Empirical model of cosmic ray spectrum in energy interval 1 MeV–100 GeV during 11-year solar cycle

The galactic cosmic rays (GCR) are the main ionization source at altitude of ∼3–35 km in the atmosphere. For high latitude anomalous cosmic ray (ACR) component has also a significant influence on the atmospheric ionization. We propose an empirical model for differential spectra D(E) of galactic and anomalous cosmic rays in energy interval 1 MeV–100 GeV during solar cycle. In the model data are used which cover three solar cycles: 20, 22 and 23. The LEAP87, IMAX92, CAPRICE94, AMS98 and BESS experimental spectra for protons and alpha particles are fitted to the proposed empirical model. The modulated GCR differential spectra are compared with force-field approximation to the one-dimensional transport equation and with solutions of two-dimensional cosmic ray transport equation. For experimental spectra, the calculation of the model parameters is performed by Levenberg–Marquardt algorithm, applied to the special case of least squares. Algorithm that combines the rapid local convergence of Newton–Raphson method with globally convergent method for non-linear systems of equations is applied for theoretically obtained differential spectra. The described programmes are realized in algorithmic language C++. The proposed model gives practical possibility for investigation of experimental data from measurements of galactic cosmic rays and their anomalous component.     

Normalized ionization yield function for various nuclei obtained with full Monte Carlo simulations

Several recent results important for production of ion pairs in the Earth atmosphere by various primary cosmic ray nuclei are presented. The direct ionization by various primary cosmic ray nuclei is explicitly obtained. The longitudinal profile of atmospheric cascades is sensitive to the energy and mass (charge) of the primary particle. In this study different cosmic ray nuclei are considered as primaries, namely Helium, Oxygen and Iron nuclei. The cosmic ray induced ionization is obtained on the basis of CORSIKA 6.52 code simulations using FLUKA 2006 and QGSJET II hadronic interaction models. The energy of the primary particles is normalized to GeV per nucleon. In addition, the ionization yield function Y is normalized as ion pair production per nucleon. The obtained ionization yield functions Y for various primaries are compared. The presented results and their application are discussed.     

Ionization effect of solar protons in the Earth atmosphere – Case study of the 20 January 2005 SEP event

The cosmic ray ground level enhancement on January 20, 2005 is among the largest recorded events in the history of cosmic ray measurements. The solar protons of MeV energies cause an excess of ionization in the atmosphere, specifically over polar caps following major solar disturbances. The ionization effect in the Earth atmosphere is obtained for various latitudes on the basis of solar proton energy spectra, reconstructed from GOES 11 measurements and subsequent full Monte Carlo simulation of cosmic ray induced atmospheric cascade. The estimation of ionization rates is based on a numerical model for cosmic ray induced ionization. The evolution of atmospheric cascade is performed with the CORSIKA 6.52 code using FLUKA 2006b and QGSJET II hadron interaction models. The atmospheric ion rate ionization is explicitly obtained for 40°N, 60°N and 80°N latitudes. The time evolution of obtained ion rates is presented. It is demonstrated that ionization effect is negative for 40°N and small for 60°N, because of accompanying Forbush decrease. The ionization effect is significant only in sub-polar and polar atmosphere during the major ground level enhancement of 20 January 2005.     

Propagation and origin of ultra high-energy cosmic rays

Propagation of UHE protons through CMB radiation leaves the imprint on energy spectrum in the form of Greisen–Zatsepin–Kuzmin (GZK) cutoff, bump (pile-up protons) and dip. The dip is a feature in energy range 1 × 10¹⁸–4 × 10¹⁹ eV, caused by electron–positron pair production on CMB photons. Calculated for power-law generation spectrum with index γ_g = 2.7, the shape of the dip is confirmed with high accuracy by data of Akeno-AGASA, HiRes, Yakutsk and Fly’s Eye detectors. The predicted shape of the dip is robust: it is valid for the rectilinear and diffusive propagation, for different discreteness in the source distribution, for local source overdensity, deficit, etc. This property of the dip allows us to use it for energy calibration of the detectors. The energy shift λ for each detector is determined by minimum χ² in comparison of observed and calculated dip. After this energy calibration the absolute fluxes, measured by AGASA, HiRes and Yakutsk detectors remarkably coincide in energy region 1 × 10¹⁸–1 × 10²⁰ eV. Below the characteristic energy E_c ≈ 1 × 10¹⁸ eV the spectrum of the dip flattens for both diffusive and rectilinear propagation, and more steep galactic spectrum becomes dominant at E < E_c. The energy of transition E_tr < E_c approximately coincides with the position of the second knee E_2kn, observed in the cosmic ray spectrum. The dip-induced transition from galactic to extragalactic cosmic rays at the second knee is compared with traditional model of transition at ankle, the feature observed at energy 1 × 10¹⁹ eV.     

