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.     

An empirical model for the 11-year cosmic-ray modulation

An analysis of monthly data from nine world-wide neutron monitoring stations over the period 1965–1975 is carried out for the study of the long-term cosmic-ray modulation. In an attempt to gain insight into the relationships which exist between solar activity, high-speed solar wind streams and various terrestrial phenomena an empirical relation for the cosmic-ray modulation has been found. Accordingly the modulated cosmic-ray intensity is equal to the galactic cosmic-ray intensity corrected by a few appropriate solar, interplanetary and terrestrial activity indices which causes the disturbances in interplanetary space, multiplying with the corresponding time-lag of cosmic-ray intensity from each of these indices. This relation is well explained by a generalization of the Simpson solar wind model which has been proved by the spherically symmetric diffusion-convection theory.     

Variations of the interplanetary magnetic field and the electron and cosmic-ray intensities under the influence of Jupiter

Analysis of experimental data on the variations in the intensities of 2–12 MeV electrons and cosmic rays and the interplanetary magnetic field (IMF) magnitude has revealed “responses” to the influence of Jupiter in these parameters. Their amplitudes, in instrumental count units, are the following: 0.15 (71%) in the electron intensity, 48 (0.8%) in the cosmic-ray intensity, and 0.19 (2.8%) in the IMF magnitude. The maximum of the response in the electron intensity and the minimum of the response in the IMF magnitude coincide and lie near the magnetic field line that runs along the Sun-Earth-Jupiter axis. The minimum of the response in the cosmic-ray intensity is shifted against the solar rotation by 75 days from the magnetic field line connecting Jupiter and the Earth. Jupiter has the strongest influence on the intensity of high-energy electrons (71% of their total intensity).     

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.     

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.     

On reproduction of long-term cosmic-ray modulation as seen by neutron monitor stations

The dependence of cosmic-ray intensity on 21st solar cycle phenomena has been studied using monthly cosmic-ray values from nine world wide Neutron Monitoring Stations.For this purpose the long-term cosmic-ray modulation is modelled by treating the most appropriate source functions among various solar, interplanetary and terrestrial activity indices as the input and the cosmic-ray intensity as the output of a linear system taking into account the corresponding time-lag. In this way the modulated galactic cosmic-ray intensity has been reproduced to a certain degree as the cosmic-ray variations follow the observations with a standard deviation of ~ 10%. Still remaining short-term variations in all stations with periods of 2.7 and 3.7 months can possibly be related to the galactic origin of cosmic-rays.The Simpson solar wind model improved by the spherically symmetric diffusion-convection theory can describe our proposed method.     

Study of the Cosmic-Ray Modulation During the Passage of ICMEs and CIRs

We compare the cosmic-ray response to interplanetary coronal mass ejections (ICMEs) and corotating interaction regions (CIRs) during their passage in near-Earth space. We study the relative importance of various structures/features identified during the passage of the ICMEs and CIRs observed during Cycle 23 (1995?–?2009). The identified ICME structures are the shock front, the sheath, and the CME ejecta. We isolate the shock arrival time, the passage of the sheath region, the arrival of ejecta, and the end time of their passage. Similarly, we isolate the CIR arrival, the associated forward shock, the stream interface, and the reverse shock during the passage of a CIR. For the cosmic-ray intensity, we utilize the data from high counting rate neutron monitors. In addition to neutron monitor data, we utilize near-simultaneous and same time-resolution data of interplanetary plasma and field, namely the solar-wind velocity, the interplanetary magnetic field (IMF) vector, and its variance. Further, we also utilize some derived interplanetary parameters. We apply the method of the superposed-epoch analysis. As the plasma and field properties are different during the passage of different structures, both in ICMEs and CIRs, we systematically vary the epoch time in our superposed-epoch analysis one by one. In this way, we study the role and effects of each of the identified individual structures/features during the passage of the ICMEs and CIRs. Relating the properties of various structures and the corresponding variations in plasma and field parameters with changes of the cosmic-ray intensity, we identify the relative importance of the plasma/field parameters in influencing the amplitude and time profiles of the cosmic-ray intensity variations during the passage of the ICMEs and CIRs.     

A search of cosmic-ray variations generated by pulsations of the heliosphere

Application of new statistical techniques to time series allow the investigation of cosmic-ray intensity variation in the periodicity range of 1 to 10 years. We can put significant levels to the existence of these oscillations and define their character as quasi-periodic and/or recurrent. Correlations between cosmic-ray intensity variations and solar activity changes during 1944–1979 are investigated. The two-year variation in cosmic rays is observed to be variable both in amplitude and phase, and not correlated with sunspot cyclic variations; but seems to depend on the magnetic polarity of the interplanetary medium. No significant evidence for the existence of longer period variations is obtained.     

