Cosmic-ray modulation and the heliospheric magnetic field

The heliospheric magnetic field plays a key role in any model for the modulation of cosmic rays. It enters into all diffusion coefficients, and its magnitude, spatial gradient and direction determine drifts patterns of cosmic rays in the heliosphere. While the first axisymmetric model of E.N. Parker proved quite successful to explain in situ measurements in the ecliptic plane, new insight into the origin and the nature of the field, especially at high heliographic latitudes, has led to the development of complex fully-three-dimensional, time-dependent models. In this review, we discuss a selection of models for the heliospheric magnetic field, and discuss how some of the more recent Fisk-type models affect the modulation of cosmic rays.     

Evolution of Dst index,cosmic rays and global temperature during solar cycles 20–23

We have studied conditions in interplanetary space, which can have an influence on galactic cosmic ray (CR) and climate change. In this connection the solar wind and interplanetary magnetic field parameters and cosmic ray variations have been compared with geomagnetic activity represented by the equatorial Dst index from the beginning 1965 to the end of 2012. Dst index is commonly used as the solar wind–magnetosphere–ionosphere interaction characteristic. The important drivers in interplanetary medium which have effect on cosmic rays as CMEs (coronal mass ejections) and CIRs (corotating interaction regions) undergo very strong changes during their propagation to the Earth. Because of this CMEs, coronal holes and the solar spot numbers (SSN) do not adequately reflect peculiarities concerned with the solar wind arrival to 1 AU. Therefore, the geomagnetic indices have some inestimable advantage as continuous series other the irregular solar wind measurements. We have compared the yearly average variations of Dst index and the solar wind parameters with cosmic ray data from Moscow, Climax, and Haleakala neutron monitors during the solar cycles 20–23. The descending phases of these solar cycles (CSs) had the long-lasting solar wind high speed streams occurred frequently and were the primary contributors to the recurrent Dst variations. They also had effects on cosmic rays variations. We show that long-term Dst variations in these solar cycles were correlated with the cosmic ray count rate and can be used for study of CR variations. Global temperature variations in connection with evolution of Dst index and CR variations is discussed.     

The Compton–Getting effect of energetic particles with an anisotropic pitch-angle distribution

This paper presents a simulation of anisotropy measurements by the low-energy charged particle (LECP) experiment on Voyager 1 for cases when the particle pitch-angle distribution function in the solar wind plasma reference frame is not isotropic. The model includes both the Compton–Getting anisotropy and perpendicular diffusion anisotropy that possibly exists in the upstream region of the termination shock. The results show that the Voyager 1 data cannot rule out either the model with zero solar wind speed or the one with a finite speed on qualitative basis. The determination of solar wind speed using the Compton–Getting effect is affected by the assumption of the magnetic field direction and perpendicular diffusion anisotropy. Because the pitch-angle distribution anisotropy is so large, a small uncertainty in the magnetic field direction can produce very different solar wind speeds ranging from ∼0 to >400 km/s. In fact, if the magnetic field is chosen to be in the Parker spiral direction, which is consistent with the magnetometer measurement on Voyager 1, the derived solar wind speed is still close to the supersonic value. Only the two lowest-energy channels of the LECP instrument may give a definitive answer to the solar wind speed. However, because these channels contain a very high level of cosmic ray background, an uncertainty of just a few percent in the background can entirely hamper the estimate of solar wind speed.     

Effective non-vertical and apparent cutoff rigidities for a cosmic ray latitude survey from Antarctica to Italy in minimum of solar activity