Periodic variations of ionization rate in the low and middle atmosphere

The cosmic ray ionization source functions which were obtained using a simplified extensive air shower model are used to calculate the eleven year cycle, seasonal and diurnal variations of ionization rate in the low and middle atmosphere. The ionization source function, as a function of the penetrating depth and the energy of cosmic ray particles, is the ionization rate per unit depth for a unit flux of incoming cosmic ray particles with certain energy.The calculation of the eleven year cycle variation of ionization rate in the low and middle atmosphere due to the modulation of galactic cosmic ray intensity by solar activity shows that the amplitude is larger at a higher magnetic latitude and is generally larger at higher altitudes. The relative amplitude of fluctuation of the ionization peak value (at altitudes near 15 km) is up to 45% in the magnetic polar region. The ionization rate, due to the seasonal variation of the atmospheric density, varies from several per cent below the ionization peak to several tens per cent above the peak. This seasonal variation of ionization rate reaches 35% at 70 km. The diurnal variation of atmospheric densities caused by atmospheric tidal oscillation can produce a diurnal variation of the ionization rate to an amplitude of several per cent at altitudes above 40 km. The diurnal oscillation is less than 1% below 35 km.     

Radio galaxies and the acceleration of the universe beyond a redshift of one

Radio galaxies provide a means to determine the coordinate distance, the luminosity distance, the dimension-less luminosity distance, or the angular size distance to sources with redshifts as large as two. Dimensionless coordinate distances for 55 supernovae and 20 radio galaxies are presented and discussed here. The radio galaxy results are consistent with those obtained using supernovae, suggesting that neither method is plagued by unknown systematic errors. The acceleration parameter q(z) and the expansion rate H(z) or dimensionless expansion rate E(z) can be determined directly from the data without having to make assumptions regarding the nature or evolution of the “dark energy”. The expansion rate E(z) can be determined from the first derivative of the dimensionless coordinate distance, (dy/dz)⁻¹, and the acceleration parameter can be determined from a combination of the first and second derivatives of the dimensionless coordinate distance. A model-independent determination of E(z) will allow the properties and redshift evolution of the “dark energy” to be determined, and a model-independent determination of q(z) will allow the redshift at which the universe transitions from acceleration to deceleration to be determined directly. Determination of E(z) and q(z) may also elucidate possible systematic errors in the determinations of the dimensionless coordinate distances.     

1998年9月24日地磁暴前宇宙线各向异性特性分析

分析了日本Nagoya 宇宙线闪烁体望远镜30°, 49°, 64° 倾角的东、西、南、北方向探测数据的变化特点, 运用小波分析方法定性地探讨了磁暴前后宇宙线南北、东西各向异性的变化特征. 研究发现, 当发 生大地磁暴时, 地面宇宙线强度的各向异性特征将发生非常大的变化, 这种变化一般在磁暴发生前10~20 h就开始出现. 当描述这种各向异性特征的各向异性指数的小波系数变化达到一定阈值时, 就可能有大地磁暴发生.      

On the possibility to check the magnetosphere’s model by CR: The strong geomagnetic storm in November 2003

We report on a study of cosmic ray cutoff rigidity variations during the strong geomagnetic storm of 18–24 November 2003. We employed the most recent Tsyganenko magnetospheric model to represent the very strong disturbed Magnetosphere. We used this magnetic field for the cosmic ray trajectory calculations to determine the geomagnetic cutoff rigidity throughout this period of severe geomagnetic disturbance. We determine the cutoff rigidity changes during this period by two methods, by trajectory calculations and by the spectrographic global survey method. The values of the change of cutoff rigidities obtained by two different methods are correlated with the D_st and interplanetary magnetic field and plasma parameters and result in correlation coefficients in the range 0.63–0.84 for the various cosmic ray stations. The result of this study indicates that the most significant contributions to the cutoff rigidity changes are due to D_st variation although the influence of solar wind density and B_z and B_y components of IMF variations is significant.     

