We postulate that the energy-momentum relation is modified for very high energy particles to violate Lorentz invariance and the speed of photon is changed from the light velocity c. The violation effect is amplified in a sensitive way to detection through the modified kinematical constraints on the conservation of energy and momentum, in the absorption process of γ-rays colliding against photons of longer wavelengths and converting into an electron-positron pair. For γ-rays of energies higher than 1013 eV, the minimum energy of the soft photons for the reaction and then the absorption mean free path of γ-rays are altered by orders of magnitude from those conventionally estimated. Consideration is similarly applied to high-energy cosmic-ray protons. The consequences may require the standard assumptions on the maximum distance from which very high energy radiation can travel to be revised.

https://iopscience.iop.org/article/10.1086/312057/pdf

Invariance Violation Extends the Cosmic Ray Horizon

The fluxes and spectra of galactic and extragalactic neutrinos at energy 1011–1019 eV are calculated In particular, the neutrino flux from the normal galaxies is calculated taking into account the spectral index distribution The only assumption that seriously affects the calculated neutrino flux atE

 v
 ≳1017 eV is the power-like generation spectrum of protons in the entire considered energy region The normal galaxies with the accepted parameters generate the metagalactic equivalent electron component (electrons+their radiation) with energy densityω
e≈85×10−7 eV cm−3, while the density of the observed diffuse X-ray radiation alone is 100 times higher This requires the existence of other neutrino sources and we found the minimized neutrino flux under two limitations: (1) the power-law generation spectrum of protons and (2) production of the observed energy density of the diffuse X-an γ-radiation These requirements are met in the evolutionary model of origin of the metagalactic cosmic rays with modern energy densityω
M8≈36×10−7 eV cm−3 The possibility of experiments with cosmic neutrinos of energyE

 v
 ≳3×1017 eV is discussed The upper bound on neutrino-nucleon cross-section σ<22×10−29 cm2 is obtained in evolutionary model from the observed zenith angular distribution of extensive air showers In Appendix 2 the diffuse X-and γ-ray flux arising together with neutrino flux is calculated It agrees with observed flux in the entire energy range from 1 keV up to 100 MeV

Cosmic neutrinos of ultra-high energies and detection possibility

Very high energy (VHE, E 100 GeV) radiation emitted at cosmological distances will pair produce on low-energy diffuse extragalactic background radiation before ever reaching us. This prevents us from directly seeing most of the VHE emission in the universe. However, a VHE γ-ray that pair produces initiates an electromagnetic pair cascade. At low energies, this secondary cascade radiation has a spectrum insensitive to the spectrum of the primary γ-radiation and, unlike the original VHE radiation, is observable. Motivated by new measurements of the extragalactic MeV-GeV diffuse γ-ray background, we discuss the constraints placed on cosmological VHE source populations by requiring that the cascade background they produce not exceed the observed levels. We use a new, accurate cascading code and pay particular attention to the dependence of the constraints on the diffuse cosmic background at infrared/optical wavelengths. Despite considerable uncertainty in this background, we find that robust constraints may still be placed on the integrated emissivity of potential VHE sources in the universe. The limits are tighter than those obtained by considering cascading on the microwave background alone and restrict significantly, for example, the parameter space available for the exotic particle physics scenarios recently proposed to explain the highest energy cosmic-ray events. If direct emission from blazar AGNs in fact accounts for most of the observed GeV background, the resulting stronger limits rule out AGN emission scenarios that produce significant power above ~300 GeV.

http://iopscience.iop.org/article/10.1086/310883/pdf

Constraints on the Very High Energy Emissivity of the Universe from the Diffuse GeV Gamma-Ray Background

VHE (Very High Energy, E>100 GeV) radiation emitted at cosmological distances will pair produce on low-energy diffuse extragalactic background radiation before ever reaching us. This prevents us from directly seeing most of the VHE emission in the Universe. However, a VHE gamma-ray that pair produces initiates an electromagnetic pair cascade. At low energies, this secondary cascade radiation has a spectrum insensitive to the spectrum of the primary gamma-radiation and, unlike the original VHE radiation, IS observable. Motivated by new measurements of the extragalactic MeV-GeV diffuse gamma-ray background, we discuss the constraints placed on cosmological VHE source populations by requiring that the cascade background they produce not exceed the observed levels. We use a new, accurate cascading code and pay particular attention to the dependence of the constraints on the diffuse cosmic background at infrared/optical wavelengths. Despite considerable uncertainty in this background, we find that robust constraints may still be placed on the integrated emissivity of potential VHE sources in the Universe. The limits are tighter than those obtained by considering cascading on the microwave background alone and restrict significantly, for example, the parameter space available for the exotic particle physics scenarios recently proposed to explain the highest energy cosmic ray events. If direct emission from blazar AGN in fact accounts for most of the observed GeV background, these limits strengthen and rule out AGN emission scenarios which produce significant power above 300 GeV.

Constraints on the VHE Emissivity of the Universe from the Diffuse GeV Gamma-Ray Background

Extragalactic propagation of ultrahigh energy cosmic-rays

THE problem of the origin of cosmic rays is well known; but in spite of considerable advances in knowledge concerning energetic extra-terrestrial objects in recent years, no satisfactory solution has appeared. It is not clear, even, whether the important sources are within the Galaxy or outside it1,2.

Consequences of a Universal Cosmic-ray Theory for γ -ray Astronomy

An estimate is made of the gamma -ray spectrum resulting from an extragalactic, evolving source model of cosmic ray origin in the absence of intergalactic gas. The experimental situation does not at present appear to allow definite rejection of this theory, since the calculated spectrum lies between the extreme observational limits. It is possible that such a theory can explain the cosmic ray spectrum, the isotropy of cosmic rays and the diffuse gamma -ray spectrum.

The gamma-ray background: a consequence of metagalactic cosmic ray origin?

An analysis is made of the implications of assuming an extragalactic origin for cosmic rays above 1017 eV. The effect of the black- body radiation on the propagation of extragalactic protons is examined in some detail and the expected spectral shape is derived for alternative assumptions about the origin and confinement of the particles. The possibility of distinguishing between the various models using contemporary extensive air shower arrays is considered.

Cosmic ray origin above 1017 eV

/pdf/the-interstellar-spectrum-of-cosmic-rays-2t1n1cx4or.pdf

The interstellar spectrum of cosmic rays.

A model is presented in which the bulk of the cosmic rays comprises two components: one, from galactic sources (probably pulsars) and the other having a universal, i.e. extragalactic, origin. Attention is directed particularly towards the particles above about 1017 eV which, like those below 1014 eV, are proposed to be of universal origin, it is shown that if these particles have a production spectrum having constant exponent (differential value=-2.75) then interaction with the black-body radiation gives a spectrum at the earth not inconsistent with observation. In this model the extragalactic sources of cosmic rays do not increase in total number or in intensity at high red shifts.

J. Wdowczyk

Papers

Consequences of a Universal Cosmic-ray Theory for γ -ray Astronomy

The gamma-ray background: a consequence of metagalactic cosmic ray origin?

Cosmic ray origin above 1017 eV

The interstellar spectrum of cosmic rays.

Cosmic rays from galactic and extragalactic sources