Numerical Toy-Model Calculation of the Nucleon Spin Autocorrelation Function in a Supernova Core

We develop a simple model for the evolution of a nucleon spin in a hot and dense nuclear medium. A given nucleon is limited to one-dimensional motion in a distribution of external, spin-dependent scattering potentials. We calculate the nucleon spin autocorrelation function numerically for a variety of potential densities and distributions which are meant to bracket realistic conditions in a supernova core. For all plausible configurations the width of the spin-density structure function is found to be less than the temperature. This is in contrast with a naive perturbative calculation based on the one-pion exchange potential which overestimates the width and thus suggests a large suppression of the neutrino opacities by nucleon spin fluctuations. Our results suggest that it may be justified to neglect the collisional broadening of the spin-density structure function for the purpose of estimating the neutrino opacities in the deep inner core of a supernova. On the other hand, we find no indication that processes such as axion or neutrino pair emission, which depend on nucleon spin fluctuations, are substantially suppressed beyond the multiple-scattering effect already discussed in the literature. Aside from these practical conclusions, our model reveals a number of interesting and unexpected insights. For example, the spin-relaxation rate saturates with increasing potential strength only if bound states are not allowed to form by including a repulsive core. There is no saturation with increasing density of scattering potentials until localized eigenstates of energy begin to form.Comment: 14 latex pages in two-column format, 15 postscript figures included, uses revtex.sty and epsf.sty. Submitted to Physical Review

Lorentz Violation for Photons and Ultra-High Energy Cosmic Rays

Lorentz symmetry breaking at very high energies may lead to photon dispersion relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed by a power n of the Planck mass M_Pl. We show that first and second order terms of size xi_1 > 10^(-14) and xi_2 < -10^(-6), respectively, would lead to a photon component in cosmic rays above 10^(19) eV that should already have been detected, if corresponding terms for electrons and positrons are significantly smaller. This suggests that Lorentz invariance breakings suppressed up to second order in the Planck scale are unlikely to be phenomenologically viable for photons.Comment: 4 revtex pages, 3 postscript figures included, version published in PR

Constructing Dirac linear fermions in terms of non-linear Heisenberg spinors

We show that the massive (or massless) neutrinos can be described as special states of Heisenberg nonlinear spinors. As a by-product of this decomposition a particularly attractive consequence appears: the possibility of relating the existence of only three species of mass-less neutrinos to such internal non-linear structure. At the same time it allows the possibility that neutrino oscillation can occurs even for massless neutrinos

Ultra-High Energy Cosmic Rays and the GeV-TeV Diffuse Gamma-Ray Flux

Ultra-high energy cosmic ray protons accelerated in astrophysical objects produce secondary electromagnetic cascades during propagation in the cosmic microwave and infrared backgrounds. We show that such cascades can contribute between ~1% and ~50% of the GeV-TeV diffuse photon flux measured by the EGRET experiment. The GLAST satellite should have a good chance to discover this flux.Comment: 4 pages, 5 figure

Ultra-High Energy Cosmic Ray Nuclei from Individual Magnetized Sources

We investigate the dependence of composition, spectrum and angular distributions of ultra-high energy cosmic rays above 10^19 eV from individual sources on their magnetization. We find that, especially for sources within a few megaparsecs from the observer, observable spectra and composition are severely modified if the source is surrounded by fields of ~ 10^-7 Gauss on scales of a few megaparsecs. Low energy particles diffuse over larger distances during their energy loss time. This leads to considerable hardening of the spectrum up to the energy where the loss distance becomes comparable to the source distance. Magnetized sources thus have very important consequences for observations, even if cosmic rays arrive within a few degrees from the source direction. At the same time, details in spectra and chemical composition may be intrinsically unpredictable because they depend on the unknown magnetic field structure. If primaries are predominantly nuclei of atomic mass A accelerated up to a maximum energy E_max with spectra not much softer than E^-2, secondary protons from photo-disintegration can produce a conspicuous peak in the spectrum at energy ~ E_max/A. A related feature appears in the average mass dependence on energy.Comment: 15 pages, 16 ps figures, published version with minor changes, see http://stacks.iop.org/1475-7516/2004/i=08/a=01

Implications of a Possible Clustering of Highest Energy Cosmic Rays

Very recently, a possible clustering of a subset of observed ultrahigh energy cosmic rays above about 40EeV (4x10^19eV) in pairs near the supergalactic plane was reported. We show that a confirmation of this effect would provide information on origin and nature of these events and, in case of charged primaries, imply interesting constraints on the extragalactic magnetic field. The observed time correlation would most likely rule out an association of these events with cosmological gamma ray bursts. If no prominent astrophysical source candidates such as powerful radiogalaxies can be found, the existence of a mechanism involving new fundamental physics would be favored.Comment: 10 latex pages, 1 postscript figure, uses aaspp4.sty, submitted to Astrophysical Journal Letter

Local Magnetic Turbulence and TeV-PeV Cosmic Ray Anisotropies

In the energy range from ~ 10^12 eV to ~ 10^15 eV, the Galactic cosmic ray flux has anisotropies both on large scales, with an amplitude of the order of 0.1%, and on scales between ~ 10 and ~ 30 degrees, with amplitudes smaller by a factor of a few. With a diffusion coefficient inferred from Galactic cosmic ray chemical abundances, the diffusion approximation predicts a dipolar anisotropy of comparable size, but does not explain the smaller scale anisotropies. We demonstrate here that energy dependent smaller scale anisotropies naturally arise from the local concrete realization of the turbulent magnetic field within the cosmic ray scattering length. We show how such anisotropies could be calculated if the magnetic field structure within a few tens of parsecs from Earth were known.Comment: 5 pages (2 columns), 3 figures. Published in Physical Review Letter

Electron-, Mu-, and Tau-Number Conservation in a Supernova Core

We study if the neutrino mixing parameters suggested by the atmospheric neutrino anomaly imply chemical equilibrium between mu- and tau-flavored leptons in a supernova (SN) core. The initial flavor-conversion rate would indeed be fast if the nu_mu-nu_tau-mixing angle were not suppressed by second-order refractive effects. The neutrino diffusion coefficients are different for nu_mu, anti-nu_mu, nu_tau and anti-nu_tau so that neutrino transport will create a net mu and tau lepton number density. This will typically lead to a situation where the usual first-order refractive effects dominate, further suppressing the rate of flavor conversion. Altogether, neutrino refraction has the nontrivial consequence of guaranteeing the separate conservation of e, mu, and tau lepton number in a SN core on the infall and cooling time scales, even when neutrino mixing angles are large.Comment: Slightly expanded version with improved presentation, no changes of substanc

On The Origin of Very High Energy Cosmic Rays

We discuss the most recent developments in our understanding of the acceleration and propagation of cosmic rays up to the highest energies. In particular we specialize our discussion to three issues: 1) developments in the theory of particle acceleration at shock waves; 2) the transition from galactic to extragalactic cosmic rays; 3) implications of up-to-date observations for the origin of ultra high energy cosmic rays (UHECRs).Comment: Invited Review Article to appear in Modern Physics Letters A, Review Sectio

Cosmological Magnetic Fields from Primordial Helical Seeds

Most early Universe scenarios predict negligible magnetic fields on cosmological scales if they are unprocessed during subsequent expansion of the Universe. We present a new numerical treatment of the evolution of primordial fields and apply it to weakly helical seeds as they occur in certain early Universe scenarios. We find that initial helicities not much larger than the baryon to photon number can lead to fields of about 10^{-13} Gauss with coherence scales slightly below a kilo-parsec today.Comment: 4 revtex pages, 2 postscript figures include