Cosmic ray modulation in the outer heliosphere: Predictions for cosmic ray intensities up to the heliopause along Voyager 1 and 2 trajectories

Time dependent cosmic ray modulation in the outer heliosphere is calculated and results are compared to Voyager 1 and 2 observations using a two-dimensional time-dependent cosmic ray transport model. We predict possible future 133–242 MeV proton observations along the Voyager 1 and 2 spacecraft trajectories. Recent theoretical advances in cosmic ray transport parameters are introduced in order to provide a time-dependence for the assumed transport parameters used in the model. This leads to results that are in general compatible with the spacecraft observations in the inner and outer heliosphere over multiple solar cycles. However, for the outer heliosphere, we find that the Voyager 1 and 2 spacecraft observations cannot be fitted with an identical set of parameters along both trajectories. This indicates a possible asymmetric heliosphere or a symmetric heliosphere but with different diffusion parameters in the northern and southern hemispheres, respectively. Furthermore, results indicate that Voyager 2 observations are still under the influence of solar cycle related changes because of the large modulation volume between the heliopause and spacecraft location in contrast to Voyager 1 which shows a steady increase in cosmic ray intensities.     

Modeling ground and space based cosmic ray observations

After entering our local astrosphere (called the heliosphere), galactic cosmic rays, as charged particles, are affected by the Sun’s turbulent magnetic field. This causes their intensities to decrease towards the inner heliosphere, a process referred to as modulation. Over the years, cosmic ray modulation has been studied extensively at Earth, utilizing both ground and space based observations. Moreover, modelling cosmic ray modulation and comparing results with observations, insight can be gained into the transport of these particles, as well as offering explanations for observed features. We review some of the most prominent cosmic ray observations made near Earth, how these observations can be modelled and what main insights are gained from this modelling approach. Furthermore, a discussion on drifts, as one of the main modulation processes, are given as well as how drift effects manifest in near Earth observations. We conclude by discussing the contemporary challenges, fuelled by observations, which are presently being investigated. A main challenge is explaining observations made during the past unusual solar minimum.     

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.     

Galactic cosmic radiation model and its applications.

A model for the differential energy spectra of galactic cosmic radiation as a function of solar activity is described. It is based on the standard diffusion-convection theory of solar modulation. Estimates of the modulation potential based on fitting this theory to observed spectral measurements from 1954 to 1989 are correlated to the Climax neutron counting rates and to the sunspot numbers at earlier times taking into account the polarity of the interplanetary magnetic field at the time of observations. These regression lines then provide a method for predicting the modulation at later times. The results of this model are quantitatively compared to a similar Moscow State University (MSU) model. These model cosmic ray spectra are used to predict the linear energy transfer spectra, differential energy spectra of light (charge < or = 2) ions, and single event upset rates in memory devices. These calculations are compared to observations made aboard the Space Shuttle.     

Radial distribution of galactic cosmic rays at solar maximum

In this paper we analyze the spatial distribution of galactic cosmic rays during periods of maximum solar activity of the cycles 21, 22 and 23. We have used a two dimensional model to solve the cosmic ray transport equation. This model includes all relevant physical processes: diffusion, convection, drift and shock effects on cosmic ray propagation inside the heliosphere. We focused on the study of the radial distribution of galactic cosmic rays, and compare our results with the spacecraft observations for two energies (175 MeV H and 265 MeV/n He). Although the radial intensities of galactic cosmic rays can be explained qualitatively with all three local interstellar spectra (LISs) used in this work, we applied a reduced chi-squared analysis to investigate the best LIS that could fit the data.     

Fluctuations of cosmic rays and IMF in the vicinity of interplanetary shocks

Fluctuations of cosmic rays and interplanetary magnetic field upstream of interplanetary shocks are studied using data of ground-based polar neutron monitors as well as measurements of energetic particles and solar wind plasma parameters aboard the ACE spacecraft. It is shown that coherent cosmic ray fluctuations in the energy range from 10 keV to 1 GeV are often observed at the Earth’s orbit before the arrival of interplanetary shocks. This corresponds to an increase of solar wind turbulence level by more than the order of magnitude upstream of the shock. We suggest a scenario where the cosmic ray fluctuation spectrum is modulated by fast magnetosonic waves generated by flux of low-energy cosmic rays which are reflected and/or accelerated by an interplanetary shock.     

