Figure 1

Effective mass squared [17] of the transverse (red full lines) and longuitudinal (blue dashed lines) photon in the external magnetic field, expressed in terms of $\alpha m_e^2$, as a function of $\kappa =(\omega /(m_e))(B/B_{\mathrm{cr}})$. Thick lines represent the real part and thin lines represent the imaginary part.Reuse & Permissions

Figure 2

Typical values of the magnetic field [37] and electron density [61, 62] in various astrophysical objects (IG: intergalactic space, MW: the Milky Way, NLR and BLR: narrow- and broadline regions in active galactic nuclei). The condition (10) is satisfied above the thick line for energies $\omega >{10}^{19}\mathrm{eV}$, above the dashed line for $\omega >1\mathrm{TeV}$ and above the thin line for $\omega >10\mathrm{MeV}$ (for $M={10}^{10}\mathrm{GeV}$).Reuse & Permissions

Figure 3

The conditions (8, 9) on the parameter plane “photon energy”—“magnetic field”. The condition (9) is satisfied above red lines (thin for $m={10}^{-5}\mathrm{eV}$, dotted for $m={10}^{-7}\mathrm{eV}$, thick for $m={10}^{-9}\mathrm{eV}$). Horizontal lines indicate typical $B$ values for various astrophysical sources, the condition (8) is satisfied below a thick dashed green line: the mixing is possible below the green line but above the red lines as indicated, for $m={10}^{-9}\mathrm{eV}$, by the thick blue parts of the horizontal lines (for $M={10}^{10}\mathrm{GeV}$).Reuse & Permissions

Figure 4

The condition (11) for $M={10}^{10}\mathrm{GeV}$ on the updated Hillas plot [37]. The condition is satisfied in the shadowed region. The Milky Way parameters are denoted by a star. Also shown are parameters for anomalous X-ray pulsars and magnetars (AXP), neutron stars (NS), central black holes (BH) and for the central few parsecs (AD) of active galaxies (low-power Seyfert galaxies (Sy), powerful radio galaxies (RG) and blazars (BL)), relativistic jets, knots (K), hot spots (HS) and lobes (L) of powerful active galaxies (RG and BL); nonrelativistic jets of low-power galaxies (Sy); starburst galaxies; gamma-ray bursts (GRB); galaxy clusters and intercluster voids.Reuse & Permissions

Figure 5

Attenuation length of different kinds of particles as compared to the distance to the nearest BL Lac (blue horizontal line) and the size of the Universe (upper bound of the plot). The green line corresponds to photons, blue to neutrons and red (shown for comparison) to protons. The lines for protons and photons are taken from the review [63].Reuse & Permissions

Figure 6

The exposure of the HiRes cosmic-ray detector—darker shaded regions have had more exposure. The red triangle data points correspond to cosmic rays correlated with the position of BL Lacs.Reuse & Permissions