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.     

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.     

Long-Term Modulation of Cosmic-Ray Intensity and Correlation Analysis Using Solar and Heliospheric Parameters

Based on the monthly sunspot numbers (SSNs), the solar-flare index (SFI), grouped solar flares (GSFs), the tilt angle of heliospheric current sheet (HCS), and cosmic-ray intensity (CRI) for Solar Cycles 21?–?24, a detailed correlation study has been performed using the cycle-wise average correlation (with and without time lag) method as well as by the “running cross-correlation” method. It is found that the slope of regression lines between SSN and SFI, as well as between SSN and GSF, is continuously decreasing from Solar Cycle 21 to 24. The length of regression lines has significantly decreased during Cycles 23 and 24 in comparison to Cycles 21 and 22. The cross-correlation coefficient (without time lag) between SSN–CRI, SFI–CRI, and GSF–CRI has been found to be almost the same during Cycles 21 and 22, while during Cycles 23 and 24 it is significantly higher between SSN–CRI and HCS–CRI than for SFI–CRI and GSF–CRI. Considering time lags of 1 to 20 months, the maximum correlation coefficient (negative) amongst all of the sets of solar parameters is observed with almost the same time lags during Cycles 21?–?23, whereas exceptional behaviour of the time lag has been observed during Cycle 24, as the correlation coefficient attains its maximum value with two time lags (four and ten months) in the case of the SSN–CRI relationship. A remarkably large time lag (22 months) between HCS and CRI has been observed during the odd-numbered Cycle 21, whereas during another odd cycle, Cycle 23, the lag is small (nine months) in comparison to that for other solar/flare parameters (13?–?15 months). On the other hand, the time lag between SSN–CRI and HCS–CRI has been found to be almost the same during even-numbered Solar Cycles 22 and 24. A similar analysis has been performed between SFI and CRI, and it is found that the correlation coefficient is maximum at zero time lag during the present solar cycle. The GSFs have shown better maximum correlation with CRI as compared to SFI during Cycles 21 to 23, indicating that GSF could also be used as a significant solar parameter to study the cosmic-ray modulation. Furthermore, the running cross-correlation coefficient between SSN–CRI and HCS–CRI, as well as between solar-flare activity parameters (SFI and GSF) and CRI is observed to be strong during the ascending and descending phases of solar cycles. The level of cosmic-ray modulation during the period of investigation shows the appropriateness of different parameters in different cycles, and even during the different phases of a particular solar cycle. We have also studied the galactic cosmic-ray modulation in relation to combined solar and heliospheric parameters using the empirical model suggested by Paouris et al. (Solar Phys.280, 255, 2012). The proposed model for the calculation of the modulated cosmic-ray intensity obtained from the combination of solar and heliospheric parameter gives a very satisfactory value of standard deviation as well as \(R^{2}\) (the coefficient of determination) for Solar Cycles 21?–?24.     

Abundances of Suprathermal Heavy Ions in CIRs During the Minimum of Solar Cycle 23

Solar Physics - In this paper we examine the elemental composition of the 0.1?–?1 MeV?nucleon?1 interplanetary heavy ions from H to Fe in corotating interaction...     

Global Heliospheric Parameters and Cosmic-Ray Modulation: An Empirical Relation for the Last Decades

We study empirical relations between the modulation of galactic cosmic rays quantified in terms of the modulation potential and the following global heliospheric parameters: the open solar magnetic flux, the tilt angle of the heliospheric current sheet, and the polarity of the heliospheric magnetic field. We show that a combination of these parameters explains the majority of the modulation potential variations during the neutron monitor era 1951 – 2005. Two empirical models are discussed: a quasi-linear model and a model assuming a power-law relation between the modulation potential and the magnetic flux. Both models describe the data fairly well. These empirical models provide a simple tool for evaluating various cosmic-ray related effects on different time scales. The models can be extended backwards in time or used for predictions, if the corresponding global heliospheric variables can be independently estimated.     

