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.     

Modelling of low-energy galactic electrons in the heliosheath

The modulation of cosmic ray electrons in the heliosphere plays an important role in improving our understanding and assessment of the processes applicable to low-energy galactic electrons. A full three-dimensional numerical model based on Parker’s transport equation is used to study the modulation of 10 MeV galactic electrons, in particular inside the heliosheath. The emphasis is placed on the role that perpendicular diffusion plays in causing the extraordinary large increase in the observed intensities of these electrons in the heliosheath. The modelling is compared with observations of 6–14 MeV electrons from the Voyager 1 mission. Results are shown for the radial intensity profiles of these electrons, as well as the modulation effects of varying the extent of the heliosheath by changing the location of the termination shock and the heliopause and the value of the local interstellar spectrum. We confirm that the heliosheath acts as a modulation ‘barrier’ for low-energy galactic electrons. The significance of this result depends on how wide the inner heliosheath is; on how high the very local interstellar spectrum is at these low energies (E < 100 MeV) and on how small perpendicular diffusion is inside the inner heliosheath.     

Modulation of cosmic rays: Perpendicular diffusion and drifts in a heliosphere with a solar wind termination shock

In this study the roles of polar perpendicular diffusion and drifts are illustrated in a model containing a heliosheath and diffusive shock acceleration as applied to the solar wind termination shock. Of particular interest is the relation of polar perpendicular diffusion to particle drifts and how the effectiveness of the termination shock acceleration of galactic and anomalous protons is influenced by this relation. We found that drifts have a more prominent effect than the polar enhancement of perpendicular diffusion so that its omission from termination shock models would produce unrealistically large shock acceleration and consequently also larger modulation effects throughout the heliosphere. The computed spectra at a heliolatitude of 35° are almost similar for the two polarity epochs indicating that the two Voyager spacecraft might not observe differences between the two cycles in future.     

The heliospheric modulation of cosmic rays: Effects of a latitude dependent solar wind termination shock

Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock and that it has begun its merger with the local interstellar medium. The compression ratio of this shock affects galactic cosmic rays when they enter the heliosphere. Hydrodynamic (HD) models show that the compression ratio can have a significant latitude dependence; with the largest value in the nose direction of the heliosphere, becoming significantly less towards the polar regions. The modulation effects of such large latitude dependence are studied, using a well-established numerical drift and shock modulation model. We focus on computing the modulated spectra for galactic protons with emphasis on the radial and polar gradients in the equatorial plane and at a polar angle of θ = 55°, corresponding to the heliolatitude of Voyager 1. Two sets of solutions are computed and compared each time; with and without a latitude dependence for the compression ratio. All computations are done for the two magnetic field polarity cycles assuming solar minimum conditions. Including the termination shock in the model allows the study of the re-acceleration of galactic protons in the outer heliosphere. We find that for the A < 0 polarity cycle the intensity between ∼200 MeV and ∼1 GeV in the vicinity of the shock in the heliospheric equatorial plane may exceed the local interstellar value specified at the heliopause. Unfortunately, at θ = 55°, the effect is reduced. This seems not possible during an A > 0 cycle because significant modulation is then predicted between the heliopause and the termination shock, depending on how strong global gradient and curvature drifts are in the heliosheath. The overall effect of the shock on galactic protons in the equatorial plane is to reduce the total modulation as a function of radial distance with respect to the interstellar spectrum. Making the compression ratio latitude dependent enhances these effects at energies E < 200 MeV in the equatorial plane. At larger heliolatitudes these effects are even more significant. The differences in the modulation between the two drift cycles are compelling when the compression ratio is made latitude dependent but at Earth this effect is insignificant. A general result is that the computed radial gradient changes for galactic protons at and close to the TS and that these changes are polarity dependent. In line with previous work, large polarity dependent effects are predicted for the inner heliosphere and also close to the shock’s position in the equatorial plane. In contrast, at θ = 55°, the largest polarity effect occurs in the middle heliosphere (50 AU), enhanced by the latitude dependence of the compression ratio. At this latitude, the amount of proton modulation between the heliopause and the termination shock is much reduced. If galactic cosmic rays were to experience some diffusive shock acceleration over the 100–1000 MeV range at the shock, the radial gradient should change its sign in the vicinity of the shock, how large, depends on the compression ratio and the amount of drifts taking place in the outer heliosphere. The effective polar gradient shows a strong polarity dependence at Earth but this dissipates at θ = 55°, especially with increasing radial distance. This tendency is enhanced by making the compression ratio latitude dependent.     

