65 research outputs found
Factorization and Lie point symmetries of general Lienard-type equation in the complex plane
We present a variational approach to a general Lienard-type equation in order
to linearize it and, as an example, the Van der Pol oscillator is discussed.
The new equation which is almost linear is factorized. The point symmetries of
the deformed equation are also discussed and the two-dimensional Lie algebraic
generators are obtained
On astrophysical solution to ultra high energy cosmic rays
We argue that an astrophysical solution to UHECR problem is viable. The
pectral features of extragalactic protons interacting with CMB are calculated
in model-independent way. Using the power-law generation spectrum as the only assumption, we analyze four features of the proton
spectrum: the GZK cutoff, dip, bump and the second dip. We found the dip,
induced by electron-positron production on CMB, as the most robust feature,
existing in energy range eV. Its shape is
stable relative to various phenomena included in calculations. The dip is well
confirmed by observations of AGASA, HiRes, Fly's Eye and Yakutsk detectors. The
best fit is reached at , with the allowed range 2.55 - 2.75. The
dip is used for energy calibration of the detectors. After the energy
calibration the fluxes and spectra of all three detectors agree perfectly, with
discrepancy between AGASA and HiRes at eV being not
statistically significant. The agreement of the dip with observations should be
considered as confirmation of UHE proton interaction with CMB. The dip has two
flattenings. The high energy flattening at eV
automatically explains ankle. The low-energy flattening at eV provides the transition to galactic cosmic rays. This transition is
studied quantitatively. The UHECR sources, AGN and GRBs, are studied in a
model-dependent way, and acceleration is discussed. Based on the agreement of
the dip with existing data, we make the robust prediction for the spectrum at
eV to be measured in the nearest future by
Auger detector.Comment: Revised version as published in Phys.Rev. D47 (2006) 043005 with a
small additio
Small Scale Anisotropy Predictions for the Auger Observatory
We study the small scale anisotropy signal expected at the Pierre Auger
Observatory in the next 1, 5, 10, and 15 years of operation, from sources of
ultra-high energy (UHE) protons. We numerically propagate UHE protons over
cosmological distances using an injection spectrum and normalization that fits
current data up to \sim 10^{20}\eV. We characterize possible sources of
ultra-high energy cosmic rays (UHECRs) by their mean density in the local
Universe, Mpc, with between 3 and 6.
These densities span a wide range of extragalactic sites for UHECR sources,
from common to rare galaxies or even clusters of galaxies. We simulate 100
realizations for each model and calculate the two point correlation function
for events with energies above 4 \times 10^{19}\eV and above 10^{20}\eV, as
specialized to the case of the Auger telescope. We find that for r\ga 4,
Auger should be able to detect small scale anisotropies in the near future.
Distinguishing between different source densities based on cosmic ray data
alone will be more challenging than detecting a departure from isotropy and is
likely to require larger statistics of events. Combining the angular
distribution studies with the spectral shape around the GZK feature will also
help distinguish between different source scenarios.Comment: 15 pages, 6 figures, 6 tables, submitted to JCA
Diffusion of Cosmic Rays in the Expanding Universe. II. Energy Spectra of Ultra-High Energy Cosmic Rays
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.Comment: 17 pages, 10 figure
GZK Photons Above 10 EeV
We calculate the flux of "GZK-photons", namely the flux of photons produced
by extragalactic nucleons through the resonant photoproduction of pions, the so
called GZK effect. This flux depends on the UHECR spectrum on Earth, of the
spectrum of nucleons emitted at the sources, which we characterize by its slope
and maximum energy, on the distribution of sources and on the intervening
cosmological backgrounds, in particular the magnetic field and radio
backgrounds. For the first time we calculate the GZK photons produced by
nuclei. We calculate the possible range of the GZK photon fraction of the total
UHECR flux for the AGASA and the HiRes spectra. We find that for nucleons
produced at the sources it could be as large as a few % and as low as 10^{-4}
above 10 EeV. For nuclei produced at the sources the maximum photon fraction is
a factor of 2 to 3 times smaller above 10 EeV but the minimum could be much
smaller than for nucleons. We also comment on cosmogenic neutrino fluxes.Comment: 20 pages, 9 figures (21 panels), iopart.cls and iopart12.clo needed
to typese
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