Cosmic ray anisotropies in the outer heliosphere

The observation of the directional distribution of energetic and cosmic ray particles has been done with the Voyager spacecraft over a long period. Since 2002, when the first flux enhancements of charged particles associated with the approach of Voyager 1 to the solar wind termination shock were observed, these anisotropy measurements have become of special interest. They play an important role to understand the magnetic field and shock structure and the basics of the modulation of cosmic ray and anomalous particles at and beyond the termination shock. They also serve as motivation to study the spatial behavior of galactic and anomalous cosmic ray anisotropies with numerical modulation models in order to illustrate how the radial anisotropy, at different energies, change from upstream to downstream of the termination shock. Observations made by Voyager 1 indicate that the termination shock is a complicated region than previously thought, hence the effects of the latitude dependence of the termination shock’s compression ratio and injection efficiency on the radial anisotropies of galactic and anomalous protons will be illustrated. We find that the magnitude and direction of the radial anisotropy strongly depends on the position in the heliosphere and the energy of particles. The effect of the TS on the radial anisotropy is to abruptly increase its value in the heliosheath especially in the A > 0 cycle for galactic protons and in both polarity cycles for anomalous protons. Furthermore, the global effect of the latitude dependence of the shock’s compression ratio is to increase the radial anisotropy for galactic protons throughout the heliosphere, while when combined with the latitude dependence of the injection efficiency this increase depends on modulation factors for anomalous protons and can even alter the direction of the radial anisotropy.     

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.     

Galactic cosmic ray modulation for sunspot cycle 23

We present a study of the galactic cosmic ray modulation for sunspot cycle 23. We use the monthly and the annual mean hourly, pressure corrected, data from neutron monitors of the global network (monthly rate is calculated as the average of the hourly pressure corrected values). We draw attention to an asymmetry in the galactic cosmic ray (GCR) recovery during odd and even cycles for the monthly mean hourly rate data. For over half a century of observations, we find that the recovery for the odd cycles is to a higher level than for the even cycles. Qualitatively the effect is ascribed to charged particle drifts in inhomogeneous interplanetary magnetic field. Even so it has not been possible to arrive at a quantitative, self-consistent, explanation in terms of drifts at higher and lower GCR rigidities. We also study the rigidity dependence of the amplitude of 11-year modulation over a wide range (1–200 GV) of GCR spectrum; it is a power law in rigidity with an exponent −1.22. We discuss the implication of these findings on quasi-linear diffusion theories of modulation. We reflect on GCR recovery pattern for 2006–2009.     

Effects of solar modulation on the cosmic ray positron fraction

We implemented a 2D Monte Carlo model to simulate the solar modulation of galactic cosmic rays. The model is based on the Parker’s transport equation which contains diffusion, convection, particle drift and energy loss. Following the evolution in time of the solar activity, we are able to modulate a local interstellar spectrum (LIS), that we assumed isotropic beyond the termination shock, down to the Earth position inside the heliosphere. In this work we focused our attention to the cosmic ray positron fraction at energy below ∼10 GeV, showing how the particle drift processes could explain different results for AMS-01 and PAMELA. We compare our modulated spectra with observations at Earth, and then make a prediction of the cosmic ray positron fraction for the AMS-02 experiment.     

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.     

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.     

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.     

Prediction of expected global climate change by forecasting of galactic cosmic ray intensity time variation in near future based on solar magnetic field data

A method of prediction of expected part of global climate change caused by cosmic ray (CR) by forecasting of galactic cosmic ray intensity time variation in near future based on solar activity data prediction and determined parameters of convection-diffusion and drift mechanisms is presented. This gave possibility to make prediction of expected part of global climate change, caused by long-term cosmic ray intensity variation. In this paper, we use the model of cosmic ray modulation in the Heliosphere, which considers a relation between long-term cosmic ray variations with parameters of the solar magnetic field. The later now can be predicted with good accuracy. By using this prediction, the expected cosmic ray variations in the near Earth space also can be estimated with a good accuracy. It is shown that there are two possibilities: (1) to predict cosmic ray intensity for 1–6 months by using a delay of long-term cosmic ray variations relatively to effects of the solar activity and (2) to predict cosmic ray intensity for the next solar cycle. For the second case, the prediction of the global solar magnetic field characteristics is crucial. For both cases, reliable long-term cosmic ray and solar activity data as well as solar magnetic field are necessary. For solar magnetic field, we used results of two magnetographs (from Stanford and Kitt Peak Observatories). The obtained forecasting of long-term cosmic ray intensity variation we use for estimation of the part of global climate change caused by cosmic ray intensity changing (influenced on global cloudiness covering).     

Empirical model of cosmic ray spectrum in energy interval 1 MeV–100 GeV during 11-year solar cycle

The galactic cosmic rays (GCR) are the main ionization source at altitude of ∼3–35 km in the atmosphere. For high latitude anomalous cosmic ray (ACR) component has also a significant influence on the atmospheric ionization. We propose an empirical model for differential spectra D(E) of galactic and anomalous cosmic rays in energy interval 1 MeV–100 GeV during solar cycle. In the model data are used which cover three solar cycles: 20, 22 and 23. The LEAP87, IMAX92, CAPRICE94, AMS98 and BESS experimental spectra for protons and alpha particles are fitted to the proposed empirical model. The modulated GCR differential spectra are compared with force-field approximation to the one-dimensional transport equation and with solutions of two-dimensional cosmic ray transport equation. For experimental spectra, the calculation of the model parameters is performed by Levenberg–Marquardt algorithm, applied to the special case of least squares. Algorithm that combines the rapid local convergence of Newton–Raphson method with globally convergent method for non-linear systems of equations is applied for theoretically obtained differential spectra. The described programmes are realized in algorithmic language C++. The proposed model gives practical possibility for investigation of experimental data from measurements of galactic cosmic rays and their anomalous component.     

