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.     

Comparative Study of MHD Modeling of the Background Solar Wind

Knowledge about the background solar wind plays a crucial role in the framework of space-weather forecasting. In-situ measurements of the background solar wind are only available for a few points in the heliosphere where spacecraft are located, therefore we have to rely on heliospheric models to derive the distribution of solar-wind parameters in interplanetary space. We test the performance of different solar-wind models, namely Magnetohydrodynamic Algorithm outside a Sphere/ENLIL (MAS/ENLIL), Wang–Sheeley–Arge/ENLIL (WSA/ENLIL), and MAS/MAS, by comparing model results with in-situ measurements from spacecraft located at 1 AU distance to the Sun (ACE, Wind). To exclude the influence of interplanetary coronal mass ejections (ICMEs), we chose the year 2007 as a time period with low solar activity for our comparison. We found that the general structure of the background solar wind is well reproduced by all models. The best model results were obtained for the parameter solar-wind speed. However, the predicted arrival times of high-speed solar-wind streams have typical uncertainties of the order of about one day. Comparison of model runs with synoptic magnetic maps from different observatories revealed that the choice of the synoptic map significantly affects the model performance.     

The Whole Heliosphere Interval in the Context of a Long and Structured Solar Minimum: An Overview from Sun to Earth

Throughout months of extremely low solar activity during the recent extended solar-cycle minimum, structural evolution continued to be observed from the Sun through the solar wind and to the Earth. In 2008, the presence of long-lived and large low-latitude coronal holes meant that geospace was periodically impacted by high-speed streams, even though solar irradiance, activity, and interplanetary magnetic fields had reached levels as low as, or lower than, observed in past minima. This time period, which includes the first Whole Heliosphere Interval (WHI 1: Carrington Rotation (CR) 2068), illustrates the effects of fast solar-wind streams on the Earth in an otherwise quiet heliosphere. By the end of 2008, sunspots and solar irradiance had reached their lowest levels for this minimum (e.g., WHI 2: CR 2078), and continued solar magnetic-flux evolution had led to a flattening of the heliospheric current sheet and the decay of the low-latitude coronal holes and associated Earth-intersecting high-speed solar-wind streams. As the new solar cycle slowly began, solar-wind and geospace observables stayed low or continued to decline, reaching very low levels by June??C?July 2009. At this point (e.g., WHI 3: CR 2085) the Sun?CEarth system, taken as a whole, was at its quietest. In this article we present an overview of observations that span the period 2008??C?2009, with highlighted discussion of CRs 2068, 2078, and 2085. We show side-by-side observables from the Sun??s interior through its surface and atmosphere, through the solar wind and heliosphere and to the Earth??s space environment and upper atmosphere, and reference detailed studies of these various regimes within this topical issue and elsewhere.     

Is the Highest Cosmic-Ray Flux Yet to Come?

The recent 2009 solar-minimum period was characterized by a record-setting high Galactic cosmic-ray flux observed at Earth. This, along with the unexpected low heliospheric magnetic-field magnitude, caused this period to be characterized as unusual compared with previous minimum epochs. In this work, selected solar-activity proxies and corresponding cosmic-ray observations for the past five solar cycles are compared with each other, and we identify those that showed unusual behaviour during the 2009 solar-minimum modulation period. Using a state-of-the-art numerical-modulation model, the proton-intensity spectra for the past solar minima are reproduced to establish which of the transport processes might be considered the main cause of this unusually high cosmic-ray flux. It is found that diffusion was more prominent during 2009 so that drift effects on the modulation of cosmic rays in the heliosphere were less evident than during previous solar-polarity epochs. However, particle drifts still occurred and because of these drift effects, the proton spectrum is predicted to be even higher during the coming A>0 solar-minimum period.     

