Calculation of the TeV prompt muon component in very high energy cosmic ray showers

HEMAS-DPM is a Monte Carlo for the simulation of very high energy cosmic ray showers, which includes the DPMJET-II code based on the two component Dual Parton Model. DPMJET-II provides also charm production in agreement with data and, for p exceeding 5 GeV/c, with perturbative QCD results in proton-proton interactions. In this respect, a new scheme has been considered for the inclusive production of D mesons at large p in hadronic collisions in the framework of perturbative fragmentation functions, allowing an analysis at the Next to Leading Order (NLO) level which goes beyond the fixed I(_s³) perturbative theory of open charm production. We have applied HEMAS-DPM to the calculation of the prompt muon component for E_μ ≥ 1 TeV in air showers considering the two extreme cases of primary protons and Fe nuclei.     

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.     

A composition dependent energy scale and the determination of the cosmic ray primary mass in the ankle region

At present there are still several open questions about the origin of the ultra high energy cosmic rays. However, great progress in this area has been made in recent years due to the data collected by the present generation of ground based detectors like the Pierre Auger Observatory and Telescope Array. In particular, it is believed that the study of the composition of the cosmic rays as a function of energy can play a fundamental role for the understanding of the origin of the cosmic rays.The observatories belonging to this generation are composed of arrays of surface detectors and fluorescence telescopes. The duty cycle of the fluorescence telescopes is ∼10% in contrast with the ∼100% of the surface detectors. Therefore, the energy calibration of the events observed by the surface detectors is performed by using a calibration curve obtained from a set of high quality events observed in coincidence by both types of detectors. The advantage of this method is that the reconstructed energy of the events observed by the surface detectors becomes almost independent of simulations of the showers because just a small part of the reconstructed energy (the missing energy), obtained from the fluorescence telescopes, comes from simulations. However, the calibration curve obtained in this way depends on the composition of the cosmic rays, which can introduce biases in composition analyses when parameters with a strong dependence on primary energy are considered. In this work we develop an analytical method to study these effects. We consider AMIGA (Auger Muons and Infill for the Ground Array), the low energy extension of the Pierre Auger Observatory corresponding to the surface detectors, to illustrate the use of the method. In particular, we study the biases introduced by an energy calibration dependent on composition on the determination of the mean value of the number of muons, at a given distance to the showers axis, which is one of the parameters most sensitive to primary mass and has an almost linear dependence with primary energy.     

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.     

Detecting filaments in the ultra-high energy cosmic ray distribution

We propose and test new statistical tools to study the distribution of cosmic rays based on the use of the minimal spanning tree. The method described is particularly sensitive to filamentary structures, as those expected to arise from strong sources of charged cosmic rays which get deflected by intervening magnetic fields. We also test the method with data available from the AGASA and SUGAR surface detector arrays.     

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.     

The synergy of the cosmic ray and high energy atmospheric physics: Particle bursts observed by arrays of particle detectors

Particle bursts detected on the earth's surface during thunderstorms by various particle detectors originated from the relativistic runaway electron avalanches (RREAs) initiated by free electrons accelerated in the strong atmospheric electric fields. Two oppositely directed dipoles in the thundercloud accelerate electrons in the direction of the earth's surface, and to the open space. The particle bursts observed by orbiting gamma ray observatories are called terrestrial gamma ray flashes (TGFs, with energies of several MeV, only sometimes reaching tens of MeV); ones registered by particle detectors located on the ground – are called thunderstorm ground enhancements (TGEs, with energies, usually reaching 40-50 MeV). Balloons and aircraft in the troposphere register gamma ray glows (with energies of several MeV). Recently, high-energy atmospheric physics includes also, so-called, downward TGFs (DTGFs), intense particle bursts with a duration of a few milliseconds.Well-known extensive air showers (EASs) originate from the interactions of galactic protons and fully-stripped nuclei with the atmosphere atoms. EAS particles have very dense cores around the shower axes. However, high-energy particles in the EAS cores comprise a very thin disc of (a few tens of ns), and a particle detector traversed by an EAS core will not register a particle burst, but only one very large pulse. Only neutron monitor, by collecting delayed thermal neutrons from EAS core particle interactions with soil, can register particle bursts. We discuss the relation between short particle bursts available from the largest particle arrays with EAS phenomena. We demonstrate that the neutron monitors can extend the EAS “lifetime” up to a few milliseconds, a time comparable with DTGFs duration. The possibility to use the network of neutron monitors for high-energy cosmic ray research is also deliberated.Plain Language Summary: Short and extended particle bursts are registered in space, the troposphere, and the earth's surface. Coordinated monitoring of the particle fluxes, near-surface electric fields, and lightning flashes makes it possible to formulate a hypothesis on the origin of intense bursts and their relation to extensive air showers and atmospheric discharges. Analysis of the observational data and possible origination scenarios of particle bursts allows us to conclude that the bursts can be explained by the electron acceleration in the thunderous atmosphere and by gigantic showers developed in the terrestrial atmosphere by high-energy protons and fully-stripped nuclei accelerated in Galaxy.     

