual natural way and following a novel fully analytic approach that leads to a very simple and practical expression. The predicted AM is shown to fully agree with the results of cosmological simulations. In Paper II, we will apply this model to infer the rotational properties of relaxed halos, accounting for shell-crossing and major mergers.