Modulation of galactic cosmic ray anisotropy in heliomagnetosphere: Average sidereal daily variation

We formulate the modulation of galactic anisotropy of cosmic rays caused by their orbital deflection in the heliomagnetosphere. According to the formulation, the average sidereal i-th harmonic daily variation (i = 1,2,…) produced from the anisotropy from an arbitrary direction can be expressed by a linear combination of three basic vectors for uni-directional anisotropy and five basic vectors for bi-directional anisotropy. These vectors are obtained by calculating trajectories of cosmic rays (20?10⁴GV) in a model magnetosphere having Parker's Archimedian spiral structure with a flat or a wavy neutral sheet in either of two polarity states, one is called “Positive” state (away field in the northern space of the neutral sheet and toward field in the southern space) and the other is called “Negative” state (reversed state of the above). Among general characteristics of the sidereal daily variations, the most remarkable features are: (1) The observable variations in low rigidity (? 2000 GV) can be produced even from an uni-directional anisotropy in the direction of the Earth's rotation axis. These variations are strongly dependent on the polarity state, i.e., they are greater in the Positive state than in the Negative. (2) Those produced from the anisotropy in the Equatorial plane also show the polarity dependence but contrary to the previous case they are greater in the Negative state than in the Positive. Their magnitude in the former state is not so small even in the extremely low rigidity (～ 100 GV) as compared with that in high rigidity region. (3) These general characteristics are not altered by the introduction of the wavy neutral sheet or the magnetic irregularities, but the variations are affected more or less, depending on the heliolatitudinal extent of the wavy sheet or the degree of cosmic ray scattering with the irregularities, (4) Sidereal daily variation for the wavy sheet shows a toward-away field dependence similar to that of Swinson-type of solar origin, but the dependence is predominant in intermediate rigidity region (～ 500 GV), in marked contrast to that of solar origin. (5) Finally, whichever its direction may be, the uni-directional anisotropy produces the sidereal diurnal variation common to two conjugate stations in the Northern and Southern hemisphere. If there is any difference between the observed variations at the stations, it should be interpreted as being due to higher order anisotropy such as the bi-directional anisotropy.     

Modulation of galactic cosmic ray anisotropy in heliomagnetosphere: Influence of cosmic ray scattering on sidereal daily variation

In previous papers, the present authors have shown that the galactic anisotropy is modulated due to cosmic ray orbital deflection in the heliomagnetosphere, and that the sidereal time daily variations of galactic origin can be expressed using the basic vectors, which have been obtained by calculating trajectories of cosmic rays in a model magnetosphere having Parker's Archimedian spiral structure with a flat or a wavy neutral sheet. In the present paper, the magnetic irregularities superposed on the Parker's spiral field have been taken into account, which cause the scattering of cosmic rays and disturb their orbits. We examined the fluctuations of asymptotic directions calculating their orbits by the Monte-Carlo simulation, based on the theory of the multiple scattering process. It is shown that the dispersion of the projected deviation angle is determined mainly by the scattering mean free path and by the structure of the order magnetic field, e.g. the polarity state of the heliomagnetosphere and the extent of the neutral sheet. We investigated also the influence of the fluctuations of asymptotic directions on the sidereal daily variation. It is found that, under some conditions, the scattering causes only the attenuation of the amplitude of the basic vector, and does not change its phase. The attenuation is negligibly small at high rigidities larger than ~ 1000 GV, but becomes more serious with decreasing rigidity. The rigidity dependence curve of the attenuation rate was calculated for various cases. A simple and approximate method is also presented for the derivation of those curves for any value of the magnitude of the mean free path and for various model magnetospheres. It is noted, however, that the lower limiting rigidity below which the present method is not applicable is relatively high in the Positive polarity state.     