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.     

Effects of the position of the solar wind termination shock and the heliopause on the heliospheric modulation of cosmic rays

The effects of changing the position of the solar wind termination shock and the position of the heliopause, and therefore the extent of the heliosheath, on the modulation of cosmic ray protons are illustrated. An improved numerical model with diffusive termination shock acceleration, a heliosheath and drifts is used. The modulation is computed in the equatorial plane and at 35 heliolatitude using recently derived diffusion coefficients applicable to a number of cosmic ray species during both magnetic polarity cycles of the Sun. It was found that qualitatively the modulation results for the different heliopause positions are similar although they differ quantitatively, e.g., clearly different radial gradients are predicted for the regions beyond the termination shock compared to inside the shock. The difference between the modulation for the two solar polarity cycles are less significant at a heliolatitude of 35° than in the equatorial plane. We found that moving the termination shock from 90 to 100 AU, with the heliopause fixed at 120 AU, caused only quantitative differences so that the exact position of the TS in the outer heliosphere seems not crucially important to global modulation. Moving the heliopause outwards, to represent the modulation in the tail region of the heliosphere, causes overall decreases in the cosmic ray intensities but not linearly as a function of energy, e.g., at 1 GeV the effect is insignificant. We conclude from this modelling that the modulation of protons in the heliospheric nose and tail regions are qualitatively similar although, clear quantitative and interesting differences occur.     

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.     

Radial and latitudinal gradients of galactic cosmic rays in the heliosphere at solar maximum

Our understanding of galactic cosmic ray (GCR) modulation has advanced greatly in the last three decades. However, we still need an appropriate knowledge of the GCR intensity gradient. Numerical simulations of the transport particle equation allow interpretation of cosmic ray intensities in the heliosphere. We use the numerical solution of the GCR transport equation during solar maximum epoch to compute the radial and latitudinal gradients. Our analysis indicates that adiabatic energy loss plays an important role in the radial distribution of GCR in the inner heliosphere, while in the outer region the diffusion and convection are the relevant processes. The latitudinal gradient is small.     

MHD modeling of the outer heliosphere: Achievements and challenges

An overview is presented of magnetic-field-related effects in the solar wind (SW) interaction with the local interstellar medium (LISM) and the different theoretical approaches used in their investigation. We discuss the possibility that the interstellar magnetic field (ISMF) introduces north–south and east–west asymmetries of the heliosphere, which might explain observational data obtained by the Voyager 1 and Voyager 2 spacecraft. The SW–LISM interaction parameters that are responsible for the deflection of the interstellar neutral hydrogen flow from the direction of propagation of neutral helium in the inner heliosheath are outlined. The possibility of a strong ISMF, which increases the heliospheric asymmetry and the H–He flow deflection, is discussed. The effect of the combination of a slow-fast solar wind during solar minimum over the Sun’s 11-year activity cycle is illustrated. The consequences of a tilt between the Sun’s magnetic and rotational axes are analyzed. Band-like areas of an increased magnetic field distribution in the outer heliosheath are sought in order to discover regions of possible 2–3 kHz radio emission.     

Time-dependent cosmic ray modulation

Time-dependent cosmic ray modulation is calculated over multiple solar cycles using our well established two-dimensional time-dependent modulation model. Results are compared to Voyager 1, Ulysses and IMP cosmic ray observations to establish compatibility. A time-dependence in the diffusion and drift coefficients, implicitly contained in recent expressions derived by , ,  and , is incorporated into the cosmic ray modulation model. This results in calculations which are compatible with spacecraft observations on a global scale over consecutive solar cycles. This approach compares well to the successful compound approach of Ferreira and Potgieter (2004). For both these approaches the magnetic field magnitude, variance of the field and current sheet tilt angle values observed at Earth are transported time-dependently into the outer heliosphere. However, when results are compared to observations for extreme solar maximum, the computed step-like modulation is not as pronounced as observed. This indicates that some additional merging of these structures into more pronounced modulation barriers along the way is needed.     

