# Halo Spin from Primordial Inner Motions

## TL;DR

This paper introduces the SPIM framework, emphasizing the role of primordial inner motions in galaxy spin, providing a more accurate and direct prediction method than traditional tidal-torque theory, with implications for understanding halo angular momentum.

## Contribution

The paper presents the SPIM concept, highlighting the importance of inner velocity fields over tidal fields in galaxy spin formation, and demonstrates its advantages over the traditional TTT approach.

## Key findings

- SPIM offers a more direct prediction of halo spins than TTT.
- Protohaloes have non-ellipsoidal shapes and retain velocity dispersion.
- Halo spin can be viewed as a sum of random contributions.

## Abstract

The standard explanation for galaxy spin starts with the tidal-torque theory (TTT), in which an ellipsoidal dark-matter protohalo, which comes to host the galaxy, is torqued up by the tidal gravitational field around it. We discuss a complementary picture, using the relatively familiar velocity field, instead of the tidal field, whose intuitive connection to the surrounding, possibly faraway matter arrangement is more obscure. In this 'spin from primordial inner motions' (SPIM) concept, implicit in TTT derivations but not previously emphasized, the angular momentum from the gravity-sourced velocity field inside a protohalo largely cancels out, but has some excess from the aspherical outskirts. At first, the net spin scales according to linear theory, a sort of comoving conservation of familiar angular momentum. Then, at collapse, it is conserved in physical coordinates. Small haloes are then typically subject to secondary exchanges of angular momentum. The TTT is useful for analytic estimates. But a literal interpretation of the TTT is inaccurate in detail, without some implicit concepts about smoothing of the velocity and tidal fields. This could lead to misconceptions, for those first learning about how galaxies come to spin. Protohaloes are not perfectly ellipsoidal and do not uniformly torque up, as in a naive interpretation of the TTT; their inner velocity fields retain substantial dispersion. Furthermore, quantitatively, given initial conditions and protohalo boundaries, SPIM is more direct and accurate than the TTT to predict halo spins. We also discuss how SPIM applies to rotating filaments, and the relation between halo mass and spin, in which the total spin of a halo can be thought of as a sum of random contributions.