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تسجيل مستخدم جديدA dip in the UHECR spectrum and the transition from galactic to extragalactic cosmic rays
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The dip is a feature in the diffuse spectrum of ultra-high energy (UHE) protons caused by electron-positron pair production on the cosmic microwave background (CMB) radiation. For a power-law generation spectrum $E^{-2.7}$, the calculated position and shape of the dip is confirmed with high accuracy by the spectra observed by the Akeno-AGASA, HiRes, Yakutsk and Flys Eye detectors. When the particle energies, measured in these detectors, are calibrated by the dip, their fluxes agree with a remarkable accuracy. The predicted shape of the dip is quite robust. The dip is only modified strongly when the fraction of nuclei heavier than protons is high at injection, which imposes some restrictions on the mechanisms of acceleration operating in UHECR sources. The existence of the dip, confirmed by observations, implies that the transition from galactic to extragalactic cosmic rays occurs at $E lsim 1times 10^{18}$ eV. We show that at energies lower than a characteristic value $E_{rm cr}approx 1times 10^{18}$ eV, the spectrum of extragalactic cosmic rays flattens in all cases of interest, and it provides a natural transition to a steeper galactic cosmic ray spectrum. This transition occurs at some energy below $E_{rm cr}$, corresponding to the position of the so-called second knee. We discuss extensively the constraints on this model imposed by current knowledge of acceleration processes and sources of UHECR and compare it with the traditional model of transition at the ankle.
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The transition from galactic to extragalactic cosmic rays is discussed. One of critical indications for transition is given by the Standard Model of Galactic cosmic rays, according to which the maximum energy of acceleration for iron nuclei is of ord
er of $E_{rm Fe}^{rm max} approx 1times 10^{17}$ eV. At $E > E_{rm Fe}^{rm max}$ the spectrum is predicted to be very steep and thus the Standard Model favours the transition at energy not much higher than $E_{rm Fe}^{rm max}$. As observations are concerned there are two signatures of transition: change of energy spectra and elongation rate (depth of shower maximum in the atmosphere $X_{rm max}$ as function of energy). Three models of transition are discussed: dip-based model, mixed composition model and ankle model. In the latter model the transition occurs at the observed spectral feature, ankle, which starts at $E_a approx 1times 10^{19}$ eV and is characterised by change of mass compostion from galactic iron to extragalactic protons. In the dip model the transition occures at the second knee observed at energy $(4 -8)times 10^{17}$ eV and is characterised by change of mass composition from galactic iron to extragalactic protons. The mixed composition model describes transition at $E sim 3times 10^{18}$ eV with mass composition changing from galactic iron to extragactic mixed composition of different nuclei. These models are confronted with observational data on spectra and elongation rates from different experiments, including Auger.
The study of the transition between galactic and extragalactic cosmic rays can shed more light on the end of the Galactic cosmic rays spectrum and the beginning of the extragalactic one. Three models of transition are discussed: ankle, dip and mixed
composition models. All these models describe the transition as an intersection of a steep galactic component with a flat extragalactic one. Severe bounds on these models are provided by the Standard Model of Galactic Cosmic Rays according to which the maximum acceleration energy for Iron nuclei is of the order of $E_{rm Fe}^{rm max} approx 1times 10^{17}$ eV. In the ankle model the transition is assumed at the ankle, a flat feature in the all particle spectrum which observationally starts at energy $E_a sim (3 - 4)times 10^{18}$ eV. This model needs a new high energy galactic component with maximum energy about two orders of magnitude above that of the Standard Model. The origin of such component is discussed. As observations are concerned there are two signatures of the transition: change of energy spectra and mass composition. In all models a heavy galactic component is changed at the transition to a lighter or proton component.
We discuss the signatures of the transition from galactic to extragalactic cosmic rays in different scenarios, giving most attention to the dip scenario. The dip is a feature in the diffuse spectrum of ultra-high energy (UHE) protons in the energy ra
nge $1times 10^{18} - 4times 10^{19}$ eV, which is caused by electron-positron pair production on the cosmic microwave background (CMB) radiation. The dip scenario provides a simple physical description of the transition from galactic to extragalactic cosmic rays. Here we summarize the signatures of the pair production dip model for the transition, most notably the spectrum, the anisotropy and the chemical composition. The main focus of our work is however on the description of the features that arise in the elongation rate and in the distribution of the depths of shower maximum $X_{rm max}$ in the dip scenario. We find that the curve for $X_{max}(E)$ shows a sharp increase with energy, which reflects a sharp transition from an iron dominated flux at low energies to a proton dominated flux at $Esim 10^{18}$ eV. We also discuss in detail the shape of the $X_{max}$ distributions for cosmic rays of given energy and demonstrate that this represents a powerful tool to discriminate between the dip scenario and other possible models of the transition.
The status of the pair-production dip as a spectral feature, produced by interaction of Ultra High Energy extragalactic protons with CMB is discussed.
From the analysis of the flux of high energy particles, $E>3cdot 10^{18}eV$, it is shown that the distribution of the power density of extragalactic rays over energy is of the power law, ${bar q}(E)propto E^{-2.7}$, with the same index of $2.7$ that
has the distribution of Galactic cosmic rays before so called knee, $E<3cdot 10^{15}eV$. However, the average power of extragalactic sources, which is of ${cal E}simeq 10^{43}erg ,s^{-1}$, at least two orders exceeds the power emitted by the Galaxy in cosmic rays, assuming that the density of galaxies is estimated as $N_gsimeq 1 Mpc^{-3}$. Considering that such power can be provided by relativistic jets from active galactic nuclei with the power ${cal E}simeq 10^{45} - 10^{46} erg , s^{-1}$, we estimate the density of extragalactic sources of cosmic rays as $N_gsimeq 10^{-2}-10^{-3}, Mpc^{-3}$. Assuming the same nature of Galactic and extragalactic rays, we conclude that the Galactic rays were produced by a relativistic jet emitted from the Galactic center during the period of its activity in the past. The remnants of a bipolar jet are now observed in the form of bubbles of relativistic gas above and below the Galactic plane. The break, observed in the spectrum of Galactic rays (knee), is explained by fast escape of energetic particle, $E>3cdot 10^{15}eV$, from the Galaxy because of the dependence of the coefficient of diffusion of cosmic rays on energy, $Dpropto E^{0.7}$. The obtained index of the density distribution of particles over energy, $N(E)propto E^{-2.7-0.7/2}=E^{-3.05}$, for $E>3cdot 10^{15}eV$ agrees well with the observed one, $N(E)propto E^{-3.1}$. Estimated time of termination of the jet in the Galaxy is $4.2cdot 10^{4}$ years ago.
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