Cosmic ray sidereal diurnal variation of galactic origin observed by neutron monitors

We have analyzed the sidereal diurnal variation of cosmic rays, using 620 station-years of neutron monitor data during the period 1958–1979. The sidereal variation averaged over the period for all the stations in the Northern Hemisphere is different from the corresponding variation in the Southern Hemisphere. The difference is statistically significant and can be identified with the spurious sidereal variation produced from the stationary anisotropy of solar origin, responsible for the solar semi-diurnal variation. The variation common to both hemispheres is also exceptionally significant from the statistical point of view and could be regarded as being due to a uni-directional galactic anisotropy. This variation has an amplitude of 0.0204 ± 0.0015% and a phase of 6.8 ± 0.3 h and is clearly different from that ( ～ 0.05%, 0 ～ 3 h) observed in the high rigidity region (500 ～ 10⁴ GV). The physical meaning of the variation is discussed from the standpoint of the heliomagnetospheric modulation of galactic anisotropy.     

The insensitivity of the cosmic ray galactic anisotropy to heliomagnetic polarity reversals

Using the cosmic ray sidereal and anti-sidereal diurnal variations observed underground in London and Hobart during the period 1958–1983, it is demonstrated that: (1) the phase changes of the apparent sidereal diurnal variation observed only in the Northern Hemisphere cannot be attributed to the change of the heliomagnetospheric modulation of galactic cosmic ray anisotropy caused by the polarity reversal of the solar magnetic field, but that they are due to the fluctuation of the spurious sidereal variation produced from the anisotropy responsible for the solar semi-diurnal variation; (2) the spurious sidereal variation can be eliminated from the apparent variation by using the observed anti-sidereal diurnal variation; and (3) after the elimination, the sidereal diurnal variations in the Northern and Southern Hemispheres almost coincide with each other and are stationary throughout the period, regardless of the polarity reversal of the heliomagnetosphere. The origin of the corrected sidereal variation is discussed.     

Solar-cycle dependence of galactic cosmic ray flux

The coronal green line intensity is inappropriate for correlation studies of galactic cosmic ray variations. Being a non-monotonic function of coronal temperature, the green line intensity is a good index of neither coronal temperature nor solar wind speed. A more appropriate measure of coronal activity is the intensity of the electron corona. Two-dimensional observations of the K-corona trace changes in coronal morphology during the solar cycle. An index based on four years of K-coronal measurements made in Hawaii shows that activity in the lower corona is not better correlated than sunspot number with long-term modulation. Correlation analysis defines the time lag of modulation much too poorly to permit its use in estimating the size of the heliosphere.     

Solar-cycle dependence of galactic cosmic ray flux

To investigate the relationship between solar activity and cosmic ray modulation, time series of the nucleonic flux and of solar plages, sunspots, centimeter radio noise, and the brightness of the white light corona at 1.1 and 1.5 solar radii from the center of Sun are cross-correlated. Data pertain to the years 1964–1967 during the ascending phase of the current solar cycle. The amplitudes and phases of correlation functions for filtered and unfiltered indices are discussed. The existence of a superior solar index for relating solar activity to long-term modulation is not yet demonstrated conclusively, and the time lag of modulation is too poorly determined to permit its use in estimating the radius of the modulation region.Presently at the Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona 85721.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

On the secondary production of galactic cosmic ray electrons

The differential energy spectrum and charge ratio of primary cosmic ray electrons produced by collisions of primary cosmic ray particles with the interstellar medium is calculated by means of the two temperature statistical model of high-energy interactions. Two realistic models for the primary cosmic ray flux are considered. Contributions to the primary cosmic ray electron intensity from both the pion and kaon decay modes have been included. The distribution of matter in the galaxy and energy loss of produced secondaries and electrons are considered. The results are compared to recent experimental data.     

Active galactic nuclei and pulsars as cosmic ray sources

Relativistic e^± particles and cosmic rays are accelerated in the magnetospheres of supermassive black holes and neutron stars. The possibility of synchrotron radiation with extremely high intensity inside the deepest regions of magnetospheres is investigated. Very high brightness temperatures are expected for such radiation by relativistic protons, which can be made even higher in the presence of non-stationary conditions, Doppler boosting and coherent processes. The main parameters for models of such high-brightness-temperature radiation are determined. Two types of active galactic nuclei (AGNs) are expected. One type is associated with the acceleration and ejection of relativistic e^± particles only (probably non-IDV sources and FR-I radio galaxies). The second type of AGN is also associated with e^± acceleration, but is dominated by the contribution of relativistic protons (probably IDV sources and FR-II radio galaxies). Analogous objects for pulsars are plerion and shell supernova remnants with neutron stars or pulsars without synchrotron nebulae, respectively.     

