Long-term changes in the cosmic-ray diurnal anisotropy

A detailed study has been conducted on the long-term changes in diurnal anisotropy of cosmic rays for the two solar cycles (20 and 21) during the period 1965–1990; this shows that the amplitude of the anisotropy is related to the characteristics of high and low amplitude days. The occurrence of high amplitude days are found to be positively correlated with the sunspot cycle while the low amplitude days are correlated negatively with the sunspot cycle. Further, the variability of the time of maximum of the aniotropy indicates that it essentially is composed of two components; one in the 1800 hours (corotation) direction and the other, an additional component in the 1500 hours direction (45° east of the S-N line) apparently caused by the reversal of the solar polar magnetic field. Our observations also suggest that the direction of the anisotropy of high- and low-amplitude days contribute significantly to the long-term behaviour of the diurnal anisotropy as it produces an additional component of cosmic rays in the radial (1200 hours) direction.     

Long-term modulation of the Galactic cosmic-ray fluctuation spectrum

We study the temporal behavior of the power spectra for Galactic cosmic-ray fluctuations during the last two solar cycles. We use the 5-min data for 1980–2002 corrected for the barometric effect from two widely separated high-latitude cosmic-ray stations, Tixie Bay and Oulu. The cosmicray fluctuation spectrum is shown to be subjected to a regular long-term modulation with a period of about 11 years in phase with the solar cycle, in accordance with the variations in the inertial part of the turbulence spectrum for the interplanetary magnetic field. Based on independent measurements, we confirm the previously detected cosmic-ray fluctuation power enhancement at the maximum of the 11-year solar cycle and its subsequent decrease at minimum solar activity using new, more extensive data sets. We reach the conclusion about the establishment of a new cosmic-ray modulation phenomenon that has not been described previously in scientific literature.     

The effect of solar wind latitudinal dependence on the cosmic-ray propagation in the heliosphere

We have investigated how the latitude dependence of the solar wind velocity (SWV) influenced the cosmic-ray (CR) modulation and distribution in the heliosphere. The dependence proposed by Fry and Akasofu (1987) is used:v _SW=v _O+v ₁(1-cos ⁿ _m , where the SWV,v _SW is a function of the heliomagnetic latitude _m andv ₀ andv ₁ are constants. An estimation of the diffusion and drift terms in the transport equation is made, which shows that towards the poles the effects of the drift transfer decrease, while the diffusion terms in the equation increase due to the change of the interplanetary magnetic field (IMF) geometry. The numerical solutions of the two-dimensional (2-D) transport equation show that when the SWV changes with latitude: (1) The CR intensities away from the neutral sheet are larger for both IMF polarity periods in comparison with the case when the SWV does not change with the latitude. (2) The latitude gradients are negative during negative magnetic polarity periods. (3) The Voyager 1 and Voyager 2 long-time observations showing greater galactic CR intensities nearer the Sun at greater distances, could be explained by the proposed model.     

In-situ observations of the latitudinal gradients of the solar wind parameters during 1976 and 1977

Interplanetary observations from Helios 1, Helios 2, and IMP-8 spacecraft during 1976 and 1977, namely the early portion of solar cycle 21, have been used to investigate the latitudinal gradients of the solar wind parameters with respect to the angular displacement from the current sheet inferred from synoptic HAO white-light maps of the solar corona at 1.75 solar radii. A latitudinal belt of ±25 deg around the current sheet has been investigated. Large gradients for solar wind flow speed, proton density and temperature have been found. Smoother gradients were also found for particle flux, kinetic, gravitational and thermal energy density flux. All these gradients revealed to become smoother going towards the solar cycle's maximum. Neither latitudinal nor temporal variations were identified for magnetic and thermal energy density. A remarkable result of this study is that the momentum flux density and the total energy flux density which other authors found to be independent of any longitudinal stream structure were also found to be independent of any latitudinal structure. Moreover, these two parameters did not show any temporal variation during the period of interest.     

Time-lag of cosmic-ray intensity

The best correlation coefficient between the monthly cosmic-ray intensity of the Inuvik Station and various kinds of solar, interplanetary, and geophysical parameters has been found. It is calculated for different time-lags of cosmic-ray intensity with respect to these parameters. The maximum of these coefficients lead us to a useful empirical model for the 11-year cosmic-ray modulation.     

