Kolmogorov–Smirnov test as a tool to study the distribution of ultra-high energy cosmic ray sources

We analyse in detail the two-dimensional Kolmogorov–Smirnov test as a tool to learn about the distribution of the sources of the ultra-high energy cosmic rays. We confront, in particular, models based on active galactic nuclei observed in X-rays, galaxies observed in H  i and isotropic distributions, discussing how this method can be used not only to reject isotropy but also to support or reject specific source models, extending results obtained recently in the literature.     

A study of solar modulation of medium energy primary cosmic ray nuclei

The energy spectra of primary cosmic rays were studied in the energy interval 150 to 450 MeV/nucl by using balloon-borne cellulose-nitrate solid-state plastic detector. Effects of solar modulation were studied using the theoretical spectrum ofH ₁ nuclei near the solar minimum in 1964 as the demodulated spectrum. The ‘force-field’ potential which fit the experimental results was estimated to be 270 MeV/nucl.     

The Galactic magnetic field as spectrograph for ultra-high energy cosmic rays

We study the influence of the regular component of the Galactic magnetic field (GMF) on the arrival directions of ultra-high energy cosmic rays (UHECRs). We find that, if the angular resolution of current experiments has to be fully exploited, deflections in the GMF cannot be neglected even for E = 10²⁰ eV protons, especially for trajectories along the Galactic plane or crossing the Galactic center region. On the other hand, the GMF could be used as a spectrograph to discriminate among different source models and/or primaries of UHECRs, if its structure would be known with sufficient precision. We compare several GMF models introduced in the literature and discuss for the example of the AGASA data set how the significance of small-scale clustering or correlations with given astrophysical sources are affected by the GMF. We point out that the non-uniform exposure to the extragalactic sky induced by the GMF should be taken into account estimating the significance of potential (auto-) correlation signals.     

Ultrahigh energy cosmic ray acceleration in Seyfert galactic nuclei

We propose a model for the particle acceleration to energy E≈10²¹ eV in Seyfert galactic nuclei. The model is based on the theory of active galactic nuclei by Vilkoviskij et al. (1999). The acceleration takes place in hot spots of relativistic jets, which decay in a dense stellar kernel at a distance of 1–3 pc from the center. The maximum energy and chemical composition of the accelerated particles depend on the jet magnetic-field strength. Fe nuclei acquire the largest energy, E≈8×10²⁰ eV, if the jet field strength is B≈16 G. At a field strength B～5–40 G, the nuclei with Z≥10 acquire energy E≥2×10²⁰ eV; the lighter nuclei are accelerated to E≤10²⁰ eV. In a field B～1000 G, only the particles with Z≥23 gain energy E≤10²⁰ eV. The protons are accelerated to E<4×10¹⁹ eV, and they do not fall within the energy range concerned at any field strength B. Interactions with infrared photons do not affect the accelerated-particle escape from the sources if the galactic luminosity L≤10⁴⁶ erg s^?1 and if the angle between the normal to the galactic plane and the line of sight is sufficiently small, i.e., if the galactic-disk axial ratio is comparatively large. The particles do not lose their energy through magnetodrift radiation if their deflection from the jet axis does not exceed 0.03–0.04 pc at a distance R≈40–50 pc from the center. The synchrotron losses are small, because the magnetic field frozen in the galactic wind at R≤40–50 pc is directed (as in the jet) predominantly along the motion. If this model is correct, then the detected protons are nuclear fragments or are accelerated in other sources. The jet magnetic fields can be estimated by using the cosmic-ray energy spectrum and chemical composition.     

Dependence of the position of the knee in the Galactic cosmic ray spectrum on the explosion energy distribution of supernovae

The position of the knee in the Galactic cosmic ray (GCR) spectrum is shown to depend on the explosion energy distribution function of supernovae (SN). The position of the knee in the GCR spectrum can be quantitatively explained by the dominating contribution of hypernovae with explosion energies of (～30–50)×10⁵¹ erg, the fraction of which must be no less than 1% of all SN. The model reproduces the main features in the spectrum of all particles measured in extensive air shower (EAS) experiments: the knee in the spectrum of all particles at energy of about 3 PeV, the change in slope by δ_γ ～ 0.3–0.5 after the knee point, and the steepening of the spectrum near 10¹⁸ eV. The model predicts a smooth knee if the SN explosion energy distribution is universal and a sharp knee if the hypernovae represent a separate class of events. The suggested model of the GCR spectrum is essentially based on the assumption that a spread in explosion energies exists and that the assumptions of the standard model for the CR acceleration in supernova remnants are valid.     