Solar Modulation of Cosmic Rays during the Declining and Minimum Phases of Solar Cycle 23: Comparison with Past Three Solar Cycles

We study solar modulation of galactic cosmic rays (GCRs) during the deep solar minimum, including the declining phase, of solar cycle 23 and compare the results of this unusual period with the results obtained during similar phases of the previous solar cycles 20, 21, and 22. These periods consist of two epochs each of negative and positive polarities of the heliospheric magnetic field from the north polar region of the Sun. In addition to cosmic-ray data, we utilize simultaneous solar and interplanetary plasma/field data including the tilt angle of the heliospheric current sheet. We study the relation between simultaneous variations in cosmic ray intensity and solar/interplanetary parameters during the declining and the minimum phases of cycle 23. We compare these relations with those obtained for the same phases in the three previous solar cycles. We observe certain peculiar features in cosmic ray modulation during the minimum of solar cycle 23 including the record high GCR intensity. We find, during this unusual minimum, that the correlation of GCR intensity is poor with sunspot number (correlation coefficient R=?0.41), better with interplanetary magnetic field (R=?0.66), still better with solar wind velocity (R=?0.80) and much better with the tilt angle of the heliospheric current sheet (R=?0.92). In our view, it is not the diffusion or the drift alone, but the solar wind convection that is the most likely additional effect responsible for the record high GCR intensity observed during the deep minimum of solar cycle 23.     

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.     

Three-Dimensional Evolution of Flux-Rope CMEs and Its Relation to the Local Orientation of the Heliospheric Current Sheet

Flux ropes ejected from the Sun may change their geometrical orientation during their evolution, which directly affects their geoeffectiveness. Therefore, it is crucial to understand how solar flux ropes evolve in the heliosphere to improve our space-weather forecasting tools. We present a follow-up study of the concepts described by Isavnin, Vourlidas, and Kilpua (Solar Phys. 284, 203, 2013). We analyze 14 coronal mass ejections (CMEs), with clear flux-rope signatures, observed during the decay of Solar Cycle 23 and rise of Solar Cycle 24. First, we estimate initial orientations of the flux ropes at the origin using extreme-ultraviolet observations of post-eruption arcades and/or eruptive prominences. Then we reconstruct multi-viewpoint coronagraph observations of the CMEs from ≈?2 to 30 R_⊙ with a three-dimensional geometric representation of a flux rope to determine their geometrical parameters. Finally, we propagate the flux ropes from ≈?30 R_⊙ to 1 AU through MHD-simulated background solar wind while using in-situ measurements at 1 AU of the associated magnetic cloud as a constraint for the propagation technique. This methodology allows us to estimate the flux-rope orientation all the way from the Sun to 1 AU. We find that while the flux-ropes’ deflection occurs predominantly below 30 R_⊙, a significant amount of deflection and rotation happens between 30 R_⊙ and 1 AU. We compare the flux-rope orientation to the local orientation of the heliospheric current sheet (HCS). We find that slow flux ropes tend to align with the streams of slow solar wind in the inner heliosphere. During the solar-cycle minimum the slow solar-wind channel as well as the HCS usually occupy the area in the vicinity of the solar equatorial plane, which in the past led researchers to the hypothesis that flux ropes align with the HCS. Our results show that exceptions from this rule are explained by interaction with the Parker-spiraled background magnetic field, which dominates over the magnetic interaction with the HCS in the inner heliosphere at least during solar-minimum conditions.     

Evidence for Planetary Forcing of the Cosmic Ray Intensity and Solar Activity Throughout the Past 9400 Years

Paleo-cosmic-ray (PCR) records based on cosmogenic ¹⁰Be and ¹⁴C data are used to study the variations in cosmic-ray intensity and solar activity over the past 9400 years. There are four strong correlations with the motion of the Jovian planets; the probability of occurring by chance being <?10^?5. They are i) the PCR periodicities at 87, 350, 510, and 710 years, which closely approximate integer multiples of half the Uranus–Neptune synodic period; ii) eight periodicities in the torques calculated to be exerted by the planets on an asymmetric tachocline that approximate the periods observed in the PCR; iii) the maxima of the long-term PCR variations are coincident with syzygy (alignment) of the four Jovian planets in 5272 and 644 BP; and iv) in the time domain, the PCR intensity decreases during the first 60 years of the ≈?172 year Jose cycle (Jose, Astron. J. 70, 193, 1965) and increases in the remaining ≈?112 years in association with barycentric anomalies in the distance between the Sun and the center of mass of the solar system. Furthermore, sunspot and neutron-monitor data show that three anomalous sunspot cycles (4th, 7th, and 20th) and the long sunspot minimum of 2006 – 2009 CE coincided with the first and second barycentric anomalies of the 58th and 59th Jose cycles. Phase lags between the planetary and heliospheric effects are ≤?five years. The 20 largest Grand Minima during the past 9400 years coincided with the latter half of the Jose cycle in which they occurred. These correlations are not of terrestrial origin, nor are they due to the planets’ contributing directly to the cosmic-ray modulation process in the heliosphere. Low cosmic-ray intensity (higher solar activity) occurred when Uranus and Neptune were in superior conjunction (mutual cancellation), while high intensities occurred when Uranus–Neptune were in inferior conjunction (additive effects). Many of the prominent peaks in the PCR Fourier spectrum can be explained in terms of the Jose cycle, and the occurrence of barycentric anomalies.     

