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

Disappointing model for ultrahigh-energy cosmic rays

Data of Pierre Auger Observatory show a proton-dominated chemical composition of ultrahigh-energy cosmic rays spectrum at (1 - 3) EeV and a steadily heavier composition with energy increasing. In order to explain this feature we assume that (1 - 3) EeV protons are extragalactic and derive their maximum acceleration energy, E_p^{max} \simeq 4 EeV, compatible with both the spectrum and the composition. We also assume the rigidity-dependent acceleration mechanism of heavier nuclei, E_A^{max} = Z x E_p^{max}. The proposed model has rather disappointing consequences: i) no pion photo-production on CMB photons in extragalactic space and hence ii) no high-energy cosmogenic neutrino fluxes; iii) no GZK-cutoff in the spectrum; iv) no correlation with nearby sources due to nuclei deflection in the galactic magnetic fields up to highest energies.Comment: 4 pages, 7 figures, the talk presented by A. Gazizov at NPA5 Conference, April 3-8, 2011, Eilat, Israe

Cosmic Rays from Cosmic Strings with Condensates

We re-visit the production of cosmic rays by cusps on cosmic strings. If a scalar field (``Higgs'') has a linear interaction with the string world-sheet, such as would occur if there is a bosonic condensate on the string, cusps on string loops emit narrow beams of very high energy Higgses which then decay to give a flux of ultra high energy cosmic rays. The ultra-high energy flux and the gamma to proton ratio agree with observations if the string scale is $\sim 10^{13}$ GeV. The diffuse gamma ray and proton fluxes are well below current bounds. Strings that are {\it lighter} and have linear interactions with scalars produce an excess of direct and diffuse cosmic rays and are ruled out by observations, while heavier strings ($\sim 10^{15}$ GeV) are constrained by their gravitational signatures. This leaves a narrow window of parameter space for the existence of cosmic strings with bosonic condensates.Comment: 9 pages, 5 figures; revised reference

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

Neutrinos from Early-Phase, Pulsar-Driven Supernovae

Neutron stars, just after their formation, are surrounded by expanding, dense, and very hot envelopes which radiate thermal photons. Iron nuclei can be accelerated in the wind zones of such energetic pulsars to very high energies. These nuclei photo-disintegrate and their products lose energy efficiently in collisions with thermal photons and with the matter of the envelope, mainly via pion production. When the temperature of the radiation inside the envelope of the supernova drops below $\sim 3\times 10^6$ K, these pions decay before losing energy and produce high energy neutrinos. We estimate the flux of muon neutrinos emitted during such an early phase of the pulsar - supernova envelope interaction. We find that a 1 km$^2$ neutrino detector should be able to detect neutrinos above 1 TeV within about one year after the explosion from a supernova in our Galaxy. This result holds if these pulsars are able to efficiently accelerate nuclei to energies $\sim 10^{20}$ eV, as postulated recently by some authors for models of Galactic acceleration of the extremely high energy cosmic rays (EHE CRs).Comment: 16 pages, 3 figures, revised version submitted to Ap

Astroparticle Physics: Puzzles and Discoveries

Puzzles often give birth to the great discoveries, the false discoveries sometimes stimulate the exiting ideas in theoretical physics. The historical examples of both are described in Introduction and in section ``Cosmological Puzzles''. From existing puzzles most attention is given to Ultra High Energy Cosmic Ray (UHECR) puzzle and to cosmological constant problem. The 40-years old UHECR problem consisted in absence of the sharp steepening in spectrum of extragalactic cosmic rays caused by interaction with CMB radiation. This steepening is known as Greisen-Zatsepin-Kuzmin (GZK) cutoff. It is demonstrated here that the features of interaction of cosmic ray protons with CMB are seen now in the spectrum in the form of the dip and beginning of the GZK cutoff. The most serious cosmological problem is caused by large vacuum energy of the known elementary-particle fields which exceeds at least by 45 orders of magnitude the cosmological vacuum energy. The various ideas put forward to solve this problem during last 40 years, have weaknesses and cannot be accepted as the final solution of this puzzle. The anthropic approach is discussed.Comment: Invited talk at TAUP 2007 conference, September 2007, Sendai, Japa

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