Using spherical wavelets to search for magnetically-induced alignment in the arrival directions of ultra-high energy cosmic rays

Due to the action of the intervening cosmic magnetic fields, ultra-high energy cosmic rays (UHECRs) can be deflected in such a way as to create clustered energy-ordered filamentary structures in the arrival direction of these particles, the so-called multiplets. In this work we propose a new method based on the spherical wavelet transform to identify multiplets in sky maps containing arrival directions of UHECRs. The method is illustrated in simulations with a multiplet embedded in isotropic backgrounds with different numbers of events. The efficiency of the algorithm is assessed through the calculation of Type I and II errors.     

Radio pulses from ultra-high energy atmospheric showers as the superposition of Askaryan and geomagnetic mechanisms

Radio emission in atmospheric showers is currently interpreted in terms of radiation due to the deviation of the charged particles in the magnetic field of the Earth and to the charge excess (Askaryan effect). Each of these mechanisms has a distinctive polarization. The complex signal patterns can be qualitatively explained as the interference (superposition) of the fields induced by each mechanism. In this work we explicitly and quantitatively test a simple phenomenological model based on this idea. The model is constructed by isolating each of the two components at the simulation level and by making use of approximate symmetries for each of the contributions separately. The results of the model are then checked against full ZHAireS Monte Carlo simulations of the electric field calculated from first principles. We show that the simple model describes radio emission at a few percent level in a wide range of shower-observer geometries and on a shower-by-shower basis. As a consequence, this approach provides a simple method to reduce the computing time needed to accurately predict the electric field of radio pulses emitted from air showers, with many practical applications in experimental situations of interest.     

Spurious contribution to cosmic ray scattering calculations

The quasi-linear theory for cosmic ray propagation is a well-known and widely accepted theory. In this paper, we discuss the different contributions to the pitch-angle Fokker–Planck coefficient from large and small scales for slab geometry using the damping model of dynamical turbulence. These examinations will give us a hint on the limitation range where the quasi-linear approximation is a good approximation.     

Study of dispersion of mass distribution of ultra-high energy cosmic rays using a surface array of muon and electromagnetic detectors

We consider a hypothetical observatory of ultra-high energy cosmic rays consisting of two surface detector arrays that measure independently electromagnetic and muon signals induced by air showers. Using the constant intensity cut method, sets of events ordered according to each of both signal sizes are compared giving the number of matched events. Based on its dependence on the zenith angle, a parameter sensitive to the dispersion of the distribution of the logarithmic mass of cosmic rays is introduced. The results obtained using two post-LHC models of hadronic interactions are very similar and indicate a weak dependence on details of these interactions.     

Transient phenomena in cosmic ray intensity during extreme events

In the present work an analysis has been made of the extreme events occurring during July 2005. Specifically, a rather intense Forbush decrease was observed at different neutron monitors all over the world during 16 July 2005. An effort has been made to study the effect of this unusual event on cosmic ray intensity as well as various solar and interplanetary plasma parameters. It is noteworthy that during 11 to 18 July 2005 the solar activity ranged from low to very active. Especially low levels occurred on 11, 15, and 17 July whereas high levels took place on 14 and 16 July 2005. The Sun is observed to be active during 11 to 18 July 2005, the interplanetary magnetic field intensity lies within 15 nT, and solar wind velocity was limited to ∼500 kms-1. The geomagnetic activity during this period remains very quiet, the Kp index did not exceed 5, the disturbance storm time Dst index remains ∼-70 nT and no sudden storm commencement has been detected during this period. It is noted that for the majority of the hours, the north/south component of the interplanetary magnetic field, Bz, remains negative, and the cosmic ray intensity increases and shows good/high correlation with Bz, as the polarity of Bz tends to shift from negative to positive values, the intensity decreases and shows good/high anti-correlation with Bz. The cosmic ray intensity tends to decrease with increase of interplanetary magnetic field strength (B) and shows anti-correlation for the majority of the days. Published in Astrofizika, Vol. 51, No. 2, pp. 255–265 (May 2008).     

