Study of the Cosmic Ray Diurnal Anisotropy During Different Solar and Magnetic Conditions

The pressure-corrected hourly counting rate data of four neutron monitor stations have been employed to study the variation of cosmic ray diurnal anisotropy for a period of about 50 years (1955–2003). These neutron monitors, at Oulu ( R _c = 0.78 GV), Deep River ( R _c = 1.07 GV), Climax ( R _c = 2.99 GV), and Huancayo ( R _c = 12.91 GV) are well distributed on the earth over different latitudes and their data have been analyzed. The amplitude of the diurnal anisotropy varies with a period of one solar cycle (∼11 years), while the phase varies with a period of two solar cycles (∼22 years). In addition to its variation on year-to-year basis, the average diurnal amplitude and phase has also been calculated by grouping the days for each solar cycle, viz. 19, 20, 21, 22, and 23. As a result of these groupings over solar cycles, no significant change in the diurnal vectors (amplitude as well as phase) from one cycle to other has been observed. Data were analyzed by arranging them into groups on the basis of the polarity of the solar polar magnetic field and consequently on the basis of polarity states of the heliosphere ( A > 0 and A < 0). Difference in time of maximum of diurnal anisotropy (shift to earlier hours) is observed during A < 0 (1970s, 1990s) polarity states as compared to anisotropy observed during A > 0 (1960s, 1980s). This shift in phase of diurnal anisotropy appears to be related to change in preferential entry of cosmic ray particles (via the helioequatorial plane or via solar poles) into the heliosphere due to switch of the heliosphere from one physical/magnetic state to another following the solar polar field reversal.     

Twenty-Seven-Day Variation of Galactic Cosmic Rays

Neutron monitor data observed at Climax (CL) and Huancayo/Haleakala (HU/HAL) have been used to calculate the amplitude A of the 27-day variation of galactic cosmic rays (CRs). The median primary rigidity of response, R _m, for these detectors encompasses the range 18 ≤R _m≤46 GV and the threshold rigidity R ₀ covers the range 2.97≤R ₀≤12.9 GV. The daily average values of CR counts have been harmonically analyzed for each Bartels solar rotation (SR) during the period 1953 – 2001. The amplitude of the 27-day CR variation is cross-correlated to solar activity as measured by the sunspot number R, the interplanetary magnetic field (IMF) strength B, the z-component B _z of the IMF vector, and the tilt angle ψ of the heliospheric current sheet (HCS). It is anticorrelated to the solar coronal hole area (CHA) index as well as to the solar wind speed V. The wind speed V leads the amplitude by 24 SRs. The amplitude of the 27-day CR variation is better correlated to each of the these parameters during positive solar polarity (A>0) than during negative solar polarity (A<0) periods. The CR modulation differs during A>0 from that during A<0 owing to the contribution of the z-component of the IMF. It differs during A ₁>0 (1971 – 1980) from that during A ₂>0 (1992 – 2001) owing to solar wind speed.     

Solar magnetic cycle dependence in corotating modulation of galactic cosmic rays

We study the temporal evolution of cosmic ray intensity during ～27-day Carrington rotation periods applying the method of superposed epoch analysis. We discuss about the average oscillations in the galactic cosmic ray intensity, as observed by ground based neutron monitors, during the course of Carrington rotation in low solar activity conditions and in different polarity states of the heliosphere (A<0 and A>0). During minimum and decreasing phases in low solar activity conditions, we compare the oscillation in one polarity state with that observed in other polarity state in similar phases of solar activity. We find difference in the evolution and amplitude of ～27-day variation during A<0 and A>0 epoch. We also compare the average variations in cosmic ray intensity with the simultaneous variations of solar wind parameters such as solar wind speed and interplanetary magnetic field strength. From the correlation analysis between the cosmic ray intensity and the solar wind speed during the course of Carrington rotation, we find that the correlation is stronger for A>0 than A<0.     