Simulation of long-term cosmic-ray intensity variation

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

Simulation of the temporal variations of the galactic cosmic-ray intensity at neutron monitor energies

We show that the temporal variations of the integrated galactic cosmic-ray intensity at neutron monitor energies (approximately above 3 GeV) can be reproduced applying a semi-empirical 1-D diffusion-convection model for the cosmic-ray transport in interplanetary space. We divide the interplanetary region into `magnetic shells' and find the relative reduction that each shell causes to the cosmic-ray intensity. Then the cosmic-ray intensity at the Earth is reproduced by the successive influence of all shells between the Earth and the heliospheric termination shock. We find that the position of the termination shock does not significantly affect the cosmic-ray intensity although there are some differences between the results for a constant and a variable termination shock radius. We also reproduce the cosmic-ray intensity applying the analytical solution of the force-field approximation (Perko, 1987) and find that the results cannot fit the observed data. Our results are compared with the Climax (geomagnetic cut-off 3 GV) and Huancayo (geomagnetic cut-off 13 GV) neutron monitor measurements for almost two solar cycles (1976–1996).     

Power-spectrum analysis of local geomagnetic disturbances and their relationship to cosmic-ray and aurora intensity

Power-spectrum analyses have been carried out on two data sets of the geomagnetic K-index from the Athens and Sofia magnetic Observatories. For the period between 1956–1984, periodicities of about 2.8 and 6 months have been obtained. Similar results were found by the auto-correlation technique. Both periods are significant to 0.05 and 0.01 level, respectively. In our attempt to explain transient geomagnetic disturbances caused by other parameters, the K-index was correlated to cosmic-ray and aurora intensity. The best correlation coefficient between K-variations and cosmic-ray data from Athens Neutron-Monitor Station was 0.58 and between K-index and Auroral, activity index was 0.47.An attempt to interpret these periodicities and relationships has been made.     

Study of Cosmic-Ray Intensity Variations Associated with Anomalous,Long-Duration High-Speed Solar Wind Streams in 2003

High-speed solar wind streams (HSWS) were identified for solar cycles 22 and 23 (up to 2004). Preliminarily, HSWS were classified in three groups according to their continuous period of occurrence. In the declining phase of solar cycle 23, 2003 is found to be anomalous, showing a very large number of HSWS events of long duration (> ten days). We have studied the effect of HSWS on the cosmic-ray intensity as well as their relationship with geomagnetic disturbance index Ap on yearly, daily, and hourly bases. The yearly average of solar-wind speed was also found to be maximum in 2003. Being within the declining phase of solar activity, the occurrence of solar flares in 2003 is quite low. In particular during HSWS, no solar flares have been observed. Associations with cosmic-ray changes do not support the notion that the HSWS are usually effective in producing significant cosmic-ray decreases. Out of 12 HSWS events observed during the period 2002 (December) to 2003, four events of significant cosmic-ray decreases at all the stations have been selected for further analysis. The cosmic-ray intensity has been found to decrease during the first phase of the event (first five days of HSWS) at all three neutron-monitor stations situated at different latitudes with different cutoff rigidities. The rigidity spectra of observed decreases in cosmic-ray intensity for these four cases have been found to be significantly different than that of Fds (Forbush decrease). In two cases the spectra are softer, whereas in the other two they are harder than that of Fds. However, if the average of all four events is considered together then the spectra of the decrease in cosmic rays during HSWS exactly match that of Fds. Such a result implies that initially individual events should be considered, instead of combining them together, as was done earlier. The Ap index is also found to generally increase in the first phase of the event. However, the four events selected on the basis of cosmic-ray decrease are not always associated with enhanced values of the Ap index. As such, the significance of our study is that further detailed investigations for much longer periods and on an event-by-event basis is required to understand the effect of coronal-hole-associated HSWS.     

Solar activity and the 11-year modulation of cosmic rays

The cosmic-ray intensity during the 18th and 19th solar cycles is examined in the light of Gnevyshev's suggestion of the presence of two maxima in each solar cycle. The 18th solar cycle (1944–54) has two prominent and widely separated cosmic-ray minima corresponding in phase with the two maxima in Bartel's A_p index. For the 19th solar cycle the existence of two minima is less prominent than for the 18th solar cycle. The maximum at higher solar latitudes is more effective in reducing cosmic-ray intensity than the maximum at the lower latitudes. A_p, however, has a larger maximum during the lower latitude solar maximum. A relation between A_p and cosmic-ray intensity is obtained. This relationship is shown to be consistent with Parker's solar-wind theory of the modulation of cosmic rays.     

