Small-Scale Anisotropies of Cosmic Rays from Relative Diffusion

TL;DR

This paper investigates how local turbulent magnetic fields cause small-scale anisotropies in cosmic ray arrival directions, linking these patterns to relative diffusion properties through a new formalism and analytic extension.

Contribution

It introduces a formalism and analytic model connecting small-scale cosmic ray anisotropies to relative diffusion in turbulent magnetic fields.

Findings

Small-scale anisotropies are related to properties of relative diffusion.

A formalism for inferring power spectra from simulations is developed.

An analytic extension of the diffusion equation accounts for observed anisotropies.

Abstract

The arrival directions of multi-TeV cosmic rays show significant anisotropies at small angular scales. It has been argued that this small-scale structure can naturally arise from cosmic ray scattering in local turbulent magnetic fields that distort a global dipole anisotropy set by diffusion. We study this effect in terms of the power spectrum of cosmic ray arrival directions and show that the strength of small-scale anisotropies is related to properties of relative diffusion. We provide a formalism for how these power spectra can be inferred from simulations and motivate a simple analytic extension of the ensemble-averaged diffusion equation that can account for the effect.