Similarities and Distinctions in Cosmic-Ray Modulation During Different Phases of Solar and Magnetic Activity Cycles

We study the solar-activity and solar-polarity dependence of galactic cosmic-ray intensity (CRI) on the solar and heliospheric parameters playing a significant role in solar modulation. We utilize the data for cosmic-ray intensity as measured by neutron monitors, solar activity as measured by sunspot number (SSN), interplanetary plasma/field parameters, solar-wind velocity [V] and magnetic field [B], as well as the tilt of the heliospheric current sheet [Λ], and we analyze these data for Solar Cycles 20?–?24 (1965?–?2011). We divide individual solar cycles into four phases, i.e. low, high, increasing, and decreasing solar activity. We perform regression analysis to calculate and compare the CRI-response to changes in different solar/interplanetary parameters during

1. different phases of solar activity and
2. similar activity phases but different polarity states.

We find that the CRI-response is different during negative (A<0) as compared to positive (A>0) polarity states not only with SSN and Λ but also with B and V. The relative CRI-response to changes in various parameters, in negative (A<0) as compared to positive (A>0) state, is solar-activity dependent; it is ≈?2 to 3 times higher in low solar activity, ≈?1.5 to 2 times higher in moderate (increasing/decreasing) activity, and it is nearly equal in high solar-activity conditions. Although our results can be ascribed to the preferential entry of charged particles via the equatorial/polar regions of the heliosphere as predicted by drift models, these results also suggest that we should look for any polarity-dependent response of solar-wind and transport parameters in modulating CRI in the heliosphere.     

Solar modulation of galactic cosmic rays during 19–23 solar cycles

We make a detailed analysis of cross-correlation and time-lag between monthly data of galactic cosmic rays (GCRs) intensity and different solar activity indices (e.g., sunspot number, sunspot area, green coronal Fe line and 10.7 cm solar radio flux) during 19–23 solar cycles. GCRs time-series data from Kiel neutron monitor station and solar data from the last 50 years period, covering five solar cycles (19–23), and alternating solar polarity states (i.e., five A < 0 and four A > 0) have been investigated. We find a clear asymmetry in the cross-correlation between GCRs and solar activity indicators for both odd and even-numbered solar cycles. The time-lags between GCRs and solar parameters are found different in different solar cycles as well as in the opposite polarity states (A < 0 and A > 0) within the same solar cycle. Possible explanations of the observed results are discussed in light of modulation models, including drift effects.     

Galactic Cosmic Ray Modulation near the Heliospheric Current Sheet

Galactic cosmic rays (GCRs) are modulated by the heliospheric magnetic field (HMF) both over decadal time scales (due to long-term, global HMF variations), and over time scales of a few hours (associated with solar wind structures such as coronal mass ejections or the heliospheric current sheet, HCS). Due to the close association between the HCS, the streamer belt, and the band of slow solar wind, HCS crossings are often associated with corotating interaction regions where fast solar wind catches up and compresses slow solar wind ahead of it. However, not all HCS crossings are associated with strong compressions. In this study we categorize HCS crossings in two ways: Firstly, using the change in magnetic polarity, as either away-to-toward (AT) or toward-to-away (TA) magnetic field directions relative to the Sun and, secondly, using the strength of the associated solar wind compression, determined from the observed plasma density enhancement. For each category, we use superposed epoch analyses to show differences in both solar wind parameters and GCR flux inferred from neutron monitors. For strong-compression HCS crossings, we observe a peak in neutron counts preceding the HCS crossing, followed by a large drop after the crossing, attributable to the so-called ‘snow-plough’ effect. For weak-compression HCS crossings, where magnetic field polarity effects are more readily observable, we instead observe that the neutron counts have a tendency to peak in the away magnetic field sector. By splitting the data by the dominant polarity at each solar polar region, we find that the increase in GCR flux prior to the HCS crossing is primarily from strong compressions in cycles with negative north polar fields due to GCR drift effects. Finally, we report on unexpected differences in GCR behavior between TA weak compressions during opposing polarity cycles.     

