Gamma-ray halos as a measure of intergalactic magnetic fields: a classical moment problem

TL;DR

This paper introduces a novel method to analyze gamma-ray halos caused by intergalactic magnetic fields, modeling magnetic deflections as a diffusion process and solving the resulting classical moment problem to infer magnetic field properties.

Contribution

It presents a new approach using diffusion equations and Pade approximations to calculate and reconstruct gamma-ray halos for isotropic sources, aiding magnetic field measurements.

Findings

Method successfully models gamma-ray halos as a diffusion process.

Reconstruction of angular distributions via classical moment problem.

Provides a practical solution using Pade approximations.

Abstract

The presence of weak intergalactic magnetic fields can be studied by their effect on electro-magnetic cascades induced by multi-TeV gamma-rays in the cosmic radiation background. Small deflections of secondary electrons and positrons as the cascade develops extend the apparent size of the emission region of distant TeV gamma-ray sources. These gamma-ray halos can be resolvable in imaging atmospheric Cherenkov telescopes and serve as a measure of the intergalactic magnetic field strength and coherence length. We present a method of calculating the gamma-ray halo for isotropically emitting sources by treating magnetic deflections in the cascade as a diffusion process. With this ansatz the moments of the halo follow from a set of simple diffusion-cascade equations. The reconstruction of the angular distribution is then equivalent to a classical moment problem. We present a simple solution using Pade approximations of the moment's generating function.