Oscillatory cosmic-ray shock structures

A multiple scales analysis is used to derive a mixed Burgers-Korteweg-de Vries (BKdV) equation in the long wavelength regime for a two-fluid MHD model used to describe cosmic-ray acceleration by the first-order Fermi process in astrophysical shocks. The BKdV equation describes the time evolution of weak shocks in the theory of diffusive shock acceleration for all possible cosmic-ray pressures. Previous work on weak shocks in the cosmic-ray MHD model has assumed that dissipation alone is sufficient to balance nonlinearity, but, as cosmic-ray pressures become small, the weak shock becomes discontinous. By including Hall current effects into the MHD model, the low cosmic-ray pressure limit leads smoothly into solitary wave behaviour. For low cosmic-ray pressures, the shock has a downstream oscillatory precursor which is smoothed into the standard Taylor shock profile with increasing cosmic-ray pressure. As a by-product of the perturbation analysis, a dissipative KdV equation is derived. In conclusion, dispersive effects on Alfvén waves are discussed and a modulational stability analysis is presented.     

Time-evolution of cosmic-ray intensity modulation

Application of analyzing time-series into trigonometric series allows the investigation of cosmic-ray intensity variations in a wide periodicity range from a few months to 10 or even more years. By this technique, the amplitude and the phase of all observed fluctuations can be given. For this purpose, cosmic-ray data of five ground-based neutron-monitor stations for the time interval 1964–1985 have been analyzed.Two kinds of periodicities appeared in these data. The first one includes occurrences at periods greater than two years, as the ones of 10.41, 8.41, and 5.50 yr, which differ very little in amplitude from station to station but are similar in phase, and the second one includes periodicities smaller than two years (24, 12, 8, and 6 months) which are similar in all stations but appeared in variable time intervals.The possible origin of each observed variation due to a contribution either of cosmic-ray interaction in the upper atmosphere or to the solar dynamics is discussed.     

Simulations of cosmic-ray particle diffusion

The diffusion of charged particles in a stochastic magnetic field (strengthB) which is superimposed on a uniform magnetic fieldB ₀ k is studied. A slab model of the stochastic magnetic field is used. Many particles were released into different realizations of the magnetic field and their subsequent displacements z in the direction of the uniform magnetic field numerically computed. The particle trajectories were calculated over periods of many particle scattering times. The ensemble average was then used to find the parallel diffusion coefficient . The simulations were performed for several types of stochastic magnetic fields and for a wide range of particle gyro-radius and the parameterB/B ₀. The calculations have shown that the theory of charged particle diffusion is a good approximation even when the stochastic magnetic field is of the same strength as the uniform magnetic field.     

Heliolatitudinal dependence of cosmic-ray anisotropy

We analyze the heliolatitudinal dependence of the cosmic-ray anisotropy using data from the Yakutsk complex of muon telescopes on the ground and underground at depths of 7, 20, and 60 m w. e. for 1972–2002. The radial cosmic-ray anisotropy component during this period at all recording levels is shown to have been systematically enhanced southward from the helioequator irrespective of the polarity of the general solar magnetic field. The azimuthal anisotropy component depends on heliolatitude only at negative polarity of the general solar magnetic field; it increases northward from the helioequator. Such a situation can take place in the case of interaction of the fast solar wind from coronal holes with the slow wind in the northern part of the heliosphere and continuous particle removal in its southern part.     

Large amplitude wave-trains of cosmic-ray intensity

The large amplitude wave-trains of cosmic-ray intensity observed during June, July and August, 1973, were analysed. These events exhibit the same characteristics as the event of May, 1973. During these days the phase of the enhanced diurnal anisotropy is shifted to a point earlier than either the corotation direction or the anti-garden-hose direction. For this analysis we used data from high- and middle-latitude neutron monitors and from the satellites HEOS-2, IMP-7 and IMP-8. The diurnal variation of these days is well understood in terms of a radially outward convective vector and a field-aligned inward diffusive vector yielding a diurnal anisotropy vector along about 1600 h in space.     