Influence of short-duration matter temperature perturbations on the cosmological hydrogen recombination spectrum

A perturbation in the ratio of the matter temperature to the radiation temperature in the form of a Gaussian with amplitude A and width σ (in units of the redshift z) centered at some redshift z _c is considered, with some “standard” temperature ratio obtained from a simultaneous solution of the cosmological recombination kinetics and energy equations being taken as the initial (unperturbed) one. Comparatively small (A = ± 0.01), fast (σ = 17) perturbations are shown to give rise to distinct narrow absorption (for A > 0) or emission (for A < 0) quasi-lines in each of the subordinate continua. The positions of these quasi-lines correlate with the position of the perturbation center, while their intensities are very sensitive to the perturbation amplitude. At the same time, the manifestation of the perturbation is much less clear in hydrogen lines (subordinate ones and the Ly-α line) and two-photon emission. As a result, the full perturbed spectrum is characterized by the presence of the narrow quasi-lines mentioned above and by a general decrease (for A > 0) or increase (for A < 0) in intensity with increasing wavelength.     

Return Meridional Flow in the Convection Zone from Latitudinal Motions of Umbrae of Sunspot Groups

We have derived the velocities of meridional flows by measuring the latitudinal motions (or drifts) of umbrae of spot groups classified into three categories of area: 0 – 5 μ, 5 – 10 μ, and >10 μ (μ area in millionths of the solar hemisphere). The latitudinal drifts (or the meridional flows) in all three categories are directed equatorward in both the northern and southern hemispheres. By sorting the spot groups into three area classes, we are able to relate the respective latitudinal drifts with the three depths in the convection zone where the footpoints of the flux loops of the spot groups of each area class are anchored. We obtain estimates of the anchor depths through a comparison of the rotation rates of the spot groups of each area class with the rotation-rate profiles from helioseismic inversions. The equatorward drifts obtained provide estimates of the meridional flows at the three depths in the convection zone and thereby suggest the presence of return meridional flows as envisaged in the flux-transport dynamo models, which have remained undetected so far. The data sources for this study are measurements of positions and areas of umbrae of sunspots from the photographic white-light images of the Sun of the Kodaikanal Observatory archives for the period 1906 – 1987 and a very similar, but independent, data set from the Mt. Wilson Observatory archives for the period 1917 – 1985.     

Butterfly diagrams of strongly spotted late type stars

At present, long-term (over 30 years) multicolor photometric observations give the possibility to determine general properties of spotted areas on late-type stars. Star-spot modeling from broadband photometric data has been carried out by Alekseev and Gershberg since 1996 under the assumption that spots are situated in two latitudinal zones. Here we propose a new analysis of their results for several G and K dwarf stars with high irregular activity. On these stars, EK Dra, VY Ari, V775 Her, and V833 Tau, two spot belts exist separately and do not merge into a single equatorial active region, as occurs on cooler red-dwarf stars. The zonal spottedness models allow us to fit simultaneously both rotational modulation and long-term variability of stellar brightness. These models give evidence for an equatorward drift of the lower latitude boundary of the spotted region, φ₀, during the rising phase of activity, beyond any possible errors concerned with our methodology. In order to evaluate the drift rate we introduce the concept of `effective' spot belt, whose width is independent of longitude. This permits us to construct butterfly diagrams for stellar spots. The equatorward drift rates of the lower boundary of the spotted region D=dφ_low/dt are (− 1)–(− 2) deg year⁻¹ in the years of increasing spottedness. These values are less than the analogous solar one D≈−4 deg year⁻¹ for the rising phase of the cycle. Thus, cyclic activity can be revealed from butterfly diagrams and derived drifts of starspots prior to a possible detection from the spectral analysis of photometric variability. Finally, we briefly discuss a possible explanation of high-latitude activity and surface drifts of starspots in the framework of the current state of dynamo theory.     