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.     

The Global Survey Method Applied to Ground-level Cosmic Ray Measurements

The global survey method (GSM) technique unites simultaneous ground-level observations of cosmic rays in different locations and allows us to obtain the main characteristics of cosmic-ray variations outside of the atmosphere and magnetosphere of Earth. This technique has been developed and applied in numerous studies over many years by the Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN). We here describe the IZMIRAN version of the GSM in detail. With this technique, the hourly data of the world-wide neutron-monitor network from July 1957 until December 2016 were processed, and further processing is enabled upon the receipt of new data. The result is a database of homogeneous and continuous hourly characteristics of the density variations (an isotropic part of the intensity) and the 3D vector of the cosmic-ray anisotropy. It includes all of the effects that could be identified in galactic cosmic-ray variations that were caused by large-scale disturbances of the interplanetary medium in more than 50 years. These results in turn became the basis for a database on Forbush effects and interplanetary disturbances. This database allows correlating various space-environment parameters (the characteristics of the Sun, the solar wind, et cetera) with cosmic-ray parameters and studying their interrelations. We also present features of the coupling coefficients for different neutron monitors that enable us to make a connection from ground-level measurements to primary cosmic-ray variations outside the atmosphere and the magnetosphere. We discuss the strengths and weaknesses of the current version of the GSM as well as further possible developments and improvements. The method developed allows us to minimize the problems of the neutron-monitor network, which are typical for experimental physics, and to considerably enhance its advantages.     

The robust detection of stars on CCD images

Two parameters are developed to analyze the CCD images from ground-based and/or space telescopes. The first parameter, deduced from the intensity profile of the object sharp, is useful to resolve stars and hot pixels. The second parameter shape distinguishes the stars from the background cosmic-ray events using geometric characteristics defined by its shapes. The parameters are applied to a simulated OMC/INTEGRAL image and a HST image.     

Shock Orientations,Magnetic Turbulence and Forbush Decreases

We have studied the effects of quasi-parallel and quasi-perpendicular shocks on the transient modulation of cosmic-ray intensity. Interplanetary magnetic field strength, its variance and solar wind velocity during their passage have also been considered for the analysis in this work. It has been demonstrated that magnetically turbulent quasi-parallel shocks are much more effective in producing Forbush decreases in cosmic-ray intensity than the non-turbulent quasi-perpendicular shocks. From these results it is inferred that turbulence in the shock environment is an important factor in causing Forbush decreases by scattering particles due to magnetic field fluctuations. Results presented in this study provide more specific information about structures responsible for Forbush decreases, physical processes mainly responsible for this phenomenon and the possibility of predicting the likely occurrence of Forbush decreases from observations in space.     

Types of interplanetary shocks and forbush decreases

Two types of interplanetary shocks have been identified and classified into two groups, those associated with a helium-enhancement and those not associated with any helium-enhancement. The cosmic-ray intensity decreases at Calgary neutron monitor are studied with respect to the arrival time of the two groups of shocks. The observations show that large Forbush decreases are caused by shocks associated with the helium-enhancement; and those not associated with He shocks show comparatively a small decrease in cosmic-ray intensity.     

Evidence for the deficiency of short cosmic ray pathlengths and a physically realistic explanation — The no-near-sources model

From our recent observations of the charge and energy spectra of cosmic-ray nuclei we have constructed secondary-to-primary charge ratios at the two ends of the charge spectrum. These ratios are found to be inconsistent with thead hoc leaky-box model of cosmic-ray propagation which leads to an exponential pathlength distribution. Models for which the pathlength distribution function is deficient in short pathlengths provide a more consistent picture. Several of these models are investigated, bothad hoc and physical. The physical model considered here is one for which detailed galactic propagation parameters and boundary conditions are used and for which there exists no near sources of cosmic rays over a time interval corresponding to a few times the cosmic-ray age.     

On the link between northern fennoscandian climate and length of the quasi-eleven-year cycle in galactic cosmic-ray flux

Bidecadal fluctuations in terrestrial climate were analyzed. It was shown that this variability might arise if Earth's climate reacts to galactic cosmic-ray intensity, integrated over its full quasi-11-year cycle. It was further shown that this integral effect should also lead to an effective link between climate and the duration of the quasi-11-year cycle in cosmic ray flux. That, in turn, must result in appearance of some connection between climate and the length of the solar cycle, which is currently a topic of active debate. Analyses of temperature proxies, obtained for northern Fennoscandia, confirmed the connection of the climate in this region and the length of the cycle in galactic cosmic-ray intensity. Decadal and bidecadal variability of integrated cosmic-ray flux was quantitatively estimated.