Time-Dependent Modulation of Cosmic Rays in the Heliosphere

The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a time-dependent modulation model. By introducing recent theoretical advances in the transport coefficients in the model, computed intensities are compared with Voyager 1, International Monitoring Platform (IMP) 8, and Ulysses proton observations in search of compatibility. The effect of different modulation parameters on computed intensities is also illustrated. It is shown that this approach produces, on a global scale, realistic cosmic-ray proton intensities along the Voyager 1 spacecraft trajectory and at Earth up to ≈?2004, whereafter the computed intensities recover much more slowly towards solar minimum than observed in the inner heliosphere. A modified time dependence in the diffusion coefficients is proposed to improve compatibility with the observations at Earth after ≈?2004. This modified time dependence led to an improved compatibility between computed intensities and the observations along the Voyager 1 trajectory and at Earth even after ≈?2004. An interesting result is that the cosmic-ray modulation during the current polarity cycle is not determined only by changes in the drift coefficient and tilt angle of the wavy current sheet, but is also largely dependent on changes in the diffusion coefficients.     

Galactic Cosmic Ray Modulation and the Last Solar Minimum

In this work the galactic cosmic ray modulation in relation to solar activity indices and heliospheric parameters during the years 1996??C?2010 covering solar cycle 23 and the solar minimum between cycles 23 and 24 is studied. A new perspective of this contribution is that cosmic ray data with a rigidity of 10 GV at the top of the atmosphere obtained from many ground-based neutron monitors were used. The proposed empirical relation gave much better results than those in previous works concerning the hysteresis effect. The proposed models obtained from a combination of solar activity indices and heliospheric parameters give a standard deviation <?10?% for all the cases. The correlation coefficient between the cosmic ray variations of 10?GV and the sunspot number reached a value of r=?0.89 with a time lag of 13.6±0.4 months. The best reproduction of the cosmic ray intensity is obtained by taking into account solar and interplanetary indices such as sunspot number, interplanetary magnetic field, CME index, and heliospheric current sheet tilt. The standard deviation between the observed and calculated values is about 7.15?% for all of solar cycle 23; it also works very well during the different phases of the cycle. Moreover, the use of the cosmic ray intensity of 10?GV during the long minimum period between cycles 23 and 24 is of special interest and is discussed in terms of cosmic ray intensity modulation.     

Fluctuations of the Solar Dynamo Observed in the Solar Wind and Interplanetary Magnetic Field at 1 AU and in the Outer Heliosphere

Recent helioseismic observations have found strong fluctuations at a period of about 1.3 years in the rotation speed around the tachocline in the deep solar convection layer. Similar mid-term quasi-periodicities (MTQP; periods between 1–2 years) are known to occur in various solar atmospheric and heliospheric parameters for centuries. Since the deep convection layer is the expected location of the solar magnetic dynamo, its fluctuations could modulate magnetic flux generation and cause related MTQP fluctuations at the solar surface and beyond. Accordingly, it is likely that the heliospheric MTQP periodicities reflect similar changes in solar dynamo activity. Here we study the occurrence of the MTQP periodicities in the near and distant heliosphere in the solar wind speed and interplanetary magnetic field observed by several satellites at 1 AU and by four interplanetary probes (Pioneer 10 and 11 and Voyager 1 and 2) in the outer heliosphere. The overall structure of MTQP fluctuations in the different locations of the heliosphere is very consistent, verifying the solar (not heliospheric) origin of these periodicities. We find that the mid-term periodicities were particularly strong during solar cycle 22 and were observed at two different periods of 1.3 and 1.7 years simultaneously. These periodicities were latitudinally organized so that the 1.3-year periodicity was found in solar wind speed at low latitudes and the 1.7-year periodicity in IMF intensity at mid-latitudes. While all heliospheric results on the 1.3-year periodicity are in a good agreement with helioseismic observations, the 1.7-year periodicity has so far not been detected in helioseismic observations. This may be due to temporal changes or due to the helioseismic method where hemispherically antisymmetric fluctuations would so far have remained hidden. In fact, there is evidence that MTQP fluctuations may occur antisymmetrically in the northern and southern solar hemisphere. Moreover, we note that the MTQP pattern was quite different during solar cycles 21 and 22, implying fundamental differences in solar dynamo action between the two halves of the magnetic cycle.     