Cosmic-Ray Modulation: An Empirical Relation with Solar and Heliospheric Parameters

Long-term variations of galactic cosmic rays were compared with the behavior of various solar activity indices and heliospheric parameters during the current solar cycle. This study continues previous works where the cosmic-ray intensity for the solar cycles 20, 21, and 22 was well simulated from the linear combination of the sunspot number, the number of grouped solar flares, and the geomagnetic index A _p. The application of this model to the current solar cycle characterized by many peculiarities and extreme solar events led us to study more empirical relations between solar-heliospheric variables, such as the interplanetary magnetic field, coronal mass ejections, and the tilt of the heliospheric current sheet, and cosmic-ray modulation. By analyzing monthly cosmic-ray data from the Neutron Monitor Stations of Oulu (cutoff rigidity 0.81 GV) and Moscow (2.42 GV) the contribution of these parameters in the ascending, maximum, and descending phases of the cycle was investigated and it is shown that a combination of these parameters reproduces the majority of the modulation potential variations during this cycle. The approach applied makes it possible to better describe the behavior of cosmic rays in the epochs of the solar maxima, which could not be done before. An extended study of the time profiles, the correlations, and the time lags of the cosmic-ray intensity against these parameters using the method of minimizing RMS over all the considered period 1996 – 2006 determines characteristic properties of this cycle as being an odd cycle. Moreover, the obtained hysteresis curves and a correlative analysis during the positive polarity (qA>0, where q is the particle charge) and during the negative polarity (qA<0) intervals of the cycle result in significantly different behavior between solar and heliospheric parameters. The time lag and the correlation coefficient of the cosmic-ray intensity are higher for the solar indices in comparison to the heliospheric ones. A similar behavior also appears in the case of the intervals with positive and negative polarity of the solar magnetic field.     

Fluctuational mechanism for the formation of proton vortices in the superfluid core of neutron stars

The Gibbs thermodynamic potential of a proton vortex interacting with the normal core of a neutron vortex of radius r << λ (λ is the penetration depth) that is parallel to it and has an outer boundary of radius b is calculated. It is shown that, under this assumption, the capture of only one vortex by the core is energetically favorable. The force acting on the proton vortex owing to the entrained current is found and it is always directed toward the core. The corresponding force for a proton antivortex is directed toward the outer boundary of the neutron vortex. The Ginzburg-Landau equation is solved for a vortex-antivortex system and its Gibbs function is calculated. It is shown that at large distances from the core, vortex-antivortex pairs can form because of fluctuations. Acted on by the entrainment current, the antivortex moves outward, while the vortex stays inside the neutron vortex. It is shown that the best conditions for fluctuational pair production, followed by separation, exist near the outer boundary. It is shown that new proton vortices can develop only in a region where the entrainment magnetic field strength H (ρ) > H_C1 (H_C1 is the lower critical field). __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 139–149 (February 2008).     

Solar Polarity Dependence of Cosmic Ray Power Spectra Observed with Mawson Underground Muon Telescopes

Power spectral density (PSD) of cosmic rays has been calculated from hourly averaged counts observed by underground muon telescopes located at Mawson over the low-frequency range 2.7×10⁻⁷ – 1.4×10⁻⁴ Hz. The first two harmonics of the solar daily variation are well defined for even cycles (20 and 22) whereas only the first harmonic is defined in cycle 21. The amplitude of the diurnal variation is lower for even cycles than for the odd cycle. The spectral power of the odd cycle exceeds those of the even cycles. The spectra are flatter and have lower power when the interplanetary magnetic field (IMF) is directed away from the Sun above the current sheet (A>0) than when the IMF is directed toward the Sun above the current sheet (A<0). The spectra imply that heliospheric magnetic turbulence may be more variable on time scales of several years than previously suspected.     

North-south asymmetry in solar, interplanetary, and geomagnetic indices

Data of hourly interplanetary plasma (field magnitude, solar wind speed, and ion density), solar (sunspot number, solar radio flux), and geomagnetic indices (Kp, Ap) over the period 1970-2010, have been used to examine the asymmetry between the solar field north and south of the heliospheric current sheet (HCS). A persistent yearly north-south asymmetry of the field magnitude is clear over the considered period, and there is no magnetic solar cycle dependence. There is a weak N-S asymmetry in the averaged solar wind speed, exhibited well at times of maximum solar activities. The solar plasma is more dense north of the current sheet than south of it during the second negative solar polarity epoch (qA < 0). Moreover, the N - S asymmetry in solar activity (Rz) can be statistically highly significant. The sign of the average N - S asymmetry depends upon the solar magnetic polarity. The annual magnitudes of N - S asymmetry depend positively on the solar magnetic cycle. Most of the solar radio flux asymmetries occurred during the period of positive IMF polarity.     

