Diffusion of Cosmic Rays in the Expanding Universe. II. Energy Spectra of Ultra-High Energy Cosmic Rays

Abstract

We consider the astrophysical implications of the diffusion equation solution for Ultra-High Energy Cosmic Rays (UHECR) in the expanding universe, obtained in paper I (V.Berezinsky & A.Gazizov, ApJ 643 (2006) 8). The UHECR spectra are calculated in a model with sources located in vertices of the cubic grid with a linear constant (source separation) d. The calculations are performed for various magnetic field configurations (B_c,l_c), where l_c is the basic scale of the turbulence and B_c is the coherent magnetic field on this scale. The main purpose of these calculations is to demonstrate the validity of the solution obtained in paper I and to compare this solution with the Syrovatsky solution used in previous works. The Syrovatsky solution must be necessarily embedded in the static cosmological model. The formal comparison of the two solutions with all parameters being fixed identically reveals the appreciable discrepancies between two spectra. These discrepancies are less if in both models the different sets of the best-fit parameters are used.

17 pages, 10 figures

References in corpus (1)

• A dip in the UHECR spectrum and the transition from galactic to extragalactic cosmic rays

Cited by in corpus (19)

• Continuous-time random-walk model for anomalous diffusion in expanding media
• Ultrahigh energy cosmic rays from a nearby extragalactic source in the diffusive regime
• Ultrahigh-Energy Cosmic Ray Production by Turbulence in Gamma-Ray Burst Jets and Cosmogenic Neutrinos
• An Exact Solution of the Fokker-Planck Equation for Isotropic Scattering
• Implications of gamma-ray observations on proton models of UHECR
• Extragalactic cosmic rays diffusing from two populations of sources
• Non-Universal Spectra of Ultra-High Energy Cosmic Ray Primaries and Secondaries in a Structured Universe
• Continuous Time Random Walk in a velocity field: Role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing
• Impact of the Magnetic Horizon on the Interpretation of the Pierre Auger Observatory Spectrum and Composition Data
• Bounds on the origin of extragalactic ultrahigh energy cosmic rays from the IceCube neutrino observations
• Magnetic diffusion and interaction effects on Ultrahigh Energy Cosmic Rays: protons and nuclei
• Lévy walk dynamics in non-static media
• Case for Centaurus A as the main source of ultrahigh-energy cosmic rays
• Magnetic Suppression of Cosmic Rays' Flux in $\mathbf{f}(\mathbf{R})$ and $\mathbf{f}(\mathbf{Q})$ Theories of Gravity
• Ultraheavy Ultrahigh-Energy Cosmic Rays
• Effects of large-scale magnetic fields on the observed composition of ultra high-energy cosmic rays
• On the relation between the astrophysical neutrino fluxes and the cosmic ray fluxes
• Modelling Cosmic Rays Flux with Pierre Auger and Telescope Array Data in $\mathbf{f}(\mathbf{R})$ and $\mathbf{f}(\mathbf{Q})$ Theories of Gravity
• Ultra-high energy cosmic rays with UFA-15 source model in Bumblebee gravity theory