[Paper Review] Are 10 EeV cosmic rays extragalactic? Theory of cosmic ray diffusion at high energy

Andrei Gruzinov|arXiv (Cornell University)|Jul 26, 2018

Astrophysics and Cosmic Phenomena1 references3 citations

TL;DR

This paper proposes that the observed dipole anisotropy in 10 EeV cosmic rays—previously interpreted as evidence for extragalactic origin—can instead arise from Galactic diffusion of intermediate-mass nuclei (Z=7) in the turbulent Galactic magnetic field. Using theoretical modeling and numerical simulations, it shows that magnetic lensing can deflect the dipole anisotropy away from the Galactic center, while predicting a quadrupole anisotropy of comparable magnitude, challenging the assumption that such a dipole direction implies extragalactic origin.

ABSTRACT

Auger Collaboration has reported a large-scale anisotropy in the arrival directions of cosmic rays above 8 EeV. The dipole direction, at 125$^\circ$ from the Galactic center, is taken as an indication of an extragalactic origin of these cosmic rays. We show, both theoretically and by direct numerical simulations, that this is not necessarily true. Intermediate mass nuclei originating in the Galaxy and diffusing in the Galactic magnetic field can have a dipole anisotropy pointing away from the Galactic center. Our theory predicts a quadrupole anisotropy of the same order of magnitude as the dipole.

Motivation & Objective

• To investigate whether the observed large-scale dipole anisotropy in cosmic rays above 8 EeV, pointing away from the Galactic center, can be explained by Galactic diffusion rather than extragalactic origin.
• To examine the role of magnetic field coherence length and Larmor radius in shaping cosmic ray anisotropies at high energies.
• To test whether intermediate-mass cosmic rays (Z=7) diffusing in the Galactic magnetic field can produce a dipole anisotropy that appears to point away from the Galactic center due to magnetic lensing.
• To predict the expected magnitude of quadrupole anisotropy from Galactic diffusion and compare it to the observed dipole.
• To assess the implications for cosmic ray source models, particularly regarding the luminosity and timescale of potential Galactic sources.

Proposed method

• Develops a theoretical framework for cosmic ray diffusion at high energy, valid when the Larmor radius ρ ≫ coherence length rc, using the diffusion coefficient D ∼ cρ²/rc.
• Derives the dipole anisotropy as d ∼ ρ²/(rcR), where R is the Galaxy size, and the dipole deflection angle as χ ∼ rc/ρ.
• Models the Galactic magnetic field as a sum of 300 Fourier harmonics with random phases and directions, yielding a Gaussian, isotropic, parity-invariant solenoidal field with k⁻¹ = 0.1 kpc and B = 10 μG.
• Performs direct numerical simulations of 30,000 cosmic ray trajectories per observation point, weighted by time spent in the source region (r < 5 kpc, |z| < 1 kpc), at 100 observation points (r = 8 kpc, z = 0).
• Calculates the dipole vector d = −3⟨v⟩p and quadrupole tensor Qij = 3⟨vivj⟩p − δij from simulated arrival directions to quantify anisotropy.
• Averages results over observation points to compute statistical moments: ⟨d²⟩¹ᐟ² = 0.26, ⟨Q²⟩¹ᐟ² = 0.12, and finds 23% of dipoles point more than 90° from the Galactic center.

Experimental results

Research questions

• RQ1 Can the observed dipole anisotropy in 10 EeV cosmic rays, pointing away from the Galactic center, be explained by Galactic diffusion of intermediate-mass nuclei?
• RQ2 What is the expected magnitude of quadrupole anisotropy from Galactic cosmic ray diffusion, and how does it compare to the observed dipole?
• RQ3 To what extent can magnetic lensing in a turbulent Galactic magnetic field deflect the local dipole anisotropy away from the Galactic center?
• RQ4 Does the theory predict a dipole anisotropy of order 10% or less, consistent with the observed 6.5% amplitude?
• RQ5 Can Galactic sources of 8 EeV cosmic rays (Z=7) with luminosity ∼3×10⁴¹ erg/s produce a detectable anisotropy despite strong deflection?

Key findings

• The theoretical dipole anisotropy is predicted to be d ∼ ρ²/(rcR), with ρ ∼ 0.1–1 kpc and rc ∼ 0.1–1 kpc, yielding d ∼ 0.01–0.3, consistent with the observed 6.5% amplitude.
• Numerical simulations show an rms dipole amplitude of 26%, which is larger than the observed 6.5%, suggesting that only a fraction (≈20%) of the observed cosmic rays need to be Galactic to explain the signal.
• In 23% of observation points, the dipole points more than 90° from the Galactic center, demonstrating that magnetic lensing can significantly deflect the anisotropy direction.
• The quadrupole anisotropy is predicted to be of order 12% (⟨Q²⟩¹ᐟ² = 0.12), roughly half the dipole amplitude, and thus potentially measurable with improved statistics.
• The theory predicts that the dipole and quadrupole anisotropies are of the same order of magnitude, with Q ∼ ρ/R ≪ d, and d ∼ ρ²/(rcR), confirming that dipole anisotropy is a natural outcome of diffusion in a turbulent field.
• The results imply that the observed dipole anisotropy does not necessarily imply extragalactic origin, as Galactic diffusion with magnetic lensing can produce a similar directional pattern.