星际空间中宇宙线重新加速的研究

本文从能量空间中具有加速的宇宙线传播方程出发,给出了泄漏箱模型图象中高能原初谱及次级与原初核之比的数学表达式,我们的结果表明星际空间中宇宙线的重新加速可能是存在的,没有必要考虑次级和原初的不同空间分布的概念。     

High-Speed Solar wind Streams and Cosmic-Ray Intensity Variations During 1991–1996

High-speed plasma streams identified in the solar wind measurements can be separated into two categories: coronal-hole-associated streams and flare-generated streams. Effects of these plasma streams on cosmic-ray intensity are studied for the period of 1991–1996. It is investigated that both of these high-speed solar wind plasma streams (CS and FGS) are found equally effective in producing the cosmic-ray intensity decrease on short-term basis.     

Kinematics of Interacting ICMEs and Related Forbush Decrease: Case Study

We study heliospheric propagation and some space weather aspects of three Earth-directed interplanetary coronal mass ejections (ICMEs), successively launched from the active region AR 11158 in the period 13?–?15 February 2011. From the analysis of the ICME kinematics, morphological evolution, and in situ observations, we infer that the three ICMEs interacted on their way to Earth, arriving together at 1 AU as a single interplanetary disturbance. Detailed analysis of the in situ data reveals complex internal structure of the disturbance, where signatures of the three initially independent ICMEs could be recognized. The analysis also reveals compression and heating of the middle ICME, as well as ongoing magnetic reconnection between the leading and the middle ICME. We present evidence showing that the propagation of these two, initially slower ICMEs, was boosted by the fastest, third ICME. Finally, we employ the ground-based cosmic ray observations, to show that this complex disturbance produced a single cosmic ray event, i.e., a simple Forbush decrease (FD). The results presented provide a better understanding of the ICME interactions and reveal effects that should be taken into account in forecasting of the arrival of such compound structures.     

Cosmic-Ray Modulation due to High-Speed Solar-Wind Streams of Different Sources,Speed, and Duration

We study the modulation of galactic cosmic rays (GCR) due to high-speed streams (HSS) identified in the solar wind. We compare the GCR modulation due to i) streams with different speed, ii) streams of different duration, and iii) streams from different solar sources. We apply the method of superposed-epoch analysis to analyze the interplanetary plasma and field parameters during the passage of streams with distinct plasma and field characteristics. We use the plasma/field characteristics to distinguish various features of solar sources and interplanetary structures, and discuss the observed differences in the cosmic-ray response. We study the influence of speed, duration, and solar sources of the streams on the GCR modulation. We discuss the relative importance of different solar-wind parameters in the modulation process.     

Cosmic-Ray Decreases and Interplanetary Disturbances During the Solar Magnetic Polarity Reversal in Solar Cycle 20

Using the cosmic-ray intensity data recorded with ground-based monitors at Mt. Washington and Deep River, and with cosmic-ray telescopes on Pioneer 8 and 9 spacecraft as well as the 2-hour averages of the IMF (magnitude and direction) and the solar wind bulk speed and density at 1 AU, the cosmic-ray decreases and interplanetary disturbances, that occurred during the period of solar magnetic polarity reversal in solar cycle 20, were investigated.We observed a two-step Forbush decrease on 22–23 November 1969, and a Forbush decrease on 26 November 1969, which are respectively consistent with the model of Barnden (1973), and of Parker (1963) and Barnden (1973). Only one Forbush decrease event was observed in December 1969, a period during which there was a solar magnetic polarity reversal; the Forbush decrease was attributed to a long-lived corotating high-speed solar wind stream. This is indicative that at heliolongitudes from 43° E to 70° W of S–E radial, covered by the observations, the solar magnetic polarity reversal in solar cycle 20 was not carried by, nor related to, individual transient structures, and that the reversal most probably evolved gradually.     

Comparison of the Variations of CMEs and ICMEs with those of other Solar and Interplanetary Parameters During Solar Cycle 23