Heliospheric Imaging of 3D Density Structures During the Multiple Coronal Mass Ejections of Late July to Early August 2010

It is usually difficult to gain a consistent global understanding of a coronal mass ejection (CME) eruption and its propagation when only near-Sun imagery and the local measurements derived from single-spacecraft observations are available. Three-dimensional (3D) density reconstructions based on heliospheric imaging allow us to “fill in” the temporal and spatial gaps between the near-Sun and in situ data to provide a truly global picture of the propagation and interactions of the CME as it moves through the inner heliosphere. In recent years the heliospheric propagation of dense structures has been observed and measured by the heliospheric imagers of the Solar Mass Ejection Imager (SMEI) and on the twin Solar TErrestrial RElations Observatory (STEREO) spacecraft. We describe the use of several 3D reconstruction techniques based on these heliospheric imaging data sets to distinguish and track the propagation of multiple CMEs in the inner heliosphere during the very active period of solar activity in late July?–?early August 2010. We employ 3D reconstruction techniques used at the University of California, San Diego (UCSD) based on a kinematic solar wind model, and also the empirical Tappin–Howard model. We compare our results with those from other studies of this active period, in particular the heliospheric simulations made with the ENLIL model by Odstrcil et al. (J. Geophys. Res., 2013) and the in situ results from multiple spacecraft provided by Möstl et al. (Astrophys. J. 758, 10?–?28, 2012). We find that the SMEI results in particular provide an overall context for the multiple-density flows associated with these CMEs. For the first time we are able to intercompare the 3D reconstructed densities with the timing and magnitude of in situ density structures at five spacecraft spread over 150° in ecliptic longitude and from 0.4 to 1 AU in radial distance. We also model the magnetic flux-rope structures at three spacecraft using both force-free and non-force-free modelling, and compare their timing and spatial structure with the reconstructed density flows.     

Study of cosmic ray intensity in relation to the interplanetary magnetic field and geomagnetic storms for solar cycle 24

In the present study, we investigate the association of cosmic ray intensity (CRI) with various solar wind parameters (i.e. solar wind speed V, plasma proton temperature, plasma proton density), interplanetary magnetic field (IMF B), geomagnetic storms (GSs), averaged planetary A-index (Ap index) and sun spot number (SSN) for the period 2009–2016 (solar cycle 24) by using their daily mean average. To find the association of CRI with various solar wind parameters, GSs, IMF B, Ap index and SSN, we incorporate the analysis technique by superposed-epoch method. We have observed that CRI decreases with the increase in IMF B. Moreover the time-lag analysis has been performed by the method of correlation coefficient and observed a time lag of 0 to 2 day between the decrease in CRI and increase in IMF B. In addition, we show that the CRI is found to decrease in a similar pattern to disturbance storm time (Dst index) for most of the period of solar cycle 24. The high and positive correlation is found between CRI and Dst index. The CRI and Ap index are better anti-correlated to each other than CRI and IMF. CRI and SSN are positively correlated with each other. Solar wind parameters such as solar wind speed V is a CR-effective parameter while plasma proton temperature and plasma proton density are not CR-effective parameters. The indicated parameters such as Dst index, Ap index, IMF B and solar wind parameters such as solar wind speed V, plasma proton temperature, plasma proton density shows a kind of irregular variations for solar cycle 23 and 24 while CRI and SSN shows distinct behaviour for the two cycle.     