IMF-sense-dependent cosmic ray anisotropy produced from diffusion-convection in heliosphere

An IMF-sense-dependent first order (or unidirectional) anisotropy of cosmic rays, which is produced perpendicularly to the ecliptic from the radial density gradient in solar system, has been confirmed by Swinson. In the present paper, we point out the existence of IMF-sense-dependent higher order anisotropies, based on the simulation of cosmic ray diffusion-convection in the heliomagnetosphere. In order to confirm their existence, we demonstrate some examples of the observed cosmic ray daily variation which is supposed to be due to these anisotropies.     

Markov stochastic technique to determine galactic cosmic ray sources distribution

A new numerical model of particle propagation in the Galaxy has been developed, which allows the study of cosmic-ray production and propagation in 2D. The model has been used to solve cosmic ray diffusive transport equation with a complete network of nuclear interactions using the time backward Markov stochastic process by tracing the particles’ trajectories starting from the Solar System back to their sources in the Galaxy. This paper describes a further development of the model to calculate the contribution of various galactic locations to the production of certain cosmic ray nuclei observed at the Solar System.     

Effects of active solar regions on the galactic cosmic ray intensity

During the year 1969 two long-lived centres were active on the Sun at Carrington longitudes 50° < L < 100° and 250° < L < 300°. About 80% of the flares of importance 1B, produced during this period, originated in these zones.The solar modulation of galactic cosmic ray intensity during 1969 was dominated by effects resulting from the activity in the two zones. In fact all the decreases can be related to the passage at the central meridian of the active centres. Persistence of the effects connected to solar regions is found also during rotations in which they do not produce flares in front of the Earth.Seventeen among the twenty-six intensity decreases, observed during this period, can also be correlated to individual flares belonging to the region at central meridian (longitudes ± 40° with respect to the CM).The data suggest that two phenomena are operative to produce decreases of the cosmic ray flux: the passage of the interplanetary corotating stream associated with the active region near the central meridian and the blast wave produced by the flares in front of the Earth.     

Variations of cosmic ray intensity in consequence of the semidiurnal anisotropy

The different types of cosmic ray intensity variations arising from the semidiurnal anisotropy are evaluated for different stations taking into consideration the effect of the Earth's axis inclination. Appropriate values of the parameters of the anisotropy together with accurate values of coupling and normalization constants are used in the calculations. The results predict the appearance of semiannual and diurnal waves as a consequence of a semidiurnal anisotropy. The form of the generated waves are found to be dependent on the characteristics of the station's asymptotic cone of acceptance as well as the season of detection. The characteristics of these waves together with that of the semidiurnal variation are discussed in detail.     

Reconstruction of the direction of the true anisotropy of galactic cosmic rays

A method of reconstructing the declination of galactic cosmic ray anisotropy is described, and its results are presented. The method is based on analysis of delay distributions in symmetrically arranged detectors of an air shower array, and it represents a modification of the crossed telescopes method. It is shown that the declination of the true anisotropy vector is close to 60° (i.e., this vector lies approximately within the galactic plane). Because of this, the true degree of anisotropy of galactic cosmic rays is severalfold higher than the first harmonic of intensity in the sidereal time (the quantity measured directly), and it equals about 0.2%.     

The anisotropy of cosmic ray arrival directions around 10 eV

Anisotropy in the arrival directions of cosmic rays with energies above 10¹⁷ eV is studied using data from the Akeno 20 km² array and the Akeno Giant Air Shower Array (AGASA), using a total of about 114 000 showers observed over 11 years. In the first harmonic analysis, we have found a strong anisotropy of 4% around 10¹⁸ eV, corresponding to a chance probability of 0.2% after taking the number of independent trials into account. with two-dimensional analysis in right ascension and declination, this anisotropy is interpreted as an excess of showers near the directions of the Galactic Center and the Cygnus region.     