On Mid-Term Periodicities in Cosmic Rays

The contributions of quasi-periodic variations of cosmic rays for T>27 days at the primary energies to which neutron monitors are sensitive have a rather complicated character. They were reported in several papers (e.g. Valdés-Galicia, Perez-Enriquez, and Otaola, 1996; Mavromichalaki et al., 2003; Kudela et al., 2002; Caballero and Valdés-Galicia, 2001) from individual stations and for various time intervals covered. The data archive of several neutron monitor stations developed within the NMDB project () now involves long time series of measurements at neutron monitors situated at different geomagnetic cut-off rigidity positions and at different altitudes. It is updated continuously. Using the daily averages of cosmic-ray intensity at three selected stations within NMDB: i) the temporal evolution of the selected quasi-periodicities, especially those of approximately 1.7 yr, 150 days and 26 – 32 days respectively, until 2008 are reviewed, ii) the similarities of the spectra are checked and iii) the occurrence of quasi-periodicities with those observed in solar, interplanetary and geomagnetic activities (Moussas et al., 2005; Richardson and Cane, 2005) as well as in energetic particles below the atmospheric threshold are discussed (Laurenza et al., 2009).     

Long-term behavior of latitudinal cosmic-ray gradients

We have used neutron monitor data covering a wide range of energy over a period of 22 years (1966–1987), as well as sea-level multidirectional meson telescope data from Nagoya to examine the latitude effect of solar diurnal vectors and its dependence on the polarity of interplanetary magnetic field (IMF). By sorting the daily cosmic-ray data according to whether the IMF is toward (T) or away (A) from the Sun, the annual mean solar diurnal variations (amplitude and phase) for the T and A days were determined separately. Results showed a northward-pointing latitudinal gradient from neutron monitors of the most northerly latitudes, and a predominant southward gradient at high southerly latitudes. The resultant latitudinal cosmic-ray gradients are the sum of two gradients: a north-south symmetry gradient (occurring in minimum and maximum solar activity years), and a north-south asymmetry gradient (occurring during different phases of solar activity cycles). The difference vector (T - A) between the solar diurnal vector for two groups was calculated, which represents a good indicator for the resultant perpendicular gradient relative to the Earth. This difference vector shows a considerable change in phase for detectors located in the northern hemisphere of the Earth. On the other hand, there exists much less change in phase for detectors located in the southern hemisphere.     

Generalized Chaplygin gas model with or without viscosity in the w–w′ plane

In this paper, we investigate the dynamics of generalized Chaplygin gas (GCG) model with or without viscosity in the w–w′ plane, which is defined by the equation of state parameter and its time derivative with respect to the logarithm of the scale factor. We show that GCG model without viscosity approaches to a late time de Sitter attractor (w _g =−1) and behaves like a “freezing” scalar field for the parameter α constrained by the latest observational data. However, introducing viscosity exerts an influence on the evolution of w and affects the location of the late time attractor (w _g >−1) in viscous GCG model. We also find numerically such a transition from w′>0 to w′<0 as the universe expands in viscous GCG model different from GCG model without viscosity (w′<0) in the w–w′ plane.     

Dark energy models with anisotropic fluid in Bianchi Type-VI 0 space-time with time dependent deceleration parameter

We present two dark energy (DE) models with an anisotropic fluid in Bianchi type-VI ₀ space-time by considering time dependent deceleration parameter (DP). The equation of state (EoS) for dark energy ω is found to be time dependent and its existing range for derived models is in good agreement with the recent observations. Under the suitable condition, the anisotropic models approach to isotropic scenario. We also find that during the evolution of the universe, the EoS parameter for DE changes from ω>−1 to ω=−1 in first model whereas from ω>−1 to ω<−1 in second model which is consistent with recent observations. The cosmological constant Λ is found to be a positive decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent type Ia supernovae observations. The cosmic jerk parameter in our derived models is also found to be in good agreement with the recent data of astrophysical observations. The physical and geometric aspects of both the models are also discussed in detail.     

