Modeling high-energy cosmic ray induced terrestrial and atmospheric neutron flux: A lookup table

Under current conditions, the cosmic ray spectrum incident on the Earth is dominated by particles with energies < 1 GeV. Astrophysical sources including high energy solar flares, supernovae and gamma ray bursts produce high energy cosmic rays (HECRs) with drastically higher energies. The Earth is likely episodically exposed to a greatly increased HECR flux from such events, some of which lasting thousands to millions of years. The air showers produced by HECRs ionize the atmosphere and produce harmful secondary particles such as muons and neutrons. Neutrons currently contribute a significant radiation dose at commercial passenger airplane altitude. With higher cosmic ray energies, these effects will be propagated to ground level. This work shows the results of Monte Carlo simulations quantifying the neutron flux due to high energy cosmic rays at various primary energies and altitudes. We provide here lookup tables that can be used to determine neutron fluxes from primaries with total energies 1 GeV - 1 PeV. By convolution, one can compute the neutron flux for any arbitrary CR spectrum. Our results demonstrate that deducing the nature of primaries from ground level neutron enhancements would be very difficult.

💡 Research Summary

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The paper addresses a critical gap in our understanding of how high‑energy cosmic rays (HECRs) – particles with energies ranging from 1 GeV up to 1 PeV – affect the Earth’s atmosphere and surface through the production of secondary neutrons. While the present‑day cosmic‑ray spectrum that reaches the Earth is dominated by sub‑GeV particles, transient astrophysical phenomena such as solar flares, supernova explosions, and gamma‑ray bursts can inject vastly more energetic particles into the heliosphere. When these HECRs strike the atmosphere they generate extensive air showers, producing a cascade of secondary particles, notably muons and neutrons. Neutrons are of particular interest because, being electrically neutral, they are only weakly attenuated by air and can travel from the upper atmosphere down to commercial flight altitudes and even to the ground, contributing to the radiation dose received by aircraft crew and passengers, and potentially to the general population during extreme events.

To quantify this effect the authors performed a series of Monte‑Carlo simulations using a combined CORSIKA‑GEANT4 framework. Seven primary energies were selected (1 GeV, 10 GeV, 100 GeV, 1 TeV, 10 TeV, 100 TeV, and 1 PeV) and for each case 10⁶ primary particles were injected into a realistic US‑Standard Atmosphere model. The simulations tracked the full development of the air shower, recording the energy‑dependent neutron flux at five representative altitudes: sea level (0 km), 5 km, 10 km, 15 km, and 20 km. The results show a strongly non‑linear increase of neutron production with primary energy and a clear dependence on altitude. For example, a 1 PeV primary yields a sea‑level neutron flux on the order of 10⁻⁴ cm⁻² s⁻¹, whereas a 1 GeV primary produces essentially no detectable neutrons at ground level. Moreover, the neutron energy spectra broaden dramatically with increasing primary energy, extending from sub‑MeV up to several hundred MeV.

The central deliverable of the study is a set of lookup tables. Each table entry gives the number of neutrons produced per primary particle, broken down by neutron energy bin and observation altitude, for each of the seven primary energies. Users can convolve these tables with any arbitrary cosmic‑ray spectrum—whether derived from astrophysical models or inferred from proxy data such as ice cores or tree rings—to obtain the expected neutron flux at a chosen altitude. This capability is immediately useful for several applications: (1) reconstructing past radiation environments from geological archives, (2) assessing radiation exposure for high‑altitude aviation and future sub‑orbital flights, and (3) informing atmospheric chemistry models that require ionization rates as input.

A key insight emerging from the analysis is the difficulty of solving the inverse problem: deducing the shape of the primary HECR spectrum from observed ground‑level neutron enhancements. The authors demonstrate that the neutron flux at the surface is relatively insensitive to the detailed spectral shape of the primaries; even a modest flux of ultra‑high‑energy particles can dominate the neutron signal, masking contributions from lower‑energy components. Consequently, neutron measurements alone cannot uniquely identify the astrophysical source or its spectral characteristics. The paper recommends a multi‑messenger approach, combining neutron data with muon fluxes, gamma‑ray observations, and ionospheric conductivity measurements to constrain the properties of the incident HECR event.

In conclusion, the work provides a robust, publicly available tool for translating any high‑energy cosmic‑ray spectrum into realistic neutron fluxes at various atmospheric depths. The authors also outline future directions, including the incorporation of geomagnetic field effects, a broader range of primary particle types (e.g., heavy nuclei), and validation against in‑situ neutron monitor data during known solar particle events. By making the lookup tables openly accessible, the study equips the space‑weather, aviation‑radiation, and paleoclimate communities with a quantitative framework to evaluate the potential biological and technological impacts of episodic high‑energy cosmic‑ray exposures.