Evolution of the Solar Flare Energetic Electrons in the Inhomogeneous Inner Heliosphere

Solar flare accelerated electrons escaping into the interplanetary space and seen as type III solar radio bursts are often detected near the Earth. Using numerical simulations we consider the evolution of energetic electron spectrum in the inner heliosphere and near the Earth. The role of Langmuir wave generation, heliospheric plasma density fluctuations, and expansion of magnetic field lines on the electron peak flux and fluence spectra is studied to predict the electron properties as could be observed by Solar Orbiter and Solar Probe Plus. Considering various energy loss mechanisms we show that the substantial part of the initial energetic electron energy is lost via wave–plasma processes due to plasma inhomogeneity. For the parameters adopted, the results show that the electron spectrum changes mostly at the distances before ～?20 R _⊙. Further into the heliosphere, the electron flux spectrum of electrons forms a broken power law relatively similar to what is observed at 1 AU.     

An Anisotropic Cosmic-Ray Enhancement Event on 07-June-2015: A Possible Origin

A usual event, called anisotropic cosmic-ray enhancement (ACRE), was observed as a small increase (\({\leq}\,5\%\)) in the count rates of polar neutron monitors during 12?–?19 UT on 07 June 2015. The enhancement was highly anisotropic, as detected only by neutron monitors with asymptotic directions in the southwest quadrant in geocentric solar ecliptic (GSE) coordinates. The estimated rigidity of the corresponding particles is \({\leq}\,1\) GV. No associated detectable increase was found in the space-borne data from the Geostationary Operational Environmental Satellite (GOES), the Energetic and Relativistic Nuclei and Electron (ERNE) on board the Solar and Heliospheric Observatory (SOHO), or the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) instruments, whose sensitivity was not sufficient to detect the event. No solar energetic particles were present during that time interval. The heliospheric conditions were slightly disturbed, so that the interplanetary magnetic field strength gradually increased during the event, followed by an increase of the solar wind speed after the event. It is proposed that the event was related to a crossing of the boundary layer between two regions with different heliospheric parameters, with a strong gradient of low-rigidity (\({<}\,1\) GV) particles. It was apparently similar to another cosmic-ray enhancement (e.g., on 22 June 2015) that is thought to have been caused by the local anisotropy of Forbush decreases, with the difference that in our case, the interplanetary disturbance was not observed at Earth, but passed by southward for this event.     

Cosmic-Ray Spectrum Approximation Model: Experimental Results and Comparison with Other Models

We discuss a model which parameterizes the cosmic-ray (CR) spectrum at different physical conditions, which include the most important effects controlling the CR intensity, like convection–diffusion and energy losses. By a suitable choice of parameters the proposed model results in two approximations: one close to a “force–field” model (describing the energy losses of CRs in the inner heliosphere) and a “convection–diffusion” equation (giving the reduction of CR intensity in the outer heliosphere). The BESS (Balloon-borne Experiment with Superconducting Spectrometer) experimental spectra of galactic protons and helium nuclei are fitted by the model spectra. The calculation of the unknown parameters is performed using a constrained least squares method as an alternative to the standard chi-square minimization method, because the data contain not only random errors, but also systematic ones. The CR spectrum approximation (CRSA) model is compared to the Moscow State University (MSU) model and the Badhwar and O’Neill (Badhwar and O’Neill, Adv. Space. Res. 14, 749, 1994; Adv. Space Res. 17, 7, 1994) model; we show that depending on the choice of the model parameters it can be examined in the context of one of these two models. We derive a relation between the parameters of the CRSA and MSU models for rigidities above about 10 GV (drift effects are ignored) during periods of low to approximately average levels of solar activity. The drawbacks of the proposed approximation are that: i) the model parameters do not depend on rigidity and ii) the model does not take into account general trends in the variations of the heliospheric magnetic field; thus, the influence of the drift effects on the shape of the spectral curves for different magnetic field polarity swings is ignored.     