A comparison of the energy spectra of cosmic ray helium and heavy nuclei

Recent observations of the spectra of cosmic ray helium, M, LH and VH nuclei in the energy range from 200 MeV/nuc to>22 GeV/nuc are reported. The differential spectra of all of these groups of nuclei are found to have a maximum at 300–400 MeV/nuc at sunspot minimum. The average exponents on the integral rigidity spectra in the range 5 to 50 GV are 1.54±0.03 for He nuclei, 1.50±0.04 for M nuclei, 1.47±0.06 for LH nuclei and 1.40±0.08 for VH nuclei. The spectra of these groups of nuclei are compared and it is found that the average He/M, He/LH and He/VH ratios are 16±1, 70±3 and 200±15 respectively. These values are reasonably constant from the highest down to the lowest energies measured although some evidence for a dip is present in the 500–1000 MeV/nuc range for both the He/LH and He/VH ratios. Solar modulation effects on these ratios are discussed and it is concluded that the ratios measured at earth are representative of those existing in interstellar space only if energy loss processes in interplanetary space are unimportant. The influence of interstellar propagation on the spectra and charge ratios at low energies arising from ionization energy loss and nuclear spallation during matter traversal is examined. It is found that propagation models that contain a large number of relatively short path lengths significantly modify the expected effects of ionization energy loss at low energies. Specifically it is suggested that the presently measured charge ratios are consistent with the passage of the average cosmic radiation through enough matter to reproduce the abundances of the so-called fragmentation nuclei, Li, Be, B and He³. Two component models are not required to explain our data. Rather we feel that a better representation of the situation results from considering a continuous spatial distribution of sources which, along with the actual interstellar propagation conditions, leads to a particular distribution of matter path lengths. It is pointed out that large differences exist in the approaches used in the literature to calculate the effects of matter traversal in interstellar space at low energies. These differences play an important role in the interpretation of the experimental results. Significant modifications of the charge ratios at low energies can also be obtained by requiring that some of the matter traversal occur in the cosmic ray sources themselves during the cosmic ray acceleration process. This may be sufficient to produce charge ratios that are essentially flat at low energies even in the presence of interstellar ionization loss.     

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.     

Heavy quark production in ultra high energy cosmic ray interactions

In this paper we present a comprehensive study of the heavy quark production in ultra high energy cosmic ray interactions in the atmosphere considering that the primary cosmic ray can be either a photon, neutrino or a proton. The analysis is performed using a unified framework – the dipole formalism – and the saturation effects, associated to the physical process of parton recombination, are taken into account. We demonstrate that the contribution of heavy quarks for cosmic ray interactions is in general non-negligible and can be dominant depending of the process considered. Moreover, our results indicate that new dynamical mechanisms should be included in order to obtain reliable predictions for the heavy quark production in pp collisions at ultra high cosmic ray energies.     

The cosmic ray energy spectrum between 10 and 10 eV

The energy spectrum of cosmic rays with primary energies between 10¹⁴ eV and 10¹⁶ eV has been studied with the CASA-MIA air shower array. The measured differential energy spectrum is a power law (dj/dE ∝ E^−y) with spectral indices γ of 2.66±0.02 below approximately 10¹⁵ eV and 3.00±0.05 above. A new method is used for measuring primary energy derived from ground-based data in a compositionally insensitive way. In contrast with some previous reports, the “knee” of the energy spectrum does not appear sharp, but rather a smooth transition over energies from 10¹⁵ eV to 3.0 × 10¹⁵ eV.     

Ionization states and the origin of low energy cosmic ray nuclei

The origin of the new component of cosmic ray nuclei in 1–30 MeV amu^–1 recently detected through space vehicles in interplanetary space is investigated in detail. It is assumed that these particles may originate from nearby sources, e.g., from novae type explosions, which have peculiar C, N and O compositions. These particles are further assumed to be accelerated and modulated within the heliosphere. The charged states of these ions in the interstellar space have been calculated in detail and it is shown that the same charged states are preserved in the heliosphere when they are accelerated to energies of the order of 10⁷eV amu^–1 from energies of 10⁵ ev amu^–1. Modulation of these ions are calculated and it is found that because of low charged states of the ions these have high rigidities and are modulated in such a way as to enhance the O-ion abundances as compared to C-ions. A comparison is made of the demodulated composition of C to Si-ions with available abundance data of some novae.     

The measurement of the decorrelation function in underground muon pairs as a probe of primary cosmic ray interactions

We discuss the measurement of the average angle within pairs of muons detected in underground experiments versus their relative distance, as a tool for studying primary Cosmic Ray interactions. We propose to call Φ(d) “decorrelation” function. Under simplifying approximation, the decorrelation function can be computed analytically to show its dependence on details of cosmic ray interactions as well as on the propagation in the rock. We argue that this new measurement is useful in a real experiment, complementing traditional ones like the decoherence function.     

