[Paper Review] Massive relic neutrinos in the galactic halo and the knee in the cosmic ray spectrum

M.T. Dova, J.D. Swain+1 more|arXiv (Cornell University)|Dec 7, 2001

Astrophysics and Cosmic Phenomena2 references3 citations

TL;DR

This paper proposes that the cosmic ray spectrum's 'knee' at ~10^15.5 eV arises from inelastic proton-neutrino collisions with massive relic neutrinos in the galactic halo, mediated by a magnetic dipole moment. The model reproduces the KASCADE data using a neutrino mass of ~100 eV and a magnetic moment of (5.4±0.6)×10⁻⁶ μB, offering a novel explanation for the spectral hardening and sharp cutoff.

ABSTRACT

Despite many efforts to find a reasonable explanation, the origin of the "knee" in the cosmic ray spectrum at energy around 10**15.5 eV remains mysterious. In this letter we suggest that the "knee" may be due to a GZK-like effect of cosmic rays interacting with massive neutrinos in the galactic halo. Simple kinematics connects the location of the "knee" with the mass of the neutrinos, and, while the required interaction cross section is larger than that predicted by the Standard Model, it can be accommodated by a small neutrino magnetic dipole moment. The values for the neutrino parameters obtained from the analysis of existing experimental data are compatible with present laboratory bounds.

Motivation & Objective

• To explain the unexplained 'knee' in the cosmic ray spectrum at ~10^15.5 eV, a sharp spectral hardening not accounted for by standard models.
• To investigate whether massive relic neutrinos in the galactic halo could induce energy loss in cosmic rays through inelastic collisions.
• To determine if a nonzero neutrino magnetic dipole moment could enhance the cross-section sufficiently to produce the observed spectral feature.
• To test the compatibility of the required neutrino parameters with existing laboratory bounds and cosmological constraints.

Proposed method

• Adapt the GZK mechanism to proton-neutrino interactions, replacing CMB photons with massive neutrinos in the galactic halo.
• Use a parameterized cross-section for quasi-elastic proton-neutrino scattering, modified by a magnetic dipole coupling term κ/(2mν)σμνqν.
• Model gravitational clustering of massive neutrinos in the galactic halo using a spheroidal density distribution with a 10 kpc core, yielding nν ≈ 1.4×10⁸ cm⁻³ for mν = 100 eV.
• Solve the energy loss rate equation dE/dt = (c/γ)∫K(w₀)σ(w₀)n dw₀ numerically, incorporating neutrino density and cross-section.
• Apply a diffusion-reaction equation for cosmic ray propagation, including energy loss, diffusion, and injection, with a power-law source term Q ∝ E⁻γ.
• Fit the model to KASCADE data using a mixed composition of protons (60%) and iron (40%), adjusting κ and residence time to match the observed knee.

Experimental results

Research questions

• RQ1 Can inelastic collisions between cosmic ray protons and massive relic neutrinos in the galactic halo explain the sharp 'knee' in the cosmic ray spectrum?
• RQ2 What values of neutrino mass and magnetic dipole moment are required to reproduce the observed spectral cutoff at ~10^15.5 eV?
• RQ3 Is the required interaction cross-section compatible with current laboratory bounds on neutrino magnetic moments?
• RQ4 Can the model simultaneously account for the observed composition changes above the knee, particularly the dominance of light nuclei in the spectral hardening?
• RQ5 How do gravitational clustering and halo density profiles affect the neutrino number density and thus the energy loss rate?

Key findings

• The model reproduces the KASCADE data around the 'knee' with a best-fit magnetic dipole moment of (5.4±0.6)×10⁻⁶ μB for a 3×10⁸ year residence time.
• A neutrino mass of approximately 100 eV is required to allow pion production via Δ resonance in proton-neutrino collisions.
• The required neutrino density in the galactic halo reaches ~1.4×10⁸ cm⁻³ for mν = 100 eV, consistent with phase-space and Pauli exclusion constraints.
• The sharpness of the 'knee' cannot be explained by smooth diffusion or galactic modulation models, supporting the inelastic interaction mechanism.
• The model predicts a 'second knee' in the iron spectrum above 10^17 eV due to similar energy loss processes, consistent with possible observations.
• The derived parameters are within the range of current accelerator limits (5×10⁻⁷ μB), making future experimental tests feasible.