The 27-Day Cosmic Ray Intensity Variations During Solar Minimum 23/24

We have studied the 27-day variations and their harmonics in Galactic cosmic ray (GCR) intensity, solar wind velocity, and interplanetary magnetic field (IMF) components during the recent prolonged solar minimum 23/24. The time evolution of the quasi-periodicity in these parameters connected with the Sun’s rotation reveals that the synodic period of these variations is ≈?26?–?27 days and is stable. This means that the changes in the solar wind speed and the IMF are related to the Sun’s near-equatorial regions in considering the differential rotation of the Sun. However, the solar wind parameters observed near the Earth’s orbit provide only the conditions in the limited local vicinity of the equatorial region in the heliosphere (within ±?7^° in latitude). We also demonstrate that the observed period of the GCR intensity connected with the Sun’s rotation increased up to ≈?33?–?36 days in 2009. This means that the process that drives the 27-day GCR intensity variations takes place not only in the limited local surroundings of the equatorial region but in the global 3-D space of the heliosphere, covering also higher latitude regions. A relatively long period (≈?34 days) found for 2009 in the GCR intensity gives possible evidence of the onset of cycle 24 due to active regions at higher latitudes and rotating slowly because of the Sun’s differential rotation. We also discuss the effect of differential rotation on the theoretical model of the 27-day GCR intensity variations.     

Hale-cycle effects in cosmic-ray intensity during the last four cycles

Monthly cosmic-ray data from Inuvik (0.16 GV) and Climax (2.96 GV) Neutron Monitor stations has been studied with the aid of solar activity parameters for the time period 1947–1995. Systematic differences in the overall shape of successive 11-year modulation cycles and similarities in the alternate 11-year cycles seem to be related to the polarity reversals of the polar magnetic field of the Sun. This suggests a possible effectiveness of the Hale cycle during even and odd solar activity cycles. Our results can be understood in terms of open and closed models of the heliosphere. Positive north pole of the Sun leads to open heliosphere where particles reach the Earth more easily when their access route is by the heliospheric oolar regions (even cycles) than when they gain access along the current sheet (odd cycles). In this case as the route of access becomes longer due to the waviness of the neutral sheet, the hysteresis effect of cosmic-rays is also longer. This interpretation is explained in terms of different contributions of convection, diffusion and drift mechanisms to the whole modulation process influencing cosmic-ray transport in the heliosphere.     

Validation of the 3D AMR SIP–CESE Solar Wind Model for Four Carrington Rotations

We carry out the adaptive mesh refinement (AMR) implementation of our solar–interplanetary space-time conservation element and solution element (CESE) magnetohydrodynamic model (SIP–CESE MHD model) using a six-component grid system (Feng, Zhou, and Wu, Astrophys. J. 655, 1110, 2007; Feng et al., Astrophys. J. 723, 300, 2010). By transforming the governing MHD equations from the physical space (x,y,z) to the computational space (ξ,η,ζ) while retaining the form of conservation (Jiang et al., Solar Phys. 267, 463, 2010), the SIP–AMR–CESE MHD model is implemented in the reference coordinates with the aid of the parallel AMR package PARAMESH available at http://sourceforge.net/projects/paramesh/ . Meanwhile, the volumetric heating source terms derived from the topology of the magnetic-field expansion factor and the minimum angular separation (at the photosphere) between an open-field foot point and its nearest coronal-hole boundary are also included. We show the preliminary results of applying the SIP–AMR–CESE MHD model for simulating the solar-wind background of different solar-activity phases by comparison with SOHO observations and other spacecraft data from OMNI. Our numerical results show overall good agreements in the solar corona and in interplanetary space with these multiple-spacecraft observations.     

Cosmic Ray Intensity Variations in Relation with Solar Flare Index and Sunspot Numbers

From the monthly data of cosmic ray intensity (CRI), sunspot numbers (SSN) and solar flare index (SFI), an attempt has been made to study the relationship between CRI and solar activity (SA) parameters SSN and SFI. The correlation between SA parameters and CRI for different neutron monitoring stations having low, middle and high cut-off rigidity has been investigated. The anti-correlation between SA and CRI is found to exist with some time lag. Based on the method of minimizing correlation coefficient and time-delayed component method, the observed time-lag between SA parameters (SSN and SFI) and CRI has been found to be large for odd solar cycles in comparison to even solar cycles. The results of time-lag analysis between CRI and SSN and between CRI-SFI have also been compared. The findings of correlative study between CRI and SSN are in agreement with earlier results, while the CRI-SFI relationship provides new insights to understand the solar modulation of cosmic rays.