Propagation: from source to Earth
Between acceleration and detection, a UHECR crosses tens to hundreds of megaparsecs of intergalactic space. That space is not empty: it is filled with the cosmic microwave background (CMB, 411 photons/cm³ at T = 2.7 K), the extragalactic background light (EBL, the accumulated infrared–optical starlight), and magnetic fields organized along the cosmic web. Propagation reshapes the spectrum, the composition, and the arrival directions of everything we detect.
See the 2D animation or 3D visualization of these processes.
Energy losses of protons
- Photopion production (the GZK effect). Above E ≈ 5×10¹⁹ eV, a CMB photon seen in the proton’s rest frame exceeds the pion production threshold: p + γ → Δ⁺ → p π⁰ or n π⁺. Each interaction removes ~20% of the proton’s energy, and the loss length drops to ~20 Mpc. Predicted independently by Greisen and by Zatsepin & Kuzmin in 1966, this process guarantees a flux suppression — a proton observed at 10²⁰ eV must come from within the GZK horizon of roughly 100–200 Mpc, no matter how powerful more distant sources are.
- Bethe–Heitler pair production. Above ~10¹⁸ eV, p + γ_CMB → p + e⁺e⁻ removes ~0.1% of the energy per interaction; its loss length is ~Gpc. This gentler drain shapes the spectrum around the ankle and is one interpretation of the dip region.
- Adiabatic losses. All particles lose energy ∝ (1+z) to cosmological expansion — relevant for distant sources.
Photodisintegration of nuclei
Nuclei do not photoproduce pions as easily; instead they are photodisintegrated. When a CMB or EBL photon reaches ε′ ≈ 10–30 MeV in the nucleus rest frame, it excites the giant dipole resonance, and the nucleus evaporates one or more nucleons: A + γ → (A−1) + n, (A−2) + 2n, … The Lorentz factor — energy per nucleon — is roughly conserved, so fragments continue with E/A ≈ const. Iron survives about as far as protons of the same energy, while intermediate-mass nuclei are fragile: propagation naturally reshuffles an injected composition. Combined fits of the Auger spectrum and Xmax data prefer sources injecting intermediate-mass nuclei (N, Si) with hard spectra and a rigidity-dependent maximum energy — an imprint of exactly these processes.
Magnetic deflections
Charged particles do not travel straight:
- Extragalactic fields are ≲ 1 nG in voids and 10–100 nG in filaments and clusters; their strength and filling factor are among the least-known quantities in astrophysics.
- The Galactic magnetic field (a few µG, coherent over kpc scales) adds a final, direction-dependent deflection of a few degrees at the highest rigidities.
The deflection scales with rigidity R = E/Z:
δθ ≈ few° × Z × (E / 10²⁰ eV)⁻¹
so a 10²⁰ eV proton points back to within a few degrees of its source, while an iron nucleus of the same energy (Z = 26) is scattered across tens of degrees. Deflections also cause time delays of 10³–10⁵ years relative to light — which is why a transient source (TDE or GRB) is long dark by the time its particles arrive.
Cosmogenic messengers
The same interactions that drain UHECR energy create secondaries: π⁺ decay yields cosmogenic neutrinos (EeV scale), and π⁰ decay feeds electromagnetic cascades down to the GeV–TeV gamma-ray band. Neither is deflected, so both point back to their production sites. The still-undetected cosmogenic neutrino flux is a key target for GRAND, IceCube-Gen2 and POEMMA: its level encodes the UHECR composition, source evolution, and the proton fraction at the highest energies.
Related
- What are UHECRs? — the energy spectrum shaped by these losses
- Candidate sources — what the horizon allows
- Open questions — GZK cutoff vs. source exhaustion