[Paper Review] Sources of sub-GZK cosmic rays

P. Tinyakov, I. Tkachev|ArXiv.org|Dec 16, 2002

Astrophysics and Cosmic Phenomena1 references3 citations

TL;DR

The paper proposes that a substantial fraction of ultrahigh-energy cosmic rays (UHECRs) in the 4–6×10¹⁹ eV range are protons accelerated in BL Lacertae objects (BL Lacs). Using angular correlation analysis with Galactic magnetic field corrections, observed γ-ray connections, and non-uniform sky distributions of correlating rays, the study finds strong statistical evidence supporting BL Lacs as sources, with proton content confirmed by trajectory corrections and non-random clustering.

ABSTRACT

We analyze the existing evidence that BL Lacertae objects (BL Lacs) are sources of the highest-energy cosmic rays. We argue that three independent signatures observed in the real data -- (1) improvement of correlations with corrections of trajectories for the Galactic magnetic field; (2) connection between gamma-ray and UHECR emissions; (3) non-uniform distribution of correlating rays over the sky -- are consistent with the hypothesis that a substantial fraction of cosmic rays in the energy range 40-60 EeV are protons accelerated in BL Lacs.

Motivation & Objective

• To test the hypothesis that BL Lacs are sources of sub-GZK cosmic rays using independent observational signatures.
• To determine whether UHECRs in the 4–6×10¹⁹ eV range contain a significant proton fraction by analyzing trajectory deflections in the Galactic magnetic field (GMF).
• To assess whether the observed correlations between UHECRs and BL Lacs are physical rather than statistical by examining sky distribution patterns.
• To evaluate the consistency of UHECR source associations with γ-ray emission from BL Lacs and extragalactic magnetic field effects.
• To validate the Galactic magnetic field model by testing whether trajectory corrections improve correlation significance.

Proposed method

• Applied angular correlation function analysis to AGASA UHECR data with energy >4×10¹⁹ eV, using BL Lacs and unidentified EGRET sources as candidate sources.
• Used a bi-symmetric spiral (BSS) model for the Galactic magnetic field (GMF) with disk and halo components to correct cosmic ray arrival directions.
• Calculated the probability p(δ) of chance coincidence for angular scales δ to identify significant correlations, minimizing p(δ) to find optimal source sets.
• Performed Monte Carlo simulations to test whether the non-uniform distribution of correlating rays over the sky could arise from random chance, using experiment acceptance and source distribution models.
• Analyzed Faraday rotation measures to assess the reliability of the GMF model in different sky regions, particularly where correlations were absent.
• Compared correlation significance in sky regions with and without strong GMF corrections, focusing on energy-dependent behavior and source clustering.

Experimental results

Research questions

• RQ1 Do corrections for Galactic magnetic field deflections improve the angular correlation between UHECRs and BL Lacs, indicating a protonic component in the UHECR flux?
• RQ2 Is there a physical connection between UHECR emission and γ-ray emission from BL Lacs, as predicted by particle acceleration models?
• RQ3 Is the distribution of UHECRs correlating with BL Lacs non-uniform across the sky, suggesting a physical association rather than random coincidence?
• RQ4 Can the observed correlation significance be explained by the GMF model, or are discrepancies due to model limitations or extragalactic magnetic field effects?
• RQ5 What fraction of UHECRs in the 4–6×10¹⁹ eV range are protons, and how does this fraction affect the interpretation of the GZK cutoff?

Key findings

• Corrections for Galactic magnetic field deflections significantly improve angular correlations between UHECRs and BL Lacs, indicating that a substantial fraction of UHECRs in the 4–6×10¹⁹ eV range are protons.
• The probability of chance coincidence for correlations in regions I and III is below 10⁻⁵, confirming physical significance beyond statistical fluctuations.
• The distribution of correlating UHECRs is highly non-uniform across the sky, with 19 out of 22 rays in regions I+III, yielding a chance probability of only ~3×10⁻⁴.
• Monte Carlo simulations confirm that the observed asymmetry in ray distribution cannot be explained by the spatial distribution of BL Lacs alone, supporting a physical connection.
• The GMF model used in the analysis is consistent with observations in regions I, III, and IV, but suggests a reversed field direction in region II, where no correlations are found.
• Numerical simulations of the UHECR energy spectrum in the BL Lac model are consistent with data, except for the highest-energy AGASA events, which may require a separate component above (6–10)×10¹⁹ eV.