In this paper we will report the results of the computation of cutoff rigidities of vertical and non-vertical incident cosmic ray particles. Non-vertical effective cutoff rigidities have been computed by tracing particle trajectories through the “real” geomagnetic magnetic field comprising the International Geomagnetic Reference Field model (IGRF95, IAGA Division 5 Working Group 8, 1996: Sabaka, T.J., Langel, R.A., Baldwin, R.T., Conrad, J.A. The geomagnetic field, 1900–1995, including the large scale fields from magnetospheric sources and NASA candidate models for the 1995 IGRF revision. J. Geomag. Geoelect. 49, 157–206, 1997.) and the Tsyganenko [Tsyganenko, N.A. A magnetospheric magnetic field model with a warped tail current sheet. Planet. Space Sci. 37, 5–20, 1989.] magnetosphere model. The computation have been done for the backward route (from Antarctica to Italy) of the Italian Antarctic ship survey 1996–1997, for geographic points corresponding to the daily average coordinates of the ship; for zenith angles 15°, 30°, 45° and 60°, and azimuth angles from 0° to 360° in steps of 45°. By means of the obtained non-vertical cutoffs the apparent cutoff rigidities have been calculated. The information on integral multiplicities of secondary neutrons detected by the neutron monitor in dependence of the zenith angle of incoming primary cosmic ray particles have also been used. This information is based on the theoretical calculations of meson-nuclear cascades of primary protons with different rigidities arriving to the Earth’s atmosphere at the zenith angles of 0°, 15°, 30°, 45°, 60° and 75°. The difference between the computed apparent and vertical cutoff rigidities reaches ∼1 GV at rigidities >7–8 GV. At rigidities of 10–16 GV, the difference between the apparent and vertical cutoff rigidities is larger than that obtained earlier by Clem et al. [Clem, J.M., Bieber, J.W., Duldig, M., Evenson, P., Hall, D., Humble, J.E. Contribution of obliquely incident particles to neutron monitor counting rate. J. Geophys. Res. 102, 26919–26926, 1997.] and Dorman et al. [Dorman, L.I., Villoresi, G., Iucci, N., Parisi, M., Tyasto, M.I., Danilova, O.A., Ptitsyna, N.G. Cosmic ray survey to Antarctica and coupling functions for neutron component near solar minimum (1996–1997), 3. Geomagnetic effects and coupling functions. J. Geophys. Res. 105, 21047–21056, 2000.].     

Observed solar cycle modulation of galactic cosmic rays over a range of rigidities

We have studied the long-term, steady-state, solar cycle modulation of galactic cosmic ray intensity for seven cycles (17–23). Our analysis is based on the data obtained with a variety of detectors on earth (neutron monitors of the global network and muon detectors) as well as telescopes flown on high altitude balloons and on-board near-earth satellites. The median rigidity of response for these detectors to galactic cosmic ray spectrum lies in the range 1–70 GV. We correlate cosmic ray data to sunspot numbers, Ap, solar wind bulk speed (V), magnetic field (B), as well as to the cycle maximum (M), minimum (m), and the epochs of the solar polar field reversals. This enables us to derive the rigidity dependence of observations, and helps us to define the characteristics of the modulation function in the heliosphere.     

α–ω Effect and peculiarities of the 27-day variations of the galactic cosmic rays intensity,solar wind and solar activity parameters

We show that the amplitudes of the 27-day variations of galactic cosmic ray (GCR) intensity, solar wind and solar activity parameters have a periodicity with duration of three to four Carrington rotation periods (3–4 CRP). We assume that the general reason for this phenomenon may be related to similar cyclicity of topological structure of the solar magnetic field lines created owing to the asymmetry of turbulent solar dynamo and solar differential rotation transforming the Sun’s poloidal magnetic field to the toroidal (α–ω effect), and vice versa.     

The heliospheric modulation of 3–10 MeV electrons: Modeling of changes in the solar wind speed in relation to perpendicular polar diffusion

The discrepancy between cosmic ray model predictions representing solar minimum conditions in the heliosphere and the 3–10 MeV post-1998 electrons observations by the Kiel Electron Telescope (KET) onboard Ulysses suggests the need for consistent changes in model parameters with increasing solar activity. In order to reduce this discrepancy, an effort is made to model the KET observations realistically during periods of increased solar activity by applying an advanced three-dimensional, steady-state electron modulation model based on Parker’s transport equation including the Jovian electron source. Some elements of the diffusion tensor which were not previously emphasized are revisited. A new relation is also established between the latitudinal dependence of the solar wind speed and the perpendicular polar diffusion. Based on this relation, a transition of an average solar wind speed from solar minimum to solar maximum conditions, as observed on board the Ulysses spacecraft, is modeled on the concept of the time-evolution of large polar coronal holes. These changes are correlated to different scenarios of the enhancement of perpendicular polar diffusion. Effects of these scenarios are illustrated, as a series of steady-state solutions, on the computed 7 MeV Jovian and galactic electrons in comparison with 3–10 MeV electrons observed from the period 1998 to the end of 2003. It is shown that this approach improves compatibility with the KET observations but it also points to the need for a time-dependent electron modulation model to fully describe modulation during moderate to extreme solar maximum conditions.     