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.     

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 role of radial perpendicular diffusion and latitude dependent acceleration along the solar wind termination shock

A numerical model, based on Parker’s transport equation, describing the modulation of anomalous cosmic rays and containing diffusive shock acceleration is applied. The role of radial perpendicular diffusion at the solar wind termination shock, and as the dominant diffusion coefficient in the outer heliosphere, is studied, in particular the role it plays in the effectiveness of the acceleration of anomalous protons and helium when its latitude dependence is changed. It is found that the latitudinal enhancement of radial perpendicular diffusion towards the heliospheric poles and along the termination shock has a prominent effect on the acceleration of these particles. It results in a ‘break’ in the energy spectrum for anomalous protons at ∼6.0 MeV, causing the spectral index to change from E^−1.38 to E^−2.23, but for anomalous helium at ∼3.0 MeV, changing the spectral index from E^−1.38 to E^−2.30. When approaching the simulated TS, the changes in the modulated spectra as they unfold to a ‘steady’ power law shape at energies below 50 MeV are much less prominent as a function of radial distances when radial perpendicular diffusion is increased with heliolatitude.     

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.     

Modeling the acceleration and modulation of anomalous cosmic ray oxygen

After the solar wind termination shock crossings of the Voyager spacecraft, the acceleration of anomalous cosmic rays has become a very contentious subject. In this paper we examine several topics pertinent to anomalous cosmic ray oxygen acceleration and transport using a numerical cosmic ray modulation model. These include the effects of drifts on a purely Fermi I accelerated spectra, the effects of introducing higher charge states of oxygen into the modulation model, examining the viability of momentum diffusion as a re-acceleration process in the heliosheath and examining energy spectra, and intensity gradients, in the inner heliosphere during consecutive drift cycles.     

27-day variations of the galactic cosmic ray intensity and anisotropy in the minimum of the 23rd solar activity cycle

We study the 27-day variations of the solar wind velocity, galactic cosmic ray (GCR) intensity and anisotropy in the last minimum epoch of solar activity (2007–2009, A < 0). The average amplitude of the 27-day variation of the galactic cosmic ray anisotropy (A27A) in the current minimum epoch of solar activity (2007–2009, A < 0) is lesser than in previous positive polarity period as it is expected from the drift theory. So, polarity dependence rule for the 27-day variation of the GCR anisotropy is fully kept. It is a universal principle for the amplitudes of the 27-day variation of the GCR anisotropy. At the same time, the average amplitude of the 27-day variation of the GCR intensity (A27I) remains at the same level as for previous minimum epoch 1995–1997 (A > 0) showing by the same token an violation of its polarity dependence rule established earlier. We assume that this phenomenon could be generally related with the well established 27-day variation of the solar wind velocity being in anti-correlation with the similar changes of the 27-day variation of the GCR intensity. Generally, a character of the heliolongitudinal asymmetry of spatial large-scale structure of the solar wind velocity (SWV) established in the recent minimum epoch, preferentially pronounces in the behavior of the 27-day variation of the GCR intensity than anisotropy. The formation of the 27-day variation of the GCR anisotropy preferentially takes place in a restricted disk like local vicinity in the helioequatorial region, whilst the 27-day variation of the GCR intensity is formed in the global three dimensional vicinity of the heliosphere.     

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.     

Solar wind structure in the outer heliosphere

A solar wind parcel evolves as it moves outward, interacting with the solar wind plasma ahead of and behind it and with the interstellar neutrals. This structure varies over a solar cycle as the latitudinal speed profile and current sheet tilt change. We model the evolution of the solar wind with distance, using inner heliosphere data to predict plasma parameters at Voyager. The shocks which pass Voyager 2 often have different structure than expected; changes in the plasma and/or magnetic field do not always occur simultaneously. We use the recent latitudinal alignment of Ulysses and Voyager 2 to determine the solar wind slowdown due to interstellar neutrals at 80 AU and estimate the interstellar neutral density. We use Voyager data to predict the termination shock motion and location as a function of time.