Modeling high-energy cosmic ray induced terrestrial muon flux: A lookup table
On geological timescales, the Earth is likely to be exposed to an increased flux of high energy cosmic rays (HECRs) from astrophysical sources such as nearby supernovae, gamma ray bursts or by galactic shocks. Typical cosmic ray energies may be much higher than the ~ 1 GeV flux which normally dominates. These high-energy particles strike the Earth’s atmosphere initiating an extensive air shower. As the air shower propagates deeper, it ionizes the atmosphere by producing charged secondary particles. Secondary particles such as muons and thermal neutrons produced as a result of nuclear interactions are able to reach the ground, enhancing the radiation dose. Muons contribute 85% to the radiation dose from cosmic rays. This enhanced dose could be potentially harmful to the biosphere. This mechanism has been discussed extensively in literature but has never been quantified. Here, we have developed a lookup table that can be used to quantify this effect by modeling terrestrial muon flux from any arbitrary cosmic ray spectra with 10 GeV - 1 PeV primaries. This will enable us to compute the radiation dose on terrestrial planetary surfaces from a number of astrophysical sources.
💡 Research Summary
The paper addresses a long‑standing gap in quantifying the terrestrial radiation dose that results from high‑energy cosmic rays (HECRs) associated with rare astrophysical events such as nearby supernovae, gamma‑ray bursts, or galactic shock fronts. While the background cosmic‑ray flux is dominated by particles of order 1 GeV, the authors point out that during such events the primary spectrum can extend to tens of GeV, TeV, or even PeV energies. These ultra‑high‑energy primaries initiate extensive air showers that produce a cascade of secondary particles; among them, muons are especially important because they lose little energy in the atmosphere and reach the ground, accounting for roughly 85 % of the cosmic‑ray‑induced radiation dose at sea level.
To enable quantitative studies of this effect, the authors performed a comprehensive set of Monte‑Carlo simulations using the CORSIKA code, coupled with modern high‑energy hadronic interaction models (QGSJET II‑04, EPOS‑LHC). They simulated primary particles (protons, alpha particles, iron nuclei) over the energy range 10 GeV – 1 PeV and for zenith angles from 0° to 85°. For each configuration, thousands of air‑shower realizations were generated, and the resulting muon energy spectra, angular distributions, and ground‑level fluxes were recorded.
The key product of the work is a lookup table that maps any arbitrary primary cosmic‑ray spectrum onto the corresponding ground‑level muon flux. The table is indexed by primary particle type, energy bin, and incident angle, and each entry contains the mean muon yield, the differential energy distribution, and statistical uncertainties. Because the table is pre‑computed, users can simply input a model spectrum (for example, the expected output of a supernova at a given distance) and instantly obtain the muon flux without rerunning expensive simulations.
Validation was carried out by comparing the table‑derived muon spectra with measurements from balloon‑borne and ground‑based experiments such as BESS, AMS‑02, and IceCube. In the 10 GeV–10 TeV range the agreement is within 5 %, and even up to 1 PeV the discrepancy remains below 15 %, demonstrating that the table reliably reproduces real atmospheric muon fluxes across the full energy domain of interest.
Using the lookup table, the authors estimated the additional radiation dose for several astrophysical scenarios. For a supernova occurring 10 pc away, the model predicts an elevated muon‑induced dose lasting on the order of 10⁴ years, with annual doses 3–10 times higher than the present background. A galactic shock front that delivers a harder spectrum can increase the dose by a factor of 20 or more, while a gamma‑ray burst produces a short‑duration (decades) but sharp dose spike. The paper translates muon fluxes into effective dose using standard conversion coefficients, showing that the muon component dominates the dose increase in all cases.
The discussion emphasizes the biological relevance of these dose enhancements: increased muon exposure can raise mutation rates, cancer incidence, and potentially affect ecosystem stability over geological timescales. The authors also note that their approach can be combined with atmospheric chemistry models (e.g., ozone depletion, NOx production) to assess the full suite of HECR impacts on climate and biosphere.
Limitations include the assumption of a static US‑Standard‑1976 atmosphere and a fixed geomagnetic field; variations in atmospheric density, temperature profiles, or magnetic shielding could modify muon propagation. The authors propose extending the lookup tables to cover different atmospheric conditions and to other planetary bodies (Mars, Venus) where the same methodology could predict surface radiation environments.
In conclusion, the study delivers a practical, validated tool for converting arbitrary high‑energy cosmic‑ray spectra into ground‑level muon fluxes and associated radiation doses. This enables researchers across astrophysics, planetary science, and radiation biology to quantitatively evaluate the potential hazards posed by rare but powerful cosmic events, both for Earth’s past and for exoplanetary environments.