On the magnitude and direction of the anisotropy of galactic cosmic rays

The results of measuring the diurnal cosmic-ray intensity variations in the energy range 1–100 TeV are discussed. Whereas the phase of the first harmonic of the sidereal daily wave directly determines the phase (right ascension) of the cosmic-ray anisotropy vector, the amplitude and declination of the true anisotropy cannot be reconstructed directly from the amplitude of the first harmonic. However, they can be determined by invoking data on the zero harmonic. The results of some recent experiments purporting to measure the cosmic-ray anisotropy with a particularly high accuracy are shown to be interpreted erroneously.     

The degree of anisotropy of cosmic ray electrons of solar origin

Data obtained by the Explorer 34 satellite regarding the degree of anisotropy of ≳ 70 keV electrons of solar origin are reported. It is shown that the anisotropies are initially field aligned, and that they decay to ≲ 10% in a time of the order of 1 hr. The decays of the concurrent ionic and electronic anisotropies for one well observed event are in good agreement with the diffusive propagation model of Fisk and Axford. The data suggest parallel diffusion coefficients for both ions and electrons that are rigidity independent. From considerations of a long lived electron event, it is shown that the electronic fluxes exhibit ‘equilibrium’ anositropies at late times. These are interpreted as indicating that convective removal at the solar wind velocity is the dominant mechanism whereby solar cosmic ray electrons (∼- 70 keV) leave the solar system. They also indicate that there is a positive density gradient at late times in a solar electron event. The data suggest that this was established prior to the establishment of a similar gradient for the cosmic ray ions. This research was supported by the National Aeronautics and Space Administration under contracts NASr-198 and NAS5-9075. The research in India was supported by funds from the Department of Atomic Energy, Government of India and funds from the grant NAS-1492 from the National Academy of Sciences, U.S.A. Support in data analysis was also provided by Air Force Cambridge Research Laboratories, and by the Australian Research Grants Committee.     

Spatial distribution of high energy cosmic ray electrons perpendicular to the galactic plane

With the help of empirical data concerning the latitudinal distribution of galactic gamma rays the contribution of inverse Compton scattered gamma rays is calculated using various models concerning the distribution of high energy cosmic ray electrons perpendicular to the galactic plane. It is shown that gamma ray astronomy from regions with vanishing stellar and interstellar matter densities at energies greater than 100 MeV provides instructive information on the cosmic ray electron density. We find evidence for the existence of a broad galactic electron disk with a total thickness of at least 6.4 kpc. The uncertainties of the cosmic ray electron spectrum measurements above 100 GeV imply an additional uncertainty in the inverse Compton source function of at least a factor 6.     

Influence of magnetic clouds on cosmic ray intensity variation

The data from a high counting rate neutron monitor has been analysed to study the nature of galactic cosmic-ray transient modulation associated with three classes of magnetic clouds, i.e., clouds associated with shock, stream interface and cold magnetic enhancement.It is found that the decreases in cosmic-ray intensity which are associated with clouds preceded by a shock, are very high (Forbush-type) and these decreases start earlier than the arrival of the cloud at the Earth. From the study of the time profile of these decreases it is found that the onset time of a Forbush-type decrease produced by a shock-associated cloud starts nearly at the time of arrival of the shock front at the Earth and the recovery is almost complete within a week.The decreases in cosmic-ray intensity associated with clouds followed by a stream interface are smaller in magnitude and larger in duration. The depression starts on the day of the arrival of the cloud.The decreases associated with the third category of clouds, i.e., clouds associated with cold magnetic enhancement (a region in which plasma temperature is anomalously low and the magnetic field strength is enhanced) are of still smaller amplitude and duration. The decrease in this case starts on the day the cloud arrives at the Earth.It seems that the Forbush decrease modulating region consists of a shock front followed by a plasma sheath in which the field intensity is high and turbulent. The amplitude of decrease is related to the field magnitude and the speed of the cloud. Both shocked plasma and the magnetic cloud are influential in determining the time profile of these decreases. In our view it is not the magnetic field strength or the topology alone which is responsible for the cosmic-ray depression. The most likely additional effect is the increased degree of turbulence.