This paper examines the variations of coronal mass ejections (CMEs) and interplanetary CMEs (ICMEs) during solar cycle 23 and compares these with those of several other indices. During cycle 23, solar and interplanetary parameters had an increase from 1996 (sunspot minimum) to ∼2000, but the interval 1998–2002 had short-term fluctuations. Sunspot numbers had peaks in 1998, 1999, 2000 (largest), 2001 (second largest), and 2002. Other solar indices had matching peaks, but the peak in 2000 was larger than the peak in 2001 only for a few indices, and smaller or equal for other solar indices. The solar open magnetic flux had very different characteristics for different solar latitudes. The high solar latitudes (45^∘–90^∘) in both N and S hemispheres had flux evolutions anti-parallel to sunspot activity. Fluxes in low solar latitudes (0^∘–45^∘) evolved roughly parallel to sunspot activity, but the finer structures (peaks etc. during sunspot maximum years) did not match with sunspot peaks. Also, the low latitude fluxes had considerable N–S asymmetry. For CMEs and ICMEs, there were increases similar to sunspots during 1996–2000, and during 2000–2002, there was good matching of peaks. But the peaks in 2000 and 2001 for CMEs and ICMEs had similar sizes, in contrast to the 2000 peak being greater than the 2001 peak for sunspots. Whereas ICMEs started decreasing from 2001 onwards, CMEs continued to remain high in 2002, probably due to extra contribution from high-latitude prominences, which had no equivalent interplanetary ICMEs or shocks. Cosmic ray intensity had features matching with those of sunspots during 2000–2001, with the 2000 peak (on a reverse scale, actually a cosmic ray decrease or trough) larger than the 2001 peak. However, cosmic ray decreases started with a delay and ended with a delay with respect to sunspot activity.     

Cosmic-Ray Variations During the Two Greatest Bursts of Solar Activity in the 23rd Solar Cycle

During two extreme bursts of solar activity in March–April 2001 and October–November 2003, the ground-based neutron monitor network recorded a series of outstanding events distinguished by their magnitude and unusual peculiarities. The important changes that lead to increased activity initiated not with the sunspot appearance, but with the large-scale solar magnetic field reconfiguration. A series of strong and moderate magnetic storms and powerful proton events (including ground-level enhancements, GLE) were registered during these periods. The largest and most productive in the 23rd solar cycle, active region 486, generated a significant series of solar flares among which the 4 November 2003 flare (X28/3B) was the most powerful X-ray solar event ever observed. The fastest arrival of the interplanetary disturbance from the Sun (after August 1972) and the highest solar wind velocity and IMF intensity were recorded during these events. Within 1 week, three GLEs of solar cosmic rays were registered by the neutron monitor network (28 and 29 October and 2 November 2003). In this work, we perform a tentative analysis of a number of the effects seen in cosmic rays during these two periods, using the neutron monitor network and other relevant data.     

Kinematic Properties of Slow ICMEs and an Interpretation of a Modified Drag Equation for Fast and Moderate ICMEs

We report kinematic properties of slow interplanetary coronal mass ejections (ICMEs) identified by SOHO/LASCO, interplanetary scintillation, and in situ observations and propose a modified equation for the ICME motion. We identified seven ICMEs between 2010 and 2011 and compared them with 39 events reported in our previous work. We examined 15 fast (V _SOHO?V _bg>500 km?s^?1), 25 moderate (0 km?s^?1≤V _SOHO?V _bg≤500 km?s^?1), and 6 slow (V _SOHO?V _bg<0 km?s^?1) ICMEs, where V _SOHO and V _bg are the initial speed of ICMEs and the speed of the background solar wind. For slow ICMEs, we found the following results: i) They accelerate toward the speed of the background solar wind during their propagation and reach their final speed by 0.34±0.03 AU. ii) The acceleration ends when they reach 479±126 km?s^?1; this is close to the typical speed of the solar wind during the period of this study. iii) When γ ₁ and γ ₂ are assumed to be constants, a quadratic equation for the acceleration a=?γ ₂(V?V _bg)|V?V _bg| is more appropriate than a linear one a=?γ ₁(V?V _bg), where V is the propagation speed of ICMEs, while the latter gives a smaller χ ² value than the former. For the motion of the fast and moderate ICMEs, we found a modified drag equation a=?2.07×10^?12(V?V _bg)|V?V _bg|?4.84×10^?6(V?V _bg). From the viewpoint of fluid dynamics, we interpret this equation as indicating that ICMEs with 0 km?s^?1≤V?V _bg≤2300 km?s^?1 are controlled mainly by the hydrodynamic Stokes drag force, while the aerodynamic drag force is a predominant factor for the propagation of ICME with V?V _bg>2300 km?s^?1.     

Inversion of the Cosmic-Ray Solar Diurnal Variations

We have bounded the upper cut-off rigidity (R_c) of the cosmic-ray diurnal anisotropy during the period 1968–1995. This period covers almost three solar cycles and includes three epochs of the solar polar field reversals. The diurnal variation observed by two detectors characterized by linearly independent kernels has been inverted in order to estimate the greatest lower bound (GLB) of R_c. We obtain a step function solution for the cosmic-ray anisotropy in free space which vanishes at the GLB of R_c. The greatest lower bound shows a magnetic cycle variation. The highest value of the amplitude of the anisotropy in free space at the GLB have been estimated as well.     

