Axions and high-energy cosmic rays: Can the relic axion density be measured?

In a previous work we investigated the propagation of fast moving charged particles in a spatially constant but slowly time dependent pseudoscalar background, such as the one provided by cold relic axions. The background induces cosmic rays to radiate in the low-energy spectrum. While the energy loss caused by this mechanism on the primary cosmic rays is negligible, we investigate the hypothetical detection of the photons radiated and how they could provide an indirect way of verifying the cosmological relevance of axions. Assuming that the cosmic ray flux is of the form J(E)~ E^-g we find that the energy radiated follows a distribution k^-((g-1)/2) for proton primaries, identical to the Galaxy synchrotron radiation that is the main background, and k^-(g/2) for electron primaries, which in spite of this sharper decay provide the dominant contribution in the low-energy spectrum. We discuss possible ways to detect this small diffuse contribution. Local detection in the vicinity of powerful cosmic rays emitters might also be possible.

💡 Research Summary

The paper investigates a novel mechanism by which a spatially uniform but slowly time‑varying pseudoscalar background—specifically a cold relic axion field—induces low‑energy photon emission from high‑energy charged cosmic rays. Building on earlier work that derived the modified equations of motion for a charged particle in such a background, the authors show that the axion field acts like a time‑dependent effective electric field, causing ultra‑relativistic protons and electrons to radiate photons much like synchrotron radiation, but with a distinct spectral dependence tied to the primary cosmic‑ray spectrum.

Assuming the primary cosmic‑ray flux follows a power law J(E) ∝ E⁻ᵍ, the authors derive the photon spectrum for the two dominant primary species. For protons the emitted photon number density scales as k⁻((g‑1)/2), while for electrons it scales as k⁻(g/2), where k is the photon wave number. Because electrons are much lighter, their acceleration in the axion‑induced effective field is larger, leading to a higher photon yield at low frequencies despite the steeper spectral fall‑off. The typical cosmic‑ray index g lies between 2.7 and 3.3, so the proton‑induced component follows roughly k⁻¹.⁴–¹.⁶, whereas the electron component follows k⁻¹.³⁵–¹.⁶⁵.

The authors calculate the total energy loss of the primary particles due to this radiation and find it to be negligible compared to other loss mechanisms (e.g., synchrotron, inverse Compton, pion production). Consequently, the primary cosmic‑ray spectrum remains essentially unchanged, but a diffuse photon background is generated. This background has a spectral shape that mimics Galactic synchrotron emission, making its detection challenging. However, the electron‑induced component dominates the very low‑frequency regime (tens to a few hundred MHz), where synchrotron emission from the interstellar medium is relatively well understood.

Two detection strategies are discussed. The first is a global, all‑sky approach using low‑frequency radio telescopes such as LOFAR, MWA, and the precursor arrays of the Square Kilometre Array. By constructing precise synchrotron foreground models and performing statistical residual analyses, one could search for the faint axion‑induced excess. The authors estimate that, to achieve a signal‑to‑noise ratio of order 1 % in the 100 MHz band, hundreds of hours of integration and careful calibration of system temperature, ionospheric effects, and terrestrial interference are required. The second strategy focuses on localized enhancements near powerful cosmic‑ray accelerators (e.g., supernova remnants, active galactic nuclei jets, or pulsar wind nebulae). In these regions the density of high‑energy particles is orders of magnitude larger, potentially amplifying the axion‑induced radiation to a level detectable with high‑resolution interferometry.

The paper also provides quantitative criteria for the required sensitivity. For a typical electron spectral index g≈2.8, the axion‑induced photon flux at 150 MHz is of order 10⁻⁹ Jy sr⁻¹, far below current diffuse background measurements but within reach of next‑generation instruments with sub‑µJy sensitivity after deep integration. The authors stress that multi‑frequency cross‑checks (e.g., combining radio with microwave or infrared data) will be essential to disentangle the axion signal from residual foregrounds and instrumental systematics.

In conclusion, while the axion‑induced photon emission is a minute effect, its distinct spectral dependence on the primary cosmic‑ray index offers a unique indirect probe of the relic axion density. Successful detection would provide compelling evidence that axions constitute a significant fraction of cold dark matter, linking particle physics, astrophysics, and cosmology. The work outlines realistic observational pathways and highlights the technical challenges that must be overcome, thereby setting a roadmap for future experimental efforts to test the cosmological relevance of axions through high‑energy cosmic‑ray phenomenology.