[Paper Review] HERMES: a Monte Carlo Code for the Propagation of Ultra-High Energy Nuclei

Manlio De Domenico, Haris Lyberis+1 more|arXiv (Cornell University)|Jul 16, 2013

Particle physics theoretical and experimental studies14 references3 citations

TL;DR

HERMES is a novel Monte Carlo code simulating the propagation of ultra-high energy (UHE) nuclei (10^16–10^22 eV) through extragalactic and Galactic magnetic fields, accounting for interactions with extragalactic background radiation. It enables realistic modeling of fluxes, GZK horizons, and arrival direction distributions, with a stable public release planned for community use in mass composition and energy spectrum analysis.

ABSTRACT

Although the recent experimental efforts to improve the observation of Ultra-High Energy Cosmic Rays (UHECRs) above $10^{18}$ eV, the origin and the composition of such particles is still unknown. In this work, we present the novel Monte Carlo code (HERMES) simulating the propagation of UHE nuclei, in the energy range between $10^{16}$ and $10^{22}$ eV, accounting for propagation in the intervening extragalactic and Galactic magnetic fields and nuclear interactions with relic photons of the extragalactic background radiation. In order to show the potential applications of HERMES for astroparticle studies, we estimate the expected flux of UHE nuclei in different astrophysical scenarios, the GZK horizons and we show the expected arrival direction distributions in the presence of turbulent extragalactic magnetic fields. A stable version of HERMES will be released in the next future for public use together with libraries of already propagated nuclei to allow the community to perform mass composition and energy spectrum analysis with our simulator.

Motivation & Objective

• To develop a flexible, modular Monte Carlo code for simulating the propagation of ultra-high energy (UHE) nuclei in magnetized cosmological environments.
• To model the effects of extragalactic and Galactic magnetic fields, including regular and turbulent components, on UHECR trajectories.
• To incorporate nuclear interactions with relic photons from the extragalactic background radiation (CMB, CIOB, URB) and secondary particle production.
• To estimate observable quantities such as fluxes, GZK horizons, and arrival direction distributions under various astrophysical scenarios.
• To provide a public, stable release of HERMES with pre-processed nuclei libraries for community-wide use in UHECR composition and spectrum analysis.

Proposed method

• HERMES uses a Friedmann-Robertson-Walker metric in a ΛCDM cosmological framework with tunable cosmological parameters.
• It models source injection via customizable luminosity, spectral index (γ), and redshift evolution (e.g., SFR, GRB, AGN, QSO, or (1+z)^m forms).
• The code incorporates the cosmic microwave background (CMB) at 2.725 K, the infrared/optical background (CIOB) via Finke et al. model, and the universal radio background (URB) with redshift evolution.
• Charged particle trajectories are computed via numerical integration of relativistic equations of motion, including synchrotron energy losses for light particles.
• Turbulent magnetic fields are simulated using a local step-by-step approach based on Giacalone & Jokipii (1999), with Kolmogorov-like statistics for r.m.s. strength and coherence length.
• Nuclear interactions are modeled via cross sections for photodisintegration and photoabsorption on relic photons, with secondary particle production.

Experimental results

Research questions

• RQ1 What is the expected flux of UHE nuclei at Earth under different astrophysical source distributions and evolution models?
• RQ2 How do GZK horizons vary for different nuclear species and source redshifts?
• RQ3 What are the predicted arrival direction distributions of UHECRs from nearby sources in the presence of turbulent extragalactic magnetic fields?
• RQ4 How do isotropic contaminations and source catalogues (e.g., 2MRS, SWIFT-BAT) affect the simulated sky maps of UHECRs?
• RQ5 To what extent can HERMES reproduce observed UHECR spectra and anisotropies when coupled with observational exposure functions?

Key findings

• HERMES successfully simulates the survival probability of UHE protons and the resulting GZK horizon, which is found to depend on nuclear mass and source redshift.
• The code reproduces expected fluxes and energy spectra for UHECRs in different astrophysical scenarios, including source evolution and varying injection indices, with results comparable to HiRes observations.
• Simulated sky maps of UHE protons from nearby sources (4–200 Mpc) show significant deflections due to extragalactic magnetic fields, with distinct patterns for 2MRS and SWIFT-BAT source catalogues.
• Inclusion of 56% isotropic events—based on Pierre Auger measurements—alters the arrival direction distribution, demonstrating the code’s sensitivity to background contamination.
• HERMES enables realistic modeling of arrival direction anisotropies, with non-uniform exposure effects from the Pierre Auger Observatory properly accounted for in sky maps.
• The code is modular and extensible, allowing integration of new models for background radiation or nuclear interactions based on updated data.