The Halo Boltzmann Equation

TL;DR

This paper derives an effective Boltzmann equation for dark matter halos that captures their clustering behavior and velocity bias, providing a new theoretical framework aligned with recent simulation results.

Contribution

It introduces a novel halo Boltzmann equation that models halo clustering and velocity bias, advancing theoretical understanding of large-scale structure formation.

Findings

The halo Boltzmann equation encodes a biased gravitational force.

It explains the velocity bias of virialized halos.

The framework aligns with recent N-body simulation observations.

Abstract

Dark matter halos are the building blocks of the universe as they host galaxies and clusters. The knowledge of the clustering properties of halos is therefore essential for the understanding of the galaxy statistical properties. We derive an effective halo Boltzmann equation which can be used to describe the halo clustering statistics. In particular, we show how the halo Boltzmann equation encodes a statistically biased gravitational force which generates a bias in the peculiar velocities of virialized halos with respect to the underlying dark matter, as recently observed in N-body simulations.