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

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

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

A Cosmic Battery

We show that the Poynting-Robertson drag effect in an optically thin advection-dominated accretion flow around active gravitating objects generates strong azimuthal electric currents which give rise to astrophysically significant magnetic fields. Although the mechanism is most effective in accreting compact objects, it seems very promising to also account for the generation of stellar dipolar fields during the late protostellar collapse phase, when the star approaches the main sequence.Comment: 12 pages Latex, 1 postscript figure, to appear in the Astrophysical Journa

Maximum Likelihood Analysis of Clusters of Ultra-High Energy Cosmic Rays

We present a numerical code designed to conduct a likelihood analysis for clusters of nucleons above 10**19 eV originating from discrete astrophysical sources such as powerful radio galaxies, gamma-ray bursts or topological defects. The code simulates the propagation of nucleons in a large-scale magnetic field and constructs the likelihood of a given observed event cluster as a function of the average time delay due to deflection in the magnetic field, the source activity time scale, the total fluence of the source, and the power law index of the particle injection spectrum. Other parameters such as the coherence length and the power spectrum of the magnetic field are also considered. We apply it to the three pairs of events above 4X10**19 eV recently reported by the Akeno Giant Air Shower Array (AGASA) experiment, assuming that these pairs were caused by nucleon primaries which originated from a common source. Although current data are too sparse to fully constrain each of the parameters considered, and/or to discriminate models of the origin of ultra-high energy cosmic rays, several tendencies are indicated. If the clustering suggested by AGASA is real, next generation experiments with their increased exposure should detect more than 10 particles per source over a few years and our method will put strong constraints on both the large-scale magnetic field parameters and the nature of these sources.Comment: 11 latex pages, 8 postscript figures included, uses revtex.sty in two-column format and epsf.sty. Submitted to Physical Review

Super-Kamiokande 0.07 eV Neutrinos in Cosmology: Hot Dark Matter and the Highest Energy Cosmic Rays

Relic neutrinos with mass in the range indicated by Super-Kamiokande results if neutrino masses are hierarchial (about 0.07 eV) are many times deemed too light to be cosmologically relevant. Here we remark that these neutrinos may significantly contribute to the dark matter of the Universe (with a large lepton asymmetry $L$) and that their existence might be revealed by the spectrum of ultra high energy cosmic rays (maybe even in the absence of a large $L$).Comment: Talk given at the ``4th International Symposium on Sources and Detection of Dark Matter in the Universe", February 23-25, 2000, Marina del Rey, CA (to appear in its proceedings) and at the ``Cosmic Genesis and Fundamental Physics" workshop, October 28-30, 1999, Sonoma State University, Santa Rosa, CA. (8 p. 1 fig.

Propagation of high-energy cosmic rays in extragalactic turbulent magnetic fields: resulting energy spectrum and composition

We extend previous studies of mixed-composition extragalactic cosmic-ray source models, by investigating the influence of a non-negligible extragalactic magnetic field on the propagated cosmic-ray spectrum and composition. We study the transport of charged particles in turbulent fields and the transition from a ballistic to a diffusive propagation regime. We introduce a method allowing a fast integration of the particle trajectories, which allows us to calculate extragalactic cosmic-ray spectra in the general case, without using either the diffusive or the rectilinear approximation. We find that the main features of the mixed-composition models -- regarding the interpretation of the ankle and the non-monotonous evolution of the average cosmic-ray mass -- remain essentially unchanged as long as the magnetic field intensity does not exceed a few nG.Comment: 15 pages, 20 figure

Clustering in Highest Energy Cosmic Rays: Physics or Statistics?

Directional clustering can be expected in cosmic ray observations due to purely statistical fluctuations for sources distributed randomly in the sky. We develop an analytic approach to estimate the probability of random cluster configurations, and use these results to study the strong potential of the HiRes, Auger, Telescope Array and EUSO/OWL/AirWatch facilities for deciding whether any observed clustering is most likely due to non-random sources.Comment: 19 pages, LaTeX, 3 figure

Ultra-High Energy Cosmic Rays in a Structured and Magnetized Universe

We simulate propagation of cosmic ray nucleons above 10^{19} eV in scenarios where both the source distribution and magnetic fields within about 50 Mpc from us are obtained from an unconstrained large scale structure simulation. We find that consistency of predicted sky distributions with current data above 4 x 10^{19} eV requires magnetic fields of ~0.1 microGauss in our immediate environment, and a nearby source density of ~10^{-4}-10^{-3} Mpc^{-3}. Radio galaxies could provide the required sources, but only if both high and low-luminosity radio galaxies are very efficient cosmic ray accelerators. Moreover, at ~10^{19} eV an additional isotropic flux component, presumably of cosmological origin, should dominate over the local flux component by about a factor three in order to explain the observed isotropy. This argues against the scenario in which local astrophysical sources of cosmic rays above ~10^{19} eV reside in strongly magnetized (B~0.1 microGauss) and structured intergalactic medium. Finally we discuss how future large scale full-sky detectors such as the Pierre Auger project will allow to put much more stringent constraints on source and magnetic field distributions.Comment: 11 revtex pages, 10 postscript figures included, final version to appear in PR

Self-Maintained Coherent Oscillations in Dense Neutrino Gases

We present analytical solutions to the nonlinear equations describing the behavior of a gas of neutrinos with two flavors. Self-maintained coherent flavor oscillations are shown to occur when the gas density exceeds a critical value determined by the neutrino masses and the mean neutrino energy in the gas. Similar oscillations may have occurred in the early Universe.Comment: To appear in Physical Review D, July 199