Rigidity spectrum of the 27-day variation of the galactic cosmic ray intensity in different epochs of solar activity

We study the temporal evolution of the power rigidity spectrum of the first (27 days) and the second (14 days) harmonics of the 27-day variation of the galactic cosmic ray intensity measured by neutron monitors in the period of 1965–2002. The rigidity spectrum of these variations can be approximated by a power law. We show the rigidity spectra of the first and the second harmonics of the 27-day variation of the galactic cosmic ray intensity have similar time profiles. These spectra are hard (γ ≈ 0.5 ± 0.1) and soft (γ ≈ 1.1 ± 0.2) during solar maximum and minimum activity, respectively. We ascribe this to the alternation of the sizes of the modulation regions responsible for the 27-day variation of the galactic cosmic ray intensity in different epochs of solar activity. Especially, the average radial sizes of the modulation regions of the 27-day variation and the heliolatitudinal extension of the heliolongitudinal asymmetry are smaller during solar minimum than during solar maximum. We show also, that the temporal changes of the power rigidity spectra of the first and the second harmonics of the 27-day variation of the galactic cosmic ray intensity are in a negative correlation with the changes of the rigidity spectrum of the corresponding 11-year variation.     

Where does the heliospheric modulation of galactic cosmic rays start?

The long outstanding question of where the heliospheric (solar) modulation of galactic cosmic rays actually begins, in terms of spatial position, as well as at what high kinetic energy, can now be answered. Both answers are possible by using the results of an advanced numerical model, together with appropriate observations. Voyager 1 has been exploring the outskirts of the heliosphere and is presently entering what can be called the very local interstellar medium. It has been generally expected, and accepted, that once the heliopause is crossed, the local interstellar spectrum (LIS) should be measured in situ by the Voyager spacecraft. However, we show that this may not be the case and that modulation effects on galactic cosmic rays can persist well beyond the heliopause. For example, proton observations at 100 MeV close to the heliopause can be lower by ∼$\sim$25% to 40% than the LIS, depending on solar modulation conditions. It is also illustrated quantitatively that significant solar modulation diminishes above ∼$\sim$50 GeV at Earth. It is found that cosmic ray observations above this energy contain less that 5%$5\%$ solar modulation effects and should therefore reflect the LIS for galactic cosmic rays. Input spectra, in other words the very LIS, for solar modulation models are now constrained by in situ observations and can therefore not any longer be treated arbitrarily. It is also possible for the first time to determine the lower limit of the very LIS from a few MeV/nuc to very high energies.     

Challenges to cosmic ray modeling: From beyond the solar wind termination shock

Voyager 1 crossed the solar wind termination shock on December 16, 2004 at a distance of 94 AU from the Sun, to become the first spacecraft to explore the termination shock region and to enter the heliosheath, the final heliospheric frontier. By the end of 2006, Voyager 1 will be at ∼101 AU, with Voyager 2 at ∼81 AU and still approaching the termination shock. Both spacecraft have been observing the modulation of galactic and anomalous cosmic rays since their launch in 1977. The recent observations close to or inside the heliosheath have provided several interesting ‘surprises’ with subsequent theoretical and modeling challenges. Examples are: what does the modulation of galactic cosmic rays amount to in this region?; how do the anomalous cosmic rays get accelerated and modulated?; why are there ‘breaks’ in the power-law slopes of the spectra of accelerated particles? Several numerical models have been applied to most of these topics over the years and comprehensive global predictions have been made the past decade, thought to be based on reasonable assumptions about the termination shock and the heliosheath. Examples of these predictions and assumptions are concisely discussed within the context of the main observed features of cosmic rays in the vicinity of the termination shock, ending with a discussion of some of the issues and challenges to cosmic ray modeling in particular.     

The dynamic heliosphere,solar activity,and cosmic rays

This brief review addresses the relation between solar activity, cosmic ray variations and the dynamics of the heliosphere. The global features of the heliosphere influence what happens inside its boundaries on a variety of time-scales. Galactic and anomalous cosmic rays are the messengers that convey vital information on global heliospheric changes in the manner that they respond to these changes. By observing cosmic rays over a large range of energies at Earth, and with various space detectors, a better understanding is gained about space weather and climate. The causes of the cosmic ray variability are reviewed, with emphasis on the 11-year and 22-year cycles, step modulation, charge-sign dependent modulation and particle drifts. Advances in this field are selectively discussed in the context of what still are some of the important uncertainties and outstanding issues.