If cosmic rays traveled in straight lines like light, identifying their sources would be straightforward — just look back along the arrival direction. But cosmic rays are charged particles, and the universe is threaded with magnetic fields. These fields bend cosmic ray paths, scrambling the directional information and making source identification one of astrophysics' greatest challenges.
The Basic Physics
A charged particle moving through a magnetic field experiences the Lorentz force:
F = q(v × B)
The force is perpendicular to both velocity and magnetic field, causing the particle to curve.
For a relativistic particle, the gyroradius (radius of curvature) is:
r_g ≈ 1.1 kpc × (E/10²⁰ eV) × (1/Z) × (1 μG/B)
where E is energy, Z is charge number (1 for protons, 26 for iron), and B is magnetic field strength.
A few key insights from this formula:
- Higher energy = less deflection: More energetic particles are stiffer and bend less
- Higher charge = more deflection: An iron nucleus deflects 26× more than a proton of the same energy
- Stronger field = more deflection: The Galactic field deflects more than intergalactic fields
The Galactic Magnetic Field
Our Milky Way contains a coherent magnetic field with typical strength of a few microgauss (μG). The field has both regular (ordered) and turbulent (random) components:
Regular Component
The regular field follows the Galaxy's spiral structure, running roughly along spiral arms. Near the Sun, it points toward Galactic longitude ~90° (toward the constellation Cygnus). The field reverses direction between some arms.
This component causes systematic deflection — cosmic rays from certain directions are bent in predictable ways. For a 60 EeV proton crossing the Galaxy, typical deflection from the regular field is ~3-5°.
Turbulent Component
Superimposed on the regular field is a turbulent component with similar strength but random directions on scales of ~100 parsecs. This causes random walk-like deflection that accumulates statistically.
The turbulent deflection scales as:
δ_turb ∝ √(L/l_c) × (Z × B × l_c / E)
where L is path length and l_c is the turbulence coherence length.
Halo Field
The Galaxy's magnetic field extends into the halo, though with uncertain structure. Poloidal (vertical) field components may deflect cosmic rays entering from high Galactic latitudes.
🌌 Galactic Deflection Estimates
| Particle | Energy | Typical Deflection |
|---|---|---|
| Proton | 10 EeV | ~15-30° |
| Proton | 60 EeV | ~3-5° |
| Proton | 100 EeV | ~2-3° |
| Iron | 60 EeV | ~80-130° |
| Iron | 100 EeV | ~50-75° |
Note: Values depend strongly on arrival direction and Galactic field model.
Extragalactic Magnetic Fields
Beyond our Galaxy, the universe contains magnetic fields of varying strength depending on environment:
Galaxy Clusters
Rich galaxy clusters contain magnetic fields of 1-10 μG in their cores, declining to ~0.1 μG in outskirts. Cosmic rays passing through clusters can be significantly deflected — potentially trapped for extended periods.
For sources within or behind clusters, this creates both deflection and time delay, further complicating source identification.
Cosmic Web Filaments
The large-scale structure of the universe — galaxy filaments and walls — likely contains magnetic fields of ~10-100 nanogauss (nG). While weaker than cluster fields, the enormous path lengths (tens to hundreds of megaparsecs) can accumulate substantial deflection.
Voids
The vast cosmic voids between structures may contain only femtogauss (10⁻¹⁵ G) fields or weaker. Cosmic rays traversing voids experience minimal deflection.
The highly uncertain structure of extragalactic magnetic fields — particularly in filaments — is one of the major unknowns in UHECR propagation.
Time Delays
Magnetic deflection doesn't just change direction — it increases path length, delaying arrival compared to light from the same source.
For a particle deflected by angle δ over distance D, the time delay is approximately:
Δt ≈ (δ²/4c) × D
For typical parameters:
- A 60 EeV proton from 100 Mpc, deflected 10°, arrives ~10,000 years late
- A 10 EeV iron nucleus from the same source might be delayed by millions of years
This means the cosmic rays arriving today may have left their sources when the electromagnetic signal (that could identify them) arrived long before human civilization existed.
Implications for Source Identification
The Composition Problem
Magnetic deflection depends critically on charge. If the highest-energy cosmic rays are protons, they might point within a few degrees of their sources. If they're iron nuclei, all directional information is essentially lost.
Unfortunately, current experiments cannot determine the composition of individual events — only statistical distributions. This fundamental uncertainty limits how confidently we can associate any cosmic ray with any source.
Statistical Approaches
Given the uncertainties, astronomers use statistical methods:
- Autocorrelation: Look for clustering of arrival directions that would suggest common sources
- Cross-correlation: Check if arrival directions cluster around catalog objects (AGN, starburst galaxies, etc.)
- Stacking: Sum the cosmic ray flux from many potential sources
- Anisotropy: Search for large-scale patterns (dipoles, higher multipoles)
The dipole anisotropy discovered by Auger — a 6.5% excess from one hemisphere — is robust because it's a large-scale pattern that survives even substantial individual deflections.
Magnetic Lensing
Just as gravitational lensing can magnify and distort galaxy images, magnetic fields can focus or defocus cosmic rays. A source might appear:
- Magnified (multiple images from different paths)
- Demagnified (field geometry disperses particles)
- Split into multiple apparent sources
Modeling magnetic lensing requires knowing the field structure — which we don't, precisely.
Correcting for Galactic Deflection
One approach is to "correct" arrival directions for Galactic magnetic deflection, tracing particles backward through field models to estimate their extragalactic directions.
This requires:
- A model of the Galactic magnetic field
- Assuming a composition (usually protons)
- Particle tracking through the model
The result depends strongly on which field model is used. Current models (JF12, Pshirkov, TF17, etc.) give different predictions, especially at low Galactic latitudes where the field is strongest.
For a 60 EeV proton, different models might predict the source direction to be anywhere within a ~10° region. For heavy nuclei, the uncertainty explodes.
The Ultimate Limit
Even with perfect field knowledge and perfect composition identification, there's a fundamental limit: the turbulent field component causes irreducible random deflection. Below some energy threshold (depending on composition), cosmic rays become a diffuse glow with no directional information.
For protons, astronomy might be possible above ~60 EeV. For iron, perhaps only above ~1,000 EeV — energies rarely or never observed.
Future Progress
Several developments could help:
Better composition measurements: AugerPrime's surface scintillators will improve event-by-event composition estimates.
Higher statistics: More events at the highest energies will strengthen statistical analyses.
Better field models: Faraday rotation measurements from upcoming radio surveys (SKA) will improve Galactic field maps.
Multi-messenger constraints: If UHECR sources also produce neutrinos (which travel straight) or gravitational waves, we can identify sources without relying on cosmic ray directions.
The magnetic deflection problem won't be solved — it's physics, not a technical limitation. But with enough data and clever analysis, we can work around it to reveal the cosmic accelerators behind the universe's most energetic particles.