Tridiurnal variations in cosmic-ray intensity

The tridiurnal wave in cosmic-ray intensity expected from a free space anisotropy is theoretically calculated for different cosmic-ray stations which are characterized by different shapes of asymptotic cones of acceptance. The amplitude A and the time of maximum Tmax are given for latitude dependence of the form cosⁿ λ and rigidity dependence of the form $\text{R}{}^{\mathrm{\beta }}\text{exp (?(R?}\text{1}\text{R}{}_0\text{))}$, where λ and R are the latitude and rigidity respectively and n, β, R₀ are constants. The values of A and Tmax, are calculated for different values of n, β and R₀ for each station. The dependence of A and Tmax on the anisotropy parameters is studied for the proper selection of cosmic-ray stations whose data may be used in determining these parameters.Available experimental data were used to find the observed amplitudes of the tridiurnal variations at five stations using power spectrum analysis with hanning applied on the averaged trains. Minimum variance analysis of the theoretical and experimental amplitudes showed that β has a value between 1 and 2, R₀ greater than 100 GV and n smaller than 3.     

On the interplanetary cosmic-ray scintillations

The equation for the two-particles cosmic-ray distribution function is derived by means of the Boltzmann kinetic equation averaging. This equation is valid for arbitrary ratio of regular and random parts of the magnetic field. For small energy particles the guiding-center approximation is used. On the basis of the derived equation the dependence between power spectra of cosmic-ray intensity and random magnetic field is obtained. If power spectra are degree functions for high energy particles ( 10 GeV nucleon^–1), then the spectral exponent of magnetic field lies between and –2, where is the spectral exponent of cosmic-ray power spectra. The experimental data concerning moderate energy particles are in accordance with =, which demonstrates that the magnetic fluctuations are isotropic or cosmic-ray space gradient is small near the Earth orbit.     

Aspects of the long-term cosmic-ray modulation

To investigate the long-term modulation of galactic cosmic rays at the ground-based detector energies, the monthly values of the neutron monitor (Climax, Mt. Washington, Deep River, and Huancayo) and ionization chamber (Cheltenham/Fredericksburg, Huancayo, and Yakutsk) intensities have been correlated with the sunspot numbers (used as a proxy index for transient solar activity) for each phase of sunspot cycles 18 to 22. Systematic differences are found for results concerning odd and even sunspot cycles. During odd cycles (19 and 21) the onset time of cosmic-ray modulation is delayed when compared with the onset time of the sunspot cycle, while they are more similar during even (18, 20, and 22) cycles. Checking the green corona data, on a half-year basis, we found typical heliolatitudinal differences during ascending phases of consecutive sunspot cycles. This finding suggests a significant role of the latitudinal coronal behaviour in the heliospherical dynamics during a Hale cycle. Such effectiveness concerns not only the transient interplanetary perturbations but also the recurrent ones. In fact, when lag between cosmic-ray data and sunspot numbers is considered, the anticorrelation between both parameters is very high (correlation coefficient |r| > 0.9) for all the phases considered, except for the declining ones of cycles 20 and 21, when high-speed solar wind streams coming from coronal holes affect the cosmic-ray propagation, and theRz parameter is no longer the right proxy index for solar-induced effects in the interplanetary medium.     

Simulation of long-term cosmic-ray intensity variation

Selecting the most appropriate source functions among the various solar, interplanetary and terrestrial activity indices we have attempted to reproduce to a certain degree the long-term modulation of galactic cosmic-rays. For this study monthly cosmic-ray data from nine world-wide neutron monitor stations for the period 1975–1985 have been analysed. The empirical formula which has been used to compute the long-term cosmic-ray variations follows the observations fairly well.It is noteworthy that the residuals in the cosmic-ray intensity between that observed and that calculated by this empirical formula exhibits a still remaining short-term variation in all stations of 2.7 and 3.7 months. Possible interpretations of these observed periodicities related to galactic origin are given.     