Sunspot activity and cosmic ray modulation at 1 a.u. for 1900–2013

The descent of sunspot cycle 23 to an unprecedented minimum of long duration in 2006–2009 led to a prolonged galactic cosmic ray (GCR) recovery to the highest level observed in the instrumental era for a variety of energetic charged particle species on Earth, over a wide range of rigidities. The remarkable GCR increase measured by several ground-based, balloon-borne, and detectors on a satellite is described and discussed. It is accompanied by a decrease in solar wind velocity and interplanetary magnetic field at 1 a.u., reaching the lowest values since measurements of the solar wind began in October 1963; the solar polar field strength (μT) measured at the Wilcox Solar Observatory (WSO) is also significantly reduced compared to prior cycles since the start of the program in 1976, the polar field in the northern hemisphere reversed in June 2012 and again in February 2014, that in the southern hemisphere reversed in July 2013. If updates of WSO data confirm the second reversal in northern solar hemisphere, it would pose a serious challenge to the Dynamo Theory. The long-term change in solar behavior may have begun in 1992, perhaps earlier. The physical underpinnings of these solar changes need to be understood and their effect on GCR modulation processes clarified. The study discusses the recent phenomena in the context of GCR modulation since 1900. These happenings affected our empirical predictions for the key parameters for the next two sunspot cycles (they may be progressively less active than sunspot cycle 24) but it enhanced support for our prediction that solar activity is descending into a Dalton-like grand minimum in the middle of the twentyfirst century, reducing the frequency of the coronal mass ejections; they determine the space weather affecting the quality of life on Earth, radiation dose for hardware and human activities in space as well as the frequency of large Forbush decreases at 1 a.u.     

宇宙线福布什下降的数值模拟

本文从银河宇宙线的太阳调制方程出发,认为激波对宇宙线的影响是由一扰动区产生的。在此扰动区中太阳风速度增加,扩散系数下降。由此进行了数值模拟,模拟结果表明:扩散系数的下降在产生福布什下降时要比太阳风速度的增加更为有效;福布什下降在近日球层内向外传播时,其幅度随径向距离的增大而衰减;两个无相互作用的激波同时存在时所产生的福布什下降为每个激波单独存在时的福布什下降的简单线性迭加。      

Modeling and experimental study of the 27-day variation of galactic cosmic-ray intensity for a solar wind velocity depending on heliolongitude

We develop a three-dimensional (3-D) model of the 27-day variation of galactic cosmic-ray (GCR) intensity with a spatial variation of the solar wind velocity. A consistent, divergence-free interplanetary magnetic field is derived by solving the corresponding Maxwell equations with a variable solar wind speed, which reproduces in situ observed experimental data for the time interval to be analyzed (24 August 2007–28 February 2008). We perform model calculations for the GCR intensity using the variable solar wind and the corresponding magnetic field. Results are compatible with experimental data; the correlation coefficient between our model predictions and observed 27-day GCR variation is 0.80 ± 0.05.     

Dependence of the 27-day variation of cosmic rays on the global magnetic field of the Sun

We show that the higher range of the heliolongitudinal asymmetry of the solar wind speed in the positive polarity period (A > 0) than in the negative polarity period (A < 0) is one of the important reasons of the larger amplitudes of the 27-day variation of the galactic cosmic ray (GCR) intensity in the period of 1995–1997 (A > 0) than in 1985–1987 (A < 0). Subsequently, different ranges of the heliolongitudinal asymmetry of the solar wind speed jointly with equally important corresponding drift effect are general causes of the polarity dependence of the amplitudes of the 27-day variation of the GCR intensity. At the same time, we show that the polarity dependence is feeble for the last unusual minimum epoch of solar activity 2007–2009 (A < 0); the amplitude of the 27-day variation of the GCR intensity shows only a tendency of the polarity dependence. We present a three dimensional (3-D) model of the 27-day variation of GCR based on the Parker’s transport equation. In the 3-D model is implemented a longitudinal variation of the solar wind speed reproducing in situ measurements and corresponding divergence-free interplanetary magnetic field (IMF) derived from the Maxwell’s equations. We show that results of the proposed 3-D modeling of the 27-day variation of GCR intensity for different polarities of the solar magnetic cycle are in good agreement with the neutron monitors experimental data. To reach a compatibility of the theoretical modeling with observations for the last minimum epoch of solar activity 2007–2009 (A < 0) a parallel diffusion coefficient was increased by ∼40%.     