The effect of gradient and curvature drifts on Forbush decreases

The average profile of Forbush decreases, produced by eastern-, central- and western-region solar flares is obtained separately by superposed epoch analysis for the periods 1966–1969 (qA < 0) and 1971–1979 (qA > 0). It is observed that the recovery of an average Forbush decrease from the maximum depression level is faster for the situation qA > 0 than for the situation qA < 0. This is in accordance with expectations from the drift theory. It is also observed that the drift effect is more pronounced for western-flare Forbush decreases which, of course, have a smaller magnitude compared to eastern- and central-flare Forbush decreases.The average profiles of simple and complex type Forbush decreases are also obtained separately for three periods 1965–1979, 1971–1979, and 1981–1987. It is found that the average profiles of simple and complex type Forbush decreases observed during the period 1965–1969 and 1971– 1979 are quite in agreement with drift theory. The anomalous behavior of average Forbush-decrease profiles during the period 1981–1987, especially in simple type Forbush decreases, is also explained by a drift current sheet tilt model.     

Gnevyshev Peaks and Gaps for Coronal Mass Ejections of Different Widths Originating in Different Solar Position Angles

The sunspot number series at the peak of sunspot activity often has two or three peaks (Gnevyshev peaks; Gnevyshev, Solar Phys. 1, 107, 1967; Solar Phys. 51, 175, 1977). The sunspot group number (SGN) data were examined for 1997 – 2003 (part of cycle 23) and compared with data for coronal mass ejection (CME) events. It was noticed that they exhibited mostly two Gnevyshev peaks in each of the four latitude belts 0° – 10°, 10° – 20°, 20 ° – 30°, and > 30°, in both N (northern) and S (southern) solar hemispheres. The SGN were confined to within latitudes ± 50° around the Equator, mostly around ± 35°, and seemed to occur later in lower latitudes, indicating possible latitudinal migration as in the Maunder butterfly diagrams. In CMEs, less energetic CMEs (of widths < 71°) showed prominent Gnevyshev peaks during sunspot maximum years in almost all latitude belts, including near the poles. The CME activity lasted longer than the SGN activity. However, the CME peaks did not match the SGN peaks and were almost simultaneous at different latitudes, indicating no latitudinal migration. In energetic CMEs including halo CMEs, the Gnevyshev peaks were obscure and ill-defined. The solar polar magnetic fields show polarity reversal during sunspot maximum years, first at the North Pole and, a few months later, at the South Pole. However, the CME peaks and gaps did not match with the magnetic field reversal times, preceding them by several months, rendering any cause – effect relationship doubtful.     

Intensity variation of cosmic rays near the heliospheric current sheet

Cosmic ray intensity variations near the heliospheric current sheet—both above and below it—have been studied during 1964–1976. Superposed epoch analysis of the cosmic ray neutron monitor data with respect to sector boundaries (i.e., heliospheric current sheet crossings) has been performed. In this analysis we have used the data from neutron monitors well distributed in latitude over the Earth's surface. First, this study has been made during the two solar activity minimum periods 1964–1965 and 1975–1976, using the data from Thule (cut-off rigidity 0 GV), Deep River (cut-off rigidity 1.02 GV), Rome (cut-off rigidity 6.32 GV) and Huancayo (cut-off rigidity 13.45 GV) neutron monitors. We have also analyzed the data from Deep River, Rome and Huancayo neutron monitors, for whom we have the data for full period (1964–1976), by dividing the periods according to the changes in solar activity, interplanetary magnetic field polarity and coronal holes. All these studies have shown a negative gradient with respect to heliomagnetic latitude (current sheet). These results have been discussed in the light of theoretical and observational evidences. Suggestions have been given to overcome the discrepancy between the observational and theoretical results. Further, possible explanations for these observational results have been suggested.