The anomalous component of cosmic rays (ACRs) was discovered in the early 1970s (Hovestadt et al., 1973; Garcia-Munoz et al., 1973). This component, with kinetic energy between 10 to 100 MeV/nuc, does not display the same spectral behaviour as galactic CRs but increases significantly with decreasing energy. Galactic CRs have harder spectra than ACRs. Their composition consists of hydrogen, helium, nitrogen, oxygen, neon, and argon and is primarily singly ionized (Cummings and Stone, 2007). They originate as interstellar neutrals that become ionized when flowing towards the Sun and then, as so-called pick-up ions, become accelerated in the solar wind (Fisk et al., 1974; Fisk, 1999). Pesses et al. (1981) suggested that ACRs were to be accelerated at the TS. Strictly speaking they are not CRs because they have a heliospheric origin, with the spectrum of ACRs determined by heliospheric processes. To become ACRs, these pick-up ions must be accelerated by four orders of magnitude. They are subjected to solar modulation and depict mostly, but not always, the same modulation features than CRs upstream of the TS (e.g., McDonald et al., 2000, 2003, 2010). Only the ACRs with the highest rigidity (oxygen) can reach Earth (e.g., Leske et al., 2011; Strauss and Potgieter, 2010). See the introductory review on this topic by Fichtner (2001) and reviews of recent developments by Giacalone et al. (2012) and Mewaldt (2012).
The principal acceleration mechanism was considered to be diffusive shock acceleration, a topic of considerable debate since Voyager 1 crossed the TS (Fisk, 2005). At the location of the TS there was no direct evidence of the effective local acceleration of ACR protons but particles with lower energies were effectively accelerated and have since become known as termination shock particles (TSP). The higher energy ACRs thus seem disappointingly unaffected by the TS but have increased gradually in intensity away from the TS (Stone et al., 2005, 2008; Decker et al., 2005). They clearly gain energy as they move inside the inner heliosheath and seem to be trapped largely in this region. It is expected that their intensity will drop sharply over the HP but some should escape out of the inner heliosheath (e.g., Scherer et al., 2008a). Several very sophisticated mechanisms have been proposed how these particles may gain their energy beyond the TS and has become one of the most severely debated issues in this field of research (e.g., Gloeckler et al., 2009; Zhang and Lee, 2011; Zhang and Schlickeiser, 2012).
Typical observed proton, helium and oxygen spectra for TSP, ACRs and galactic CRs are shown in Figure 4 for early in 2005 when Voyager 1 already had crossed the TS (2004.96) when at 94.01 AU. Computed ACR spectra at the TS are shown for comparison. Figure 5 displays how the observed TSPs, ACRs, and galactic CRs for helium evolved and unfolded at Voyager 1 and Voyager 2 from late in 2004 to early in 2008.
Adding to the controversy, comparing computational results with spacecraft observations, it was found by Strauss et al. (2010a) that the inclusion of multiply charged ACRs (Mewaldt et al., 1996a,b; Jokipii, 1996) in a modulation model could explain the observed strange spectrum of anomalous oxygen in the energy range from 10 – 70 MeV per nucleon (Webber et al., 2007). The more effective acceleration of these multiply charged anomalous particles at the TS causes a significant deviation from the usual exponential cut-off spectrum to display instead of a power law decrease up to 70 MeV per nucleon where galactic oxygen starts to dominate. This can only happen if some acceleration takes place at the TS. In addition, the model reproduces the features of multiply charged oxygen at Earth so that a good comparison is obtained between computations and observations. An extensive study on the intensity gradients of anomalous oxygen was done by Cummings et al. (2009) and Strauss and Potgieter (2010). For a comprehensive review on ACR measurements at Earth and interesting conclusions, see Leske et al. (2011).
Undoubtedly, the controversy indicates that we do not yet understand what is really happening to the ACRs in the inner heliosheath and only future observations with inquisitive modeling may enlighten us. On the other hand, the TSPs are accelerated at the TS. Surely, TSPs and ACRs are fascinating topics, from how they originate to their acceleration and modulation inside the heliosheath, and for the highest rigidity ACRs also up to Earth. For additional reviews of how these aspects have developed over time, see Heber and Potgieter (2008), Potgieter (2008), and Florinski (2009).
