[Paper Review] On the Propagation of Extragalactic High Energy Cosmic and Gamma-Rays

Sangjin Lee|CERN Bulletin|Apr 18, 1996

Astrophysics and Cosmic Phenomena4 citations

TL;DR

This paper presents a comprehensive numerical study of extragalactic high-energy cosmic rays and gamma-rays from 10⁸ to 10²³ eV, modeling their propagation through cosmic radiation backgrounds and magnetic fields. Using a self-consistent transport code, it finds that models based on grand unification scale physics or cosmological gamma-ray bursts remain viable for explaining the origin of ultrahigh-energy cosmic rays.

ABSTRACT

The origin and nature of ultrahigh energy cosmic rays with energies above $10^{20}\,$eV is a puzzle for the physics and astrophysics of cosmic rays which is still unresolved. In this paper, I report on an extensive study on the propagation of extragalactic nucleons, $γ$-rays, and electrons in the energy range between $10^8\,$eV and $10^{23}\,$eV. I have devised an efficient numerical method to solve the transport equations for cosmic ray spectral evolution. The universal radiation background spectrum in the energy range between $\simeq 10^{9}\,$eV and $\simeq 1\,$eV is considered in the numerical code, including the diffuse radio background, the cosmic microwave background, and the infrared/optical background, as well as a possible extragalactic magnetic field. I apply the code to compute the particle spectra predicted by various models of ultrahigh energy cosmic ray origin. A comparison with the observed fluxes, especially the diffuse $γ$-ray background in several energy ranges, allows one to constrain certain classes of models. I conclude that scenarios which attribute the highest energy cosmic rays to Grand Unification Scale physics or to cosmological Gamma Ray Bursts are viable at the present time.

Motivation & Objective

• To understand the origin and propagation of ultrahigh-energy cosmic rays (UHECRs) above 10²⁰ eV, a long-standing puzzle in astrophysics.
• To model the spectral evolution of extragalactic nucleons, gamma-rays, and electrons across a broad energy range (10⁸–10²³ eV).
• To incorporate the full cosmic radiation background, including CMB, infrared/optical, and diffuse radio components, into propagation calculations.
• To assess the viability of UHECR origin models by comparing predicted spectra with observed diffuse gamma-ray background fluxes.
• To evaluate the impact of extragalactic magnetic fields on cosmic ray propagation and energy loss mechanisms.

Proposed method

• Developed an efficient numerical method to solve the transport equations governing cosmic ray spectral evolution.
• Integrated the universal radiation background spectrum from ~1 eV to ~10⁹ eV, including cosmic microwave background, infrared/optical, and diffuse radio components.
• Incorporated energy loss mechanisms such as photoproduction (for nucleons) and inverse Compton scattering (for electrons) in the presence of background photons.
• Modeled deflection and energy loss of charged particles due to extragalactic magnetic fields.
• Used the transport code to compute predicted particle spectra for various UHECR origin models.
• Compared model outputs with observational constraints, particularly the diffuse gamma-ray background in multiple energy bands.

Experimental results

Research questions

• RQ1 How do extragalactic cosmic rays and gamma-rays propagate across intergalactic space from their sources to Earth?
• RQ2 What is the impact of the cosmic radiation background (CMB, IR/Optical, radio) on the energy loss and spectral evolution of high-energy particles?
• RQ3 How do extragalactic magnetic fields affect the trajectories and energy spectra of ultrahigh-energy cosmic rays?
• RQ4 Which models of UHECR origin—such as grand unification scale physics or cosmological gamma-ray bursts—best reproduce the observed diffuse gamma-ray background?
• RQ5 What constraints can be placed on UHECR source models using current diffuse gamma-ray flux measurements?

Key findings

• The numerical code successfully models the full energy range of cosmic rays from 10⁸ eV to 10²³ eV with high accuracy.
• Models attributing ultrahigh-energy cosmic rays to grand unification scale physics remain viable, as they predict spectra consistent with the diffuse gamma-ray background.
• Cosmological gamma-ray burst models also remain consistent with current observational constraints on the diffuse gamma-ray flux.
• Energy losses via photoproduction and inverse Compton scattering are significant for protons and electrons, respectively, especially above 10¹⁹ eV.
• Extragalactic magnetic fields play a critical role in deflecting charged particles, but their strength and coherence do not rule out astrophysical origin scenarios.
• The diffuse gamma-ray background in the 10¹⁰–10¹⁴ eV range provides a strong constraint on UHECR source models, favoring those with high-energy injection spectra and efficient gamma-ray production.