Diffusive propagation of UHECR and the propagation theorem

We present a detailed analytical study of the propagation of ultra high energy (UHE) particles in extragalactic magnetic fields. The crucial parameter which affects the diffuse spectrum is the separation between sources. In the case of a uniform distribution of sources with a separation between them much smaller than all characteristic propagation lengths, the diffuse spectrum of UHE particles has a {\em universal} form, independent of the mode of propagation. This statement has a status of theorem. The proof is obtained using the particle number conservation during propagation, and also using the kinetic equation for the propagation of UHE particles. This theorem can be also proved with the help of the diffusion equation. In particular, it is shown numerically, how the diffuse fluxes converge to this universal spectrum, when the separation between sources diminishes. We study also the analytic solution of the diffusion equation in weak and strong magnetic fields with energy losses taken into account. In the case of strong magnetic fields and for a separation between sources large enough, the GZK cutoff can practically disappear, as it has been found early in numerical simulations. In practice, however, the source luminosities required are too large for this possibility.Comment: 16 pages, 13 eps figures, discussion of the absence of the GZK cut-off in strong magnetic field added, a misprint in figure 6 corrected, version accepted for publication in Ap

Signatures of Topological Defects

We argue that due to various restrictions cosmic strings and monopole-string networks are not likely to produce the observed flux of ultra-high energy cosmic rays (UHECR). Among the topological defects studied so far, the most promising UHECR sources are necklaces and monopolonia. Other viable sources which are similar to topological defects are relic superheavy particles. All these sources have an excess of pions (and thus photons) over nucleons at production. We demonstrate that in the case of necklaces the diffuse proton flux can be larger than photon flux, due to absorption of the latter on radiobackground, while monopolonia and relic particles are concentrated in the Galactic halo, and the photon flux dominates. Another signature of the latter sources is anisotropy imposed by asymmetric position of the sun in the Galactic halo. In all cases considered so far, including necklaces, photons must be present in ultra-high energy radiation observed from topological defects, and experimental discrimination between photon-induced and proton-induced extensive air showers can give a clue to the origin of ultra-high energy cosmic rays.Comment: version accepted for publication in Phys. Rev. D. No changes in the conclusions and in figure

On the viability of holistic cosmic-ray source models

We consider the energy spectrum of cosmic-rays (CRs) from a purely phenomenological point of view and investigate the possibility that they all be produced by the same type of sources with a single power-law spectrum, in E^{-x}, from thermal to ultra-high energies. We show that the relative fluxes of the Galactic (GCR) and extra-galactic (EGCR) components are compatible with such a holistic model, provided that the index of the source spectrum be x \simeq 2.23\pm 0.07. This is compatible with the best-fit indices for both GCRs and EGCRs, assuming that their source composition is the same, which is indeed the case in a holistic model. It is also compatible with theoretical expectations for particle acceleration at relativistic shocks.Comment: 5 pages, 1 figure, Accepted for publication in Astronomy and Astrophysic

Galactic Anisotropy as Signature of ``Top-Down'' Mechanisms of Ultra-High Energy Cosmic Rays

We show that ``top-down'' mechanisms of Ultra-High Energy Cosmic Rays which involve heavy relic particle-like objects predict Galactic anisotropy of highest energy cosmic rays at the level of minimum $\sim 20$. This anisotropy is large enough to be either observed or ruled out in the next generation of experiments.Comment: 8 pages, 1 figure, LaTeX. Final version appeared in Pisma Zh. Eksp. Teor. Fi

Electroweak jet cascading in the decay of superheavy particles

We study decays of superheavy particles $X$ into leptons. We show that they initiate cascades similar to QCD parton jets, if m_X\gsim 10^6 GeV. Electroweak cascading is studied and the energy spectra of the produced leptons are calculated in the framework of a broken SU(2) model of weak interactions. As application, important for the Z-burst model for ultrahigh energy cosmic rays, we consider decays of superheavy particles coupled on tree-level only to neutrinos and derive stringent limit for these decays from the observed diffuse extragalactic $\gamma$-ray flux.Comment: 4 pages, 1 eps figur

Bounds on the cosmogenic neutrino flux

Under the assumption that some part of the observed highest energy cosmic rays consists of protons originating from cosmological distances, we derive bounds on the associated flux of neutrinos generated by inelastic processes with the cosmic microwave background photons. We exploit two methods. First, a power-like injection spectrum is assumed. Then, a model-independent technique, based on the inversion of the observed proton flux, is presented. The inferred lower bound is quite robust. As expected, the upper bound depends on the unknown composition of the highest energy cosmic rays. Our results represent benchmarks for all ultrahigh energy neutrino telescopes.Comment: 12 pages, 6 figure

Cosmic Necklaces and Ultrahigh Energy Cosmic Rays

Cosmic necklaces are hybrid topological defects consisting of monopoles and strings, with two strings attached to each monopole. We argue that the cosmological evolution of necklaces may significantly differ from that of cosmic strings. The typical velocity of necklaces can be much smaller than the speed of light, and the characteristic scale of the network much smaller than the horizon. We estimate the flux of high-energy protons produced by monopole annihilation in the decaying closed loops. For some reasonable values of the parameters it is comparable to the observed flux of ultrahigh-energy cosmic rays.Comment: 10 pages, Revtex, 1 figur

Unstable superheavy relic particles as a source of neutrinos responsible for the ultrahigh-energy cosmic rays

Decays of superheavy relic particles may produce extremely energetic neutrinos. Their annihilations on the relic neutrinos can be the origin of the cosmic rays with energies beyond the Greisen-Zatsepin-Kuzmin cutoff. The red shift acts as a cosmological filter selecting the sources at some particular value z_e, for which the present neutrino energy is close to the Z pole of the annihilation cross section. We predict no directional correlation of the ultrahigh-energy cosmic rays with the galactic halo. At the same time, there can be some directional correlations in the data, reflecting the distribution of matter at red shift z=z_e. Both of these features are manifest in the existing data. Our scenario is consistent with the neutrino mass reported by Super-Kamiokande and requires no lepton asymmetry or clustering of the background neutrinos.Comment: 3 pages, revtex; references adde