Observation of enhanced sub-iron (Sc---Cr) to iron ration in low energy cosmic rays of 50–100 MeV/N in spacelab-3

Relative abundances of sub-iron (Sc-Cr) to iron nuclei in low energy (50–100 MeV/N) galactic cosmic rays have been determined from an analysis of about 100 events of heavy ions (Z = 10−28) recorded in a detector assembly flown in the Anuradha cosmic ray experiment in the Spacelab-3 on a six day mission in April–May 1985. The measured abundance ratio of (Sc-Cr)/Fe nuclei in 50–100 MeV/N energy range is 1.1 ± 0.3, and the present result of enhanced ratio of sub-iron to iron nuclei is in agreement with other experimental results in 200–800 MeV/N range. The over-abundance of iron secondaries at these low energies cannot be explained in the conventional models for propagation of cosmic rays. Available experimental data indicate a very different time history for the low energy iron-group, as compared to those of lighter nuclei in galactic cosmic rays.     

Heavy ion observations by MARIE in cruise phase and Mars orbit

The charged particle spectrum for nuclei from protons to neon, (charge Z=10) was observed during the cruise phase and orbit around Mars by the MARIE charged particle spectrometer on the Odyssey spacecraft. The cruise data were taken between April 23, 2001 and mid-August 2001. The Mars orbit data were taken March 5, 2002 through May 2002 and are scheduled to continue until August 2004. Charge peaks are clearly separated for charges up to Z=10. Especially prominent are the carbon and oxygen peaks, with boron and nitrogen also clearly visible. Although heavy ions are much less abundant than protons in the cosmic ray environment, it is important to determine their abundances because their ionization energy losses (proportional to Z²) are far more dangerous to humans and to instruments. Thus the higher charged nuclei make a significant contribution to dose and dose equivalent received in space. Results of the charged particle spectrum measurements will be reported.     

Heavy particle fluxes in Salyut space station orbit

Results of a detailed analysis of heavy ion fluences measured on the Salyut and MIR orbital stations from 1978 to 1990 are presented. The analysis has made use of new models that describe the cosmic ray fluxes and their transition through the magnetosphere. The penetration of solar cosmic ray particles to the orbit, the increase of the (ScCr)/Fe flux ratio in the orbit, and the occurrences of 200–500 MeV/nucl heavy nuclei in <30° latitudes have been analyzed.     

Ion production and ionization effect in the atmosphere during the Bastille day GLE 59 due to high energy SEPs

The influence of high energy particles, specifically cosmic rays, on atmospheric physics and chemistry is highly discussed. In most of the proposed models the role of ionization in the atmosphere due to cosmic rays is not negligible. Moreover, effect(s) on minor constituents and aerosols are recently observed, specifically over the polar regions during strong solar particle events. According to the recent findings for such effects it is necessary an essential increase of ion production, specifically during the winter period. The galactic cosmic rays are the main source of ionization in the Earth’s stratosphere and troposphere. Occasionally, the atmospheric ionization is significantly enhanced during strong solar energetic particles events, specifically over the polar caps. During the solar cycle 23 several strong ground level enhancements were observed. One of the strongest was the Bastille day event occurred on 14 July 2000. Using a full Monte Carlo 3-D model, we compute the atmospheric ionization, considering explicitly the contribution of cosmic rays with galactic and solar origin, focusing on high energy particles. The model is based on atmospheric cascade simulation with the PLANETOCOSMICS code. The ion production rate is computed as a function of the altitude above the sea level. The ion production rate is computed on a step ranging from 10 to 30?min throughout the event, considering explicitly the spectral and angular characteristics of the high energy part of solar protons as well as their time evolution. The corresponding event averaged ionization effect relative to the average due to galactic cosmic rays is computed in lower stratosphere and upper troposphere at various altitudes, namely 20?km, 15?km, 12?km and 8?km above the sea level in a sub-polar and polar regions. The 24^h and the weekly ionization effects are also computed in the troposphere and low stratosphere. Several applications are discussed.     

Effect of random nature of cosmic ray sources – Supernova remnants – on cosmic ray intensity fluctuations,anisotropy, and electron energy spectrum

The random nature of sources (the supernova remnants) leads to the fluctuations of cosmic ray intensity in space and time. We calculate the expected fluctuations in a flat-halo diffusion model for particles with energies from 0.1 to 10³ TeV. The data on energy spectra and anisotropy of very high energy protons, nuclei and electrons, and the astronomical data on supernova remnants, the potential sources of cosmic rays, are used to constrain the value of the cosmic-ray diffusion coefficient and its dependence on energy.     