一个基于观测的太阳风背景模型

建立由太阳光球磁场和日冕偏振亮度等观测约束的单流体太阳风模型,包括日冕和太阳风的等离子体密度、速度和磁场,温度还有待于以后处理.这里采用高山观测台(HAO)MKⅢ的日冕偏振亮度(pB)在1.36Rs上的观测概图,根据Guhathakurta在1996年发展的日冕电子密度反演模型确定日冕的电子密度分布.同时采用Wilcox太阳观测台(WSO)的光球磁场视向分量的观测概图作为底部边界,根据Zhao等在1994年发展的水平电流-电流片(HCCS)模型得到全球磁场.Phillips在1995年及McComas在2003年分别用Ulysses第一次和第二次跨极飞行的观测发现,归一化到1 AU的太阳风动量流密度除了在10°～30°的纬度范围内略低以外几乎不变.根据这一结论,结合已经得到的密度数据,就可以得到日冕和太阳风的速度.将上面的模型应用于1918卡林顿自转周稳态太阳风的研究,结果与太阳活动极小期的观测基本相符,但是与观测相比较低速高密度区偏大,因此密度模型还有待改进.      

On the long-term variability of the heliosphere–magnetosphere environment

Annual means of measured and reconstructed solar, heliospheric, and magnetospheric parameters are used to infer solar activity signatures at the Hale and Gleissberg cycles timescales. Available open solar flux, modulation strength, cosmic ray flux, total solar irradiance data, reconstructed back to 1700, solar wind parameters (speed and density) and the magnitude of the heliospheric magnetic field at 1 AU, reconstructed back to 1870, as well as the time series of geomagnetic activity indices (aa, IDV, IHV), going back to 1870, have been considered. Simple filtering procedures (successive 11-, 22-, and 88-year running averages and differences between them) and scaling by the standard deviation from the average value for the common interval covered by the data show that the long-discussed variation in the 20th century (a pronounced increase since ∼1900, followed by a depression in the ‘60s and a new, slower, increase) seen in the 11-year averages of parameters such as geomagnetic activity indices and reconstructed heliospheric magnetic field strength, solar wind speed, open solar flux, is a result of the superposition in data of solar activity signatures at Hale and Gleissberg cycles timescales. The Hale and Gleissberg signals were characterized and similarities and differences in the temporal behavior of the analyzed parameters at these timescales are discussed. The similarities in the studied parameters point to a common pacing source, the solar dynamo.     

Cosmic rays in the dynamic heliosheath

Cosmic ray modulation in the outer heliosphere is discussed from a modeling perspective. Emphasis is on the transport and acceleration of these particles at and beyond the solar wind termination shock in the inner heliosheath region and how this changes over a solar cycle. We will show that by using numerical models, and by comparing results to spacecraft observations, much can be learned about the dependence of cosmic ray modulation on solar cycle changes in the solar wind and heliospheric magnetic field. While the first determines the heliospheric geometry and shock structure, the latter results in a time-dependence of the transport coefficients. Depending on energy, both these effects contribute to cosmic ray intensities in the inner heliosheath changing over a solar cycle.     

The charge-sign dependent effect in the solar modulation of cosmic rays

The centennial anniversary of the discovery of cosmic rays was in 2012. Since this discovery considerable progress has been made on several aspects related to galactic cosmic rays in the heliosphere. It is known that they encounter a turbulent solar wind with an imbedded heliospheric magnetic field when entering the Sun’s domain. This leads to significant global and temporal changes in their intensity inside the heliosphere, a process known as the solar modulation of cosmic rays. The prediction of a charge-sign dependent effect in solar modulation in the late 1970s and the confirmatory observational discoveries can also be considered as a milestone. A short review is given of these predictions based on theoretical and numerical modelling work, the observational confirmation and related issues.     

Early history of cosmic rays and solar wind – Some personal remembrances

The early history of solar wind was replete with prejudices and strong opposition to Parker’s formulation. It was only after conclusive evidence from satellite data was obtained that the idea of solar wind was accepted. Some personal experiences of mine during my stay at the University of Chicago in 1953–1954, including the encounter of Dr. Simpson with Dr. Biermann and the inconclusive discussion between them about a possible perpetual solar outflow of particles are presented and further developments when Parker came to Chicago in 1956 and formulated his idea of solar wind, as narrated to me later by Dr. Simpson, are described.     