The propagation of solar cosmic-ray bursts

A model is presented in which we show analytically the three phases of anisotropy which occur during solar cosmic-ray events observed in the 7.5 MeV to 21 MeV kinetic-energy interval and reported by McCracken et al. (1971): (i) a highly anisotropic, near field-aligned, initial phase, (ii) a convective phase, and (iii) a late-time phase in which the anisotropy is approximately perpendicular to the mean interplanetary magnetic field. The model is based on the cosmic-ray particles being convectively transported out from the Sun, undergoing anisotropic diffusion along the interplanetary magnetic-field lines, and losing energy by adiabatic deceleration or by collision processes. The event is seen simply as a pulse moving outward from the Sun after a cosmic-ray burst with a negative density-gradient in front of it and a positive gradient behind. The convective phase (ii) occurs as the spatial peak moves past the observer and has a propagation speed V _d associated with it; the anisotropy vector late in the decay phase (iii) is the result of a residual balance between the radial outward convection and the inward radial component of the anisotropic diffusion. The mathematical solutions are based upon a diffusion coefficient proportional to heliocentric radius and independent of energy and are thus rather special. However they yield formulae for the propagation speed of the convective phase and the direction in space of the long-time anisotropy which are useful as a guide to the dependence of these quantities on the solar wind speed V, the diffusion coefficient and the spectral index . In this model V _d increases with V, , and ; and , the angle between the anisotropy vector at infinite time and the outward radial direction increases with /V and decreases as is increased. These predictions of the dependence of and V _d upon V, , and are open to observational verification.     

Consequences of CP-violation in cosmic-ray sources

In this paper we show that CP-violation is operating in most cosmic-ray sources such as black holes, active galactic nuclei, supernova remnants, and that this leads to the in-equality of the electron—positron component of cosmic rays.Further implications of this result are also discussed.     

The diffusion model of cosmic-ray propagation

We set up diffusion equations for the nuclear component of cosmic rays and solve these to find the ratio of light to medium nuclei in the cosmic rays as well as the gamma-ray distribution in our Galaxy. From a comparison of our calculated quantities with observational data we determine the values of various parameters appearing in the model. We find that best agreement between theory and observations is obtained if the cosmic-ray confinement region consists of a narrow disk of total height 160 pc and radius 16 kpc, where the cosmic-ray sources are located, and an extensive halo of height 20 kpc. The diffusion coefficient near the Sun must be between 10²⁶ and 10²⁷ cm² s^–1 while it equals 10²⁸ to 10²⁹ cm² s^–1 in the halo. Finally, we find that the diffusion coefficient in the Galaxy must depend on the gas density as a power law with an index of the order of –1.     

Long-term optical color behavior of a sample of blazars

We report on the optical color variability of a sample of 24 blazars, consisting of nine flat spectrum radio quasars(FSRQs) and 15 BL Lacertae objects(BL Lacs), on timescales of years using simultaneous V-and R-band observations observed by the Kanata telescope at Higashi-Hiroshima Observatory.The correlations between color indices V-R and magnitudes reveal that 11 BL Lacs and one FSRQ exhibited significant(i.e., r 0.2 and P 0.01) bluer-when-brighter(BWB) trend and two FSRQs followed the redder-when-brighter(RWB) tend, indicating a possibility that the BWB chromatic trend is dominant for BL Lacs and the RWB trend is especially found in FSRQs, which has been presented occasionally in different samples of blazars.The superpositions of the red emission component from the Doppler-boosted relativistic jet and the blue component arising from the accretion disk might be a possible interpretation for the long-term color behaviors.     

High-energy cosmic-ray neutrinos and tau particles

We propose a possible scheme that will accommodate the newly discovered tau particle in the generic relation between cosmic-ray particles at high energy. The scheme imposes a new lower mass limit on the tau-neutrino, 139 < < 250 MeV. A possible contribution of the tau-neutrino to high-energy neutrino flux is discussed. We then analyse the possible astrophysical situations suitable for the production of the tau particle and its neutrino.     

Variations of cosmic-ray energy in interplanetary space

A consistent theory of energy exchange between high-energy charged cosmic-ray particles and the random inhomogeneities of a magnetic field frozen in the moving solar wind plasma is developed. It is shown that the mode of the particle energy variations at a given law of plasma velocity variation in space is determined by the specific form of the particle distribution function. The equation for the density of cosmic-ray energy is obtained. Consideration is given to the generation of a charged particle energy spectrum in the course of multiple scatterings by the random inhomogeneities of the magnetic field.