On the contribution of nearby sources to the observed cosmic ray nuclei

The presence of nearby discrete cosmic ray (CR) sources can lead to many interesting effects on the observed properties of CRs. In this paper, we study about the possible effects on the CR primary and secondary spectra and also the subsequent effects on the CR secondary-to-primary ratios. For the study, we assume that CRs undergo diffusive propagation in the Galaxy and we neglect the effect of convection, energy losses and reacceleration. In our model, we assume that there exists a uniform and continuous distribution of CR sources in the Galaxy generating a stationary CR background at the Earth. In addition, we also consider the existence of some nearby sources which inject CRs in a discrete space–time model. Assuming a constant CR source power throughout the Galaxy, our study has found that the presence of nearby supernova remnants (SNRs) produces noticeable variations in the primary fluxes mainly above ∼100 GeV n⁻¹, if CRs are assumed to be released instantaneously after the supernova explosion. The variation reaches a value of ∼45 per cent at around 10⁵ GeV n⁻¹. Respect to earlier studies, the variation in the case of the secondaries is found to be almost negligible. We also discuss about the possible effects of the different particle release times from the SNRs. For the particle release time of ∼10⁵ yr, predicted by the diffusive shock acceleration theories in SNRs, we have found that the presence of the nearby SNRs hardly produces any significant effects on the CRs at the Earth.     

Chaos in cosmic ray air showers

Unexpected chaotic features are found in time series of arrival time intervals of successive air showers with (E > 3 × 10¹⁴ eV). Over 99 % of air shower arrival time intervals obey the Poisson distribution law representing stochastic behaviors, but occasionally there are air showers showing real chaotic behaviors as distinguished from both random and colored noises. With two systems of the Kinki university installations, we found 13 cases showing chaotic time series in 3.36 yr with the system-1 and the 1.37 yr with the system-2. Five out of 10 chaotic air showers of the Kinki installation are detected during the same time zone also by the Osaka City university installation which is at 115 km distance from the Kinki one. In a remarkable example of September 19, 1991, the correlation dimension was observed to have dropped from about 4 to the minimum of 1.3 and recovered smoothly in about 38 h. The chaos structure in this case is detected in nearly the same time zone at the Ohya station of the Institute for Cosmic Ray Research, University of Tokyo, which is separated from the Kinki one by 460 km. Formation of chaos structure due to energetic cosmic ray dust particles is suggested. Progress of cosmic ray physics may be expected with the study of air showers marked with chaos.     

Primordial black holes as a source of extremely high energy cosmic rays

The origin of observed extremely high energy cosmic rays remains an astrophysical enigma. We show that a single evaporating primordial black hole should produce 8.5·10¹⁴ particles over a 10²⁰ eV threshold. This emission results from direct production of fundamental constituents and from hadronization of quarks and gluons. The induced flux on the Earth is studied as a function of the local density of exploding black holes and compared with experimental data. The discovery potential of future detectors is finally reviewed.     

Gamma ray signatures of ultra high energy cosmic ray accelerators: electromagnetic cascade versus synchrotron radiation of secondary electrons

We discuss the possibility of observing ultra high energy cosmic ray sources in high energy gamma rays. Protons propagating away from their accelerators produce secondary electrons during interactions with cosmic microwave background photons. These electrons start an electromagnetic cascade that results in a broad band gamma ray emission. We show that in a magnetized Universe (B≳10⁻¹² G) such emission is likely to be too extended to be detected above the diffuse background. A more promising possibility comes from the detection of synchrotron photons from the extremely energetic secondary electrons. Although this emission is produced in a rather extended region of size ∼10 Mpc, it is expected to be point-like and detectable at GeV energies if the intergalactic magnetic field is at the nanogauss level.      

The maximum energy and spectra of cosmic rays accelerated in active galactic nuclei

Astronomy Letters - We computed the energy spectra of the incident (on an air shower array) ultrahigh-energy (E&;gt;4×1019eV) cosmic rays (CRs) that were accelerated in nearby Seyfert...     

Structures in the cosmic ray energy spectra

All the components of Cosmic Rays (CR) have ‘structure’ in their energy spectra at some level, i.e. deviations from a simple power law, and their examination is relevant to the origin of the particles. Emphasis, here, is placed on the large-scale structures in the spectra of nuclei (the ‘knee’ at about 3 PeV), that of electrons plus positrons (a shallow ‘upturn’ at about 100 GeV) and the positron to electron plus positron ratio (an upturn starting at about 5 GeV).Fine structure is defined as deviations from the smooth spectra which already allow for the large-scale structure. Search for the fine structure has been performed in the precise data on positron to electron plus positron ratio measured by the AMS-02 experiment. Although no fine structure is indicated, it could in fact be present at the few percent level.