Cosmic rays are defined for the purpose of this overview as fully ionized nuclei as well as anti-protons, electrons, and positrons that are not produced on the Sun or somewhere in the heliosphere. As a rule they have kinetic energy .
A crucially important aspect of the modulation modeling of galactic CRs in the heliosphere is that the local interstellar spectra (LIS) need to be specified as input spectra at an assumed modulation boundary and then be modulated throughout the heliosphere as a function of position, energy, and time. A primary objective of the Voyager mission is to measure these LIS once the spacecraft enter the interstellar medium. Because of solar modulation and the fact that the nature of the heliospheric diffusion coefficients is not yet fully established, all cosmic ray LIS at kinetic energies remain contentious. This is true from an astrophysical and heliospheric point of view.
Galactic spectra (GS), from a solar modulation point of view, are referred to as spectra that are produced from astrophysical sources, usually assumed to be evenly distributed through the Galaxy, typically very far from the heliosphere. Computed GS usually do not contain the contributions of any specific (local) sources within parsecs from the heliosphere so that an interstellar spectrum may be different from an average GS, which may again be different from a LIS (thousands of AU away) from the Sun, which might be different from a very LIS or what may be called a heliopause spectrum, right at the edge of the heliosphere, say 200 AU away from the Sun. Proper understanding of the extent of modulation cycles of galactic CRs in the heliosphere up to energies of 30 GeV requires knowledge of these GS and LIS for the various species. More elaborate approaches to the distribution of sources have also been followed (e.g., Büsching and Potgieter, 2008), even considering contributions of sources or regions relatively closer to the heliosphere (e.g., Büsching et al., 2008) with newer developments (e.g., Blasi et al., 2012). These spectra are calculated using various approaches based on different assumptions but mostly using numerical models, e.g., the well-known GALPROP propagation model (Moskalenko et al., 2002; Strong et al., 2007). For energies below 10 GeV, which is of great interest to solar modulation studies, the galactic propagation processes are acknowledged as less precise as illustrated comprehensively by Ptuskin et al. (2006) and Webber and Higbie (2008, 2009).
The situation for galactic electrons at low energies has always been considered somewhat better because electrons radiate synchrotron radiation so that radio data assist in estimating the electron GS at these low energies. For a discussion of this approach and some examples of consequent electron spectra, see Langner et al. (2001), Webber and Higbie (2008), Strong et al. (2011), Potgieter and Nndanganeni (2013b), and references therein.
Potgieter and Ferreira (2002) and Potgieter and Langner (2004a) showed that the heliospheric TS could in principle re-accelerate low-energy galactic electrons to energies as high as 1 GeV so that a heliopause spectrum could be different from a TS spectrum. Such a spectrum may even be higher than a LIS, depending on the energies considered. However, because the TS was observed as rather weak (Richardson et al., 2008), obtaining such high energies now seems improbable. In fact, only a factor of 2 increase was observed close to the TS for 6 – 14 MeV electrons but since then Voyager 1 has observed an increase of a factor of 60 on its way to the HP (Webber et al., 2012; Nkosi et al., 2011). It seems that the influence of the heliospheric TS on all LIS, in terms of the re-acceleration of these CRs, may generally thus be neglected.
The formation of a magnetic wall (barrier) at the HP, if significant, may cause a drop in low energy CRs, surely in the flux of TSPs and the ACRs while high energy CRs are not expected to change much. If low energy particles are partially trapped inside the inner heliosheath, the LIS of low energy CRs will not be known until well beyond the HP.
For a compilation of computed galactic spectra based on the GALPROP code for CR protons, anti-protons, electrons, positrons, helium, boron and carbon and many more, see Moskalenko et al. (2002). Peculiarly, the solar modulation of many of these species and their isotopes has not been properly modeled, probably because of uncertainties in their LIS.