Effects of Geometries and Substructures of ICMEs on Geomagnetic Storms

To better understand geomagnetic storm generations by ICMEs, we consider the effect of substructures (magnetic cloud, MC, and sheath) and geometries (impact location of flux-rope at the Earth) of the ICMEs. We apply the toroidal magnetic flux-rope model to 59 CDAW CME–ICME pairs to identify their substructures and geometries, and select 20 MC-associated and five sheath-associated storm events. We investigate the relationship between the storm strength indicated by minimum Dst index \((\mathrm{Dst}_{\mathrm{min}})\) and solar wind conditions related to a southward magnetic field. We find that all slopes of linear regression lines for sheath-storm events are steeper (\({\geq}\,1.4\)) than those of the MC-storm events in the relationship between \(\mathrm{Dst}_{\mathrm{min}}\) and solar wind conditions, implying that the efficiency of sheath for the process of geomagnetic storm generations is higher than that of MC. These results suggest that different general solar wind conditions (sheaths have a higher density, dynamic and thermal pressures with a higher fluctuation of the parameters and higher magnetic fields than MCs) have different impact on storm generation. Regarding the geometric encounter of ICMEs, 100% (2/2) of major storms (\(\mathrm{Dst}_{\mathrm{min}} \leq -100~\mbox{nT}\)) occur in the regions at negative \(P_{Y}\) (relative position of the Earth trajectory from the ICME axis in the \(Y\) component of the GSE coordinate) when the eastern flanks of ICMEs encounter the Earth. We find similar statistical trends in solar wind conditions, suggesting that the dependence of geomagnetic storms on 3D ICME–Earth impact geometries is caused by asymmetric distributions of the geoeffective solar wind conditions. For western flank events, 80% (4/5) of the major storms occur in positive \(P_{Y}\) regions, while intense geoeffective solar wind conditions are not located in the positive \(P_{Y}\). These results suggest that the strength of geomagnetic storms depends on ICME–Earth impact geometries as they determine the solar wind conditions at Earth.     

Magnetic Cycle Dependence of the Cosmic-Ray Diurnal Anisotropy

The two components of the solar diurnal variation observed with two detectors characterized by linearly independent coupling functions have been used to estimate the free space anisotropy vector during the period 1968–1995 using the least-squares method (LSM). The values of R_cshow 20-year magnetic cycle with the lowest values at solar activity minima for positive polarity (qA>0). A good correlation is obtained between R_cand the IMF magnitude. The amplitude of the radial anisotropy (A_R) shows 20-year magnetic cycle with the highest values around solar activity minima for qA>0 (1975–1976 and 1995), whereas that of the east-west (A) is minimum. This results in shifting the anisotropy vector to the earliest hours. The amplitude of the anisotropy is high around solar maxima and low around solar minima. It is also enhanced during the declining phase of solar activity (1971, 1984–1985, and 1991). Our results of the anisotropy have been used to calculate the cosmic-ray radial and transverse gradients. The value of the radial gradient exhibits a magnetic polarity dependence as well, with larger value during qA<0 than during qA>0.     

Study of the Geoeffectiveness and Galactic Cosmic-Ray Response of VarSITI-ISEST Campaign Events in Solar Cycle 24

We analyze and compare the geomagnetic and galactic cosmic-ray (GCR) response of selected solar events, particularly the campaign events of the group International Study of Earth-affecting Solar Transients (ISEST) of the program Variability of the Sun and Its Terrestrial Impact (VarSITI). These selected events correspond to Solar Cycle 24, and we identified various of their features during their near-Earth passage. We evaluated the hourly data of geomagnetic indices and ground-based neutron monitors and the concurrent data of interplanetary plasma and field parameters. We recognized distinct features of these events and solar wind parameters when the geomagnetic disturbance was at its peak and when the cosmic-ray intensity was most affected. We also discuss the similarities and differences in the geoeffectiveness and GCR response of the solar and interplanetary structures in the light of plasma and field variations and physical mechanism(s), which play a crucial role in influencing the geomagnetic activity and GCR intensity.