On the modulation and energy spectrum of highly charged cosmic ray nuclei

The intensity and energy spectrum of cosmic ray VH-nuclei (20Z30) has been measured in a stack of nuclear emulsions exposed over Fort Churchill in 1968. The integral intensity above 300 MeV/nucleon was 1.04±0.04 nuclei m^–2 sr^–1 s^–1 and three differential intensities were measured below 750 MeV/nucleon. Because of the current controversy regarding the true intensities of helium nuclei at this phase of the solar cycle we have also measured these nuclei, obtaining results intermediate between those quoted by other workers. Comparison of these results on the VH-and helium nuclei with those obtained in previous observations made at times of low solar modulation leads to the conclusion that there is no significant charge dependence in the modulation process. This conclusion is in conflict with an earlier analysis but depends on results of improved statistical weight and greater reliability for the VH nuclei and on our measurement of the helium nuclei in the same detector.Supported by the Office of Naval Research under Contract No. N00014-67-A-0113-0021.     

The energy spectrum of cosmic ray electrons between 10 and 1000 GeV

Measurements made by the Bombay Group on the fluxes of cosmic ray electrons in the energy range 10–1000 GeV have been compared with those of other workers in the same energy domain with a view to understand the present confused situation on the existing observations at these high energies. Such an analysis clearly brings out the current situation in its true perspective and highlights the care and emphasis to be placed on future experimentation in this important field.     

Anisotropy characteristics of low energy cosmic ray population of solar origin

Comparison of Explorer 34 observations on solar protons in the energy range 0.7–55 MeV with similar observations from other spacecrafts show that the large field aligned anisotropies which are observed during the rise time of a flare event change to an equilibrium anisotropy coming radially from the sunward direction due to the convective removal of the solar particles. At very late times during the decay (T 4 days) the anisotropy is observed to be from a direction 45° E of the satellite-Sun line which is interpreted as indicative of positive density gradient of solar cosmic ray population. The dependence of both types of equilibrium anisotropies on the energy and the velocity of the particles and on plasma velocity are shown to be in agreement with the theoretical predictions. The amplitude of the large field aligned anisotropies observed earlier in the event is found to be independent of the rise time of the event and to vary as (Vt)^–1.Interplanetary magnetic sector crossings during a flare event, cause abrupt changes in both the amplitude and phase of the non-equilibrium anisotropy whereas they have no significant effect on equilibrium anisotropy. The effect of azimuthal density gradients on the decay time constants of flare enhancements are also examined in an attempt to understand the complicated structures, often observed, in the time intensity profiles at low energies.Part of this work was done while the author was at the University of Texas as Dallas, U.S.A.Now at the National Academy of Sciences, Washington, D.C.     

The cosmic ray primary composition between 10 and 10 eV from Extensive Air Showers electromagnetic and TeV muon data

The cosmic ray primary composition in the energy range between 10¹⁵ and 10¹⁶ eV, i.e., around the “knee” of the primary spectrum, has been studied through the combined measurements of the EAS-TOP air shower array (2005 m a.s.l., 10⁵ m² collecting area) and the MACRO underground detector (963 m a.s.l., 3100 m w.e. of minimum rock overburden, 920 m² effective area) at the National Gran Sasso Laboratories. The used observables are the air shower size (N_e) measured by EAS-TOP and the muon number (N_μ) recorded by MACRO. The two detectors are separated on average by 1200 m of rock, and located at a respective zenith angle of about 30°. The energy threshold at the surface for muons reaching the MACRO depth is approximately 1.3 TeV. Such muons are produced in the early stages of the shower development and in a kinematic region quite different from the one relevant for the usual N_μ−N_e studies. The measurement leads to a primary composition becoming heavier at the knee of the primary spectrum, the knee itself resulting from the steepening of the spectrum of a primary light component (p, He) of Δγ=0.7±0.4 at E₀4×10¹⁵ eV. The result confirms the ones reported from the observation of the low energy muons at the surface (typically in the GeV energy range), showing that the conclusions do not depend on the production region kinematics. Thus, the hadronic interaction model used (CORSIKA/QGSJET) provides consistent composition results from data related to secondaries produced in a rapidity region exceeding the central one. Such an evolution of the composition in the knee region supports the “standard” galactic acceleration/propagation models that imply rigidity dependent breaks of the different components, and therefore breaks occurring at lower energies in the spectra of the light nuclei.     

Origin of low energy cosmic ray positrons at energies ≳2 MeV

It is shown that an appreciable flux of positrons below a few MeV in the cosmic radiation could arise from the decay of cobalt nuclei in the decay chain⁵⁶Ni⁵⁶Co⁵⁶Fe, which occurs in the silicon burning shells of supernovae just after their ejection at relativistic velocities. The equilibrium spectrum of positrons in the interstellar space has been calculated on the assumption that the observed abundance of iron nuclei in the cosmic radiation is the result of the above process. It is found that the observation below about 10 MeV can be well explained with a moderate acceleration of the positrons in the expanding envelope of supernovae prior to their propagation in the interstellar space. The total⁵⁶Ni content in the shells of supernova necessary to account for the observed positrons is in agreement with that required to explain the peak luminosity during the supernova outburst. Since this model deals with positrons created at the time of injection of cosmic rays into the interstellar space, it becomes possible to study the shape of the injection spectrum of cosmic rays.On leave from Tata Institute of Fundamental Research, Bombay, India.