The dominant and the most important time scale in CRs related to solar activity is the 11-year cycle. This quasi-periodicity is convincingly reflected in the records of sunspots since the early 1600s and also in the galactic CR intensity observed at ground and sea level since the 1950s. This was the period when neutron monitors (NMs) were widely deployed as Earth bound CR detectors, especially during the International Geophysical Year (IGY). The year 2007 was celebrated as the 50th anniversary if the IGY and was called the International Heliophysical Year (IHY). These NMs have been remarkably reliable with good statistics over five full 11-year cycles.
The discovery of another important cycle, the 22-year cycle, was a milestone in the exploration and modeling of CRs in the heliosphere. It is directly related to the reversal of the HMF during each period of extreme solar activity. The causes of these cycles will be discussed in more detail in later sections. Figure 6 displays the 11-year and 22-year cycles in galactic CRs as observed by the Hermanus NM in South Africa at a cut-off rigidity of 4.6 GV and a mean response energy of 18 GeV.
Additional short periodicities are evident in NM and other CR data, e.g., the 25 – 27-day variation owing to the rotational Sun, and the daily variation owing to the Earth’s rotation (e.g., Alania et al., 2011, and references therein). These variations seldom have magnitudes of more than 1% with respect to the previous quite time fluxes. Corotating interaction regions (CIRs), caused when a fast solar wind region catches up with a lower region, usually merge as they propagate outwards to form various types of larger interaction regions. The largest ones are known as global merged interaction regions (GMIRs), discussed in some detail later. They are related to coronal mass ejections (CMEs) that are prominent with increased solar activity but dissipating during solar minimum. Although CIRs may be spread over a large region in azimuthal angle, they do not cause long-term CR periodicities on the scale (amplitude) of the 11-year cycle. An isolated GMIR may cause a decrease similar in magnitude than the 11-year cycle but it usually lasts only several months (as happened in 1991). A series of GMIRs, on the other hand, may contribute significantly to long-term CR modulation during periods of increased solar activity, in the form of large discrete steps, increasing the overall amplitude of the 11-year cycle (e.g., Potgieter and le Roux, 1992; Le Roux and Potgieter, 1995).
The galactic CR flux is not expected to be constant along the trajectory of the solar system in the galaxy. Interstellar conditions should differ significantly over very long time-scales, for example, when the Sun moves in and out of the galactic spiral arms (Büsching and Potgieter, 2008). It is accepted that the concentration of Be10 nuclei in polar ice exhibits temporal variations on a very long time scale in response to changes in the flux of the primary CRs. Exploring CR modulation over time scales of hundreds of years and longer and during times when the heliosphere was significantly different from the present epoch is a very interesting topic and a work in progress. See the reviews by, e.g., Scherer et al. (2006), McCracken and Beer (2007), and Usoskin (2013).
There are indications of CR periods of 50 – 65 years and 90 – 130 years, also for a periodicity of about 220 and 600 years. Quasibiennial oscillations have also been detected as a prominent scale of variability in CR data (Laurenza et al., 2012). It is not yet clear whether these variabilities should be considered ‘perturbations’, stochastic in nature or truly time-structured to be figured as superposition of several periodic processes. Cases of strong ‘perturbations’ of the consecutive 11-year cycles are the ‘grand minima’ in solar activity, with the prime example the Maunder minimum (1640 – 1710) when sunspots almost completely disappeared. Assuming the HMF to have vanished as well or without any reversals during the Maunder minimum would be an oversimplification. The heliospheric modulation of CRs could have continued during this period but much less pronounced (with a small amplitude). It is reasonable to infer that less CMEs occurred so that the total flux of CRs at Earth then should have been higher than afterwards. In this context, see the reviews by, e.g., Beer et al. (2011) and McCracken et al. (2011).
An interesting reoccurring phenomenon, called the Gnevyshev Gap has been observed in all solar-terrestrial parameters and consists of a relatively short period of decreased solar activity during the extreme maximum phase of each 11-year cycle, yielding structured maxima with a first peak at the end of the increasing activity phase and a second one at the start of the declining phase. For a review, see Storini et al. (2003).