Inverse problem for the equation of ultrahigh energy cosmic ray transport

The propagation of ultrahigh energy nuclei in an expanding universe filled with background electromagnetic radiation is considered. A numerical method for solving the inverse problem for the equation of cosmic ray transport is developed. The method allows us to determine a source spectrum from the cosmic ray spectrum observed near Earth. The spectra of injected protons and nuclei of iron were found in extragalactic sources under the assumption that these types of particles predominate in the composition of the sources. The method of calculation is illustrated using observational data obtained in the Auger and Telescope Array experiments.     

Solving the inverse transport problem in intergalactic space and determining the energy spectrum and composition of extragalactic sources of ultrahigh-energy particles

The propagation of ultrahigh-energy nuclei in an expanding Universe filled with background electromagnetic radiation is considered. A numerical method for solving the inverse problem for the equation of cosmic-ray transport is developed that allows the spectrum of sources to be determined from the cosmic-ray spectrum observed near the Earth. The spectra of injected protons and nuclei in extragalactic sources are found by assuming that they are functions of the magnetic rigidity of particles. The data from observations obtained in the Auger experiment are used.     

Maximum energy of cosmic rays accelerated in supernova remnants

Amplification of the magnetic field in young supernova remnants leads to the corresponding increase in the maximum energy of particles approximately to the knee energy 3 × 10¹⁵ eV at the end of the free expansion stage. The knee in the spectrum of cosmic rays is due to the transition of the supernova remnant from the free expansion stage to the Sedov stage. The knee energy is calculated for different types of supernovae. The maximum energy of accelerated particles teaches Z × 10¹⁷ eV for the observed remnant expansion velocities.     

Nonlinear propagation of cosmic rays in the galaxy

Propagation of cosmic rays in the interstellar medium after their emergence from sources—supernova remnants—may be accompanied by the development of flow instability which forms high magnetohydrodynamic turbulence and leads to nonlinear cosmic ray diffusion. A self-similar solution to the nonlinear diffusion equations is found and it is shown that the noted mechanism leads to an effective diffusion coefficient of cosmic rays, which coincides with the empirical value.     

Tunka-133: Status 2008 and development of methods for data analysis

The activity on creation of a array with an area of 1 km² for recording extensive air showers using Cherenkov light began in the Tunka valley in 2006. The new array will allow one to study cosmic rays in the energy range 10¹⁵–10¹⁸ eV by the unified method. In the winter of 2007–2008, the array operated with 4 clusters, 7 detectors in each cluster. Experimental data obtained during 270 h of fair weather in moonless nights demonstrated unique capabilities of the new array, related with the possibility of recording the pulse shape with a step of 5 ns from each detector.     

Cosmic ray spectrum produced by galactic supernova remnants

Cosmic ray acceleration by supernova shocks is considered. A new numerical code is used to describe the cosmic ray acceleration and shock wave evolution. The magnetohydrodynamic turbulence generation in the shock precursor by streaming instability of accelerated particles is taken into account. The cosmic ray spectrum produced by supernova explosion in uniform interstellar medium is simulated.     

Spectrum of galactic cosmic rays accelerated in supernova remnants

The spectra of protons, nuclei, and electrons accelerated by shocks in supernova remnants of different types were determined. The calculations were made using a numerical code that allows us to model spherical shock evolution and particle acceleration with allowance for the back reaction of accelerating particles on a hydrodynamic flow. The effect of Alfvenic particle drift in the amplified magnetic field in the regions upstream and downstream of the shock was taken into consideration. The maximum energy of accelerated particles is as high as ∼5 × 10¹⁸ eV for iron nuclei in Type IIb supernova remnants. The calculated spectrum and composition of cosmic rays in the interstellar medium are in good agreement with observations.     

Modeling Source Spectra and Composition of Ultrahigh Energy Cosmic Rays

The inverse problem of cosmic ray transport of ultra-high energy cosmic rays is considered. The source spectrum and composition are derived based on the recent Auger data on energy spectrum, energy dependence of mean logarithm of atomic mass number and its variance. The dependence of results on the extrapolation of observable spectrum beyond energies 10²⁰ eV is investigated.

     

Acceleration of ultra-high energy cosmic rays by galaxy cluster accretion shocks

Acceleration of protons and nuclei by shock waves arising during accretion on galaxy clusters is considered. The generation of magnetohydrodynamic turbulence by streaming instability of accelerated particles in a shock precursor, cluster mass distribution, and particle energy loss upon interaction with cosmic microwave background and IR background radiation are taken into account. The contribution of these sources to the cosmic ray intensity observed at energies of 10¹⁷–10²⁰ eV is calculated.