Propagation of secondary antiprotons and cosmic rays in the Galaxy

Recent measurements of the cosmic ray (CR) antiproton flux have been shown to challenge existing CR propagation models. It was shown that the reacceleration models designed to match secondary to primary nuclei ratios (e.g., B/C) produce too few antiprotons. In the present paper, we discuss one possibility to overcome these difficulties. Using the measured antiproton flux and B/C ratio to fix the diffusion coefficient, we show that the spectra of primary nuclei as measured in the heliosphere may contain a fresh local “unprocessed” component at low energies perhaps associated with the Local Bubble, thus decreasing the measured secondary to primary nuclei ratio. The independent evidence for SN activity in the solar vicinity in the last few Myr supports this idea. The model reproduces antiprotons, B/C ratio, and elemental abundances up to Ni (Z ⩽ 28). Calculated isotopic distributions of Be and B are in perfect agreement with CR data. The abundances of three “radioactive clock” isotopes in CR, ¹⁰Be, ²⁶Al, ³⁶Cl, are all consistent and indicate a halo size z_h ∼ 4 kpc based on the most accurate data taken by the ACE spacecraft.     

Galactic cosmic ray composition and energy spectra.

Galactic cosmic ray nuclei represent a significant risk to long-duration spaceflight outside the magnetosphere. We review briefly existing measurements of the composition and energy spectra of heavy cosmic ray nuclei, pointing out which species and energy ranges are most critical to assessing cosmic ray risks for spaceflight. Key data sets are identified and a table of cosmic ray abundances is presented for elements from H to Ni (Z = 1 to 28). Because of the 22-year nature of the solar modulation cycle, data from the approaching 1998 solar minimum is especially important to reducing uncertainties in the cosmic ray radiation hazard. It is recommended that efforts to model this hazard take advantage of approaches that have been developed to model the astrophysical aspects of cosmic rays.     

On ultra-high energy cosmic rays: Origin in AGN jets and transport in expanding universe

The cosmic ray source spectrum produced by AGN (active galactic nucleus) jets is calculated. A distinctive feature of these calculations is the account for the jet distribution on kinetic energy. The expected cosmic ray spectrum at the Earth is determined with the use of a simple numerical code which takes into account interactions of ultra-high energy protons and nuclei with the background radiation in an expanding universe.     

The Tien-Shan mountain cosmic ray station of the Ionosphere Institute of Kazakhstan Republic

The mountain cosmic ray (CR) station of the Ionosphere Institute of Kazakhstan Republic (CR station Alma-Ata B, 43.1N latitude, 76.6E longitude, geomagnetic rigidity cutoff 6.69 GV) is a center for an experimental study of the non-stationary processes caused by cosmic rays of different origin in the interplanetary and near-Earth space, so as their influence on the state of the Earth’s magnetosphere and the upper atmosphere layers. This paper summarizes efforts performed over the years by the Almaty CR group till its present status.     

Energetic positive ions in the cometary “foreshock” region

Ions produced by ionization of the cometary neutrals interact with the solar wind protons to produce large amplitude oscillations of the ambient magnetic field. Such oscillations are convected towards the comet at the unperturbed solar wind speed far from the shock and at a lower speed closer to the shock (due to the solar wind mass loading); hence, they can energize the incoming ions by Fermi acceleration. The spatial extension of the acceleration region is of the order of 10⁶ km and the resulting energy spectrum is harder than in the Earth's bow shock case. The energization of cometary ions produces an additional deceleration of the solar wind. It is suggested that Comet Halley may be the most efficient “cosmic ray shock” in the solar system.     

Long-term (50 years) measurements of cosmic ray fluxes in the atmosphere

Since the middle of 1957 till present time the group of researchers of P.N. Lebedev Physical Institute of the Russian Academy of Sciences has carried out the regular balloon borne measurements of charged particle fluxes in the atmosphere. The measurements are performed at polar (northern and southern) and middle latitudes and cover the interval of heights from the ground level up to 30–35 km. Standard detectors of particles (gas-discharged counters) have been used. More than 80,000 measurements of cosmic ray fluxes in the atmosphere have been performed to the present time. In the data analysis the geomagnetic field and the Earth’s atmosphere are used as cosmic ray spectrometers.