Mid 19th century minimum of galactic cosmic ray flux inferred from Ti in Allegan meteorite

Measurements of ⁴⁴Ti activity in meteorites show that the galactic cosmic ray (GCR) intensity has been declining in the interplanetary space during the past three centuries and has a component of cyclic variation, with periodicity of about 87 years [Taricco, C., Bhandari, N., Cane, D., et al. Galactic cosmic ray flux decline and periodicities in the interplanetary space during the last 3 centuries revealed by ⁴⁴Ti in meteorites. J. Geophys. Res. 111, A08102, 2006.]. In order to verify these results, we have measured ⁴⁴Ti activity in Allegan meteorite which fell in 1899 and in some other meteorites with better precision. The measurements confirm low cosmic ray flux and consequently high solar activity near the middle of 19th century.     

Modulation of galactic cosmic rays in a north–south asymmetrical heliosphere

Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock. Voyager 1 crossed this termination shock at ∼94 AU in 2004, while Voyager 2 crossed it in 2007 at a different heliolatitude, about 10 AU closer to the Sun. These different positions of the termination shock confirm the dynamic and cyclic nature of the shock’s position. Observations from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that apart from the dynamic nature caused by changing solar activity there also may exist a global asymmetry in the north–south (polar) dimensions of the heliosphere, in addition to the expected nose–tail asymmetry. This relates to the direction in which the heliosphere is moving in interstellar space and its orientation with respect to the interstellar magnetic field. In this paper we focus on illustrating the effects of this north–south asymmetry on modulation of galactic cosmic ray Carbon, between polar angles of 55° and 125°, using a numerical model which includes all four major modulation processes, the termination shock and the heliosheath. This asymmetry is incorporated in the model by assuming a significant dependence on heliolatitude of the thickness of the heliosheath. When comparing the computed spectra between the two polar angles, we find that at energies E < ∼1.0 GeV the effects of the assumed asymmetry on the modulated spectra are insignificant up to 60 AU from the Sun but become increasingly more significant with larger radial distances to reach a maximum inside the heliosheath. In contrast, with E > ∼1.0 GeV, these effects remain insignificant throughout the heliosphere even very close to the heliopause. Furthermore, we find that a higher local interstellar spectrum for Carbon enhances the effects of asymmetric modulation between the two polar angles at lower energies (E < ∼300 MeV). In conclusion, it is found that north–south asymmetrical effects on the modulation of cosmic ray Carbon depend strongly on the extent of the geometrical asymmetry of the heliosheath together with the assumed value of the local interstellar spectrum.     

Modeling and data analysis of a Forbush decrease

We study the Forbush decrease of the galactic cosmic ray intensity observed in 9–25 September 2005 using the experimental data and a newly developed time-dependent three dimensional modeling. We analyze neutron monitors and muon telescopes, and the interplanetary magnetic field data. We demonstrate a clear relationship between the rigidity (R) spectrum exponent (γ) of the Forbush decrease and the exponent (ν) of the power spectral density of the components of the interplanetary magnetic field in the frequency range of ∼ 10⁻⁶–10 ⁻⁵ Hz. We confirm that an inclusion of the time-dependent changes of the exponent ν makes the newly developed nonstationary three dimensional model of the Forbush decrease compatible with the experimental data. Also, we show that the changes of the rigidity spectrum exponent γ does not depend on the level of convection of the galactic cosmic rays stream by solar wind; depending on the changes of the exponent ν, i.e. on the state of the turbulence of the interplanetary magnetic field.     

Energetic positive ions in the cometary “foreshock” region

Ions produced by ionization of the cometary neutrals interact with the solar wind protons to produce large amplitude oscillations of the ambient magnetic field. Such oscillations are convected towards the comet at the unperturbed solar wind speed far from the shock and at a lower speed closer to the shock (due to the solar wind mass loading); hence, they can energize the incoming ions by Fermi acceleration. The spatial extension of the acceleration region is of the order of 10⁶ km and the resulting energy spectrum is harder than in the Earth's bow shock case. The energization of cometary ions produces an additional deceleration of the solar wind. It is suggested that Comet Halley may be the most efficient “cosmic ray shock” in the solar system.