2 The Global Heliosphere and its Main Features

2.1 Physical boundaries

The heliosphere moves through the interstellar medium so that an interface is formed. In the process the solar wind undergoes transitions with the main constituents its termination shock (TS), the heliopause (HP), and a bow wave (BW), with the regions between the TS, the HP, and the BW defined as the inner and outer heliosheath, respectively. An important goal of the heliospheric exploration by the two Voyager spacecraft has always been to observe this TS and HP. The TS is predicted to be highly dynamic in its location and structure, both globally and locally, and is as such confirmed observationally by Voyager 1 to be at 94 AU in December 2004 and at 84 AU by Voyager 2 in August 2007 (Stone et al., 2005Jump To The Next Citation Point, 2008Jump To The Next Citation Point). Observing the TS in situ was a true milestone. According to Voyager 2 plasma observations, the low solar wind dynamic pressure beyond the TS lead to an inward movement of the TS of about 10 AU to an assumed minimum position of 73 AU in 2010 (Richardson and Wang, 2011Jump To The Next Citation Point). By the end of 2013, Voyager 1 will be at 126.4 AU while Voyager 2 will be at 103.6 AU, both moving into the nose region of the heliosphere but at a totally different heliolatitude, about 60° apart in terms of heliocentric polar angles, and with a significant azimuthal difference (see External Link

Webber and McDonald (2013Jump To The Next Citation Point) reported that Voyager 1 might have crossed the HP (or something that behaves like it) at the end of August 2012, a conclusion based on various CR observations. This is another major milestone for the Voyager mission. Since their launch in 1977, the two spacecraft have explored heliospace from Earth to the HP over almost four decades and will next explore a region probably very close to the pristine local interstellar medium. The passage of the Voyager 1 and 2 spacecraft through the inner heliosheath has revealed a region somewhat unlike than what was observed up-stream of the TS (towards the Sun). The question arises if the modulation of CRs in this region is actually different from the rest of the heliosphere?

Based on magnetohydrodynamic (MHD) modeling, it is generally accepted that the heliospheric structure is asymmetric in terms of a nose-tail (azimuthal) direction, yielding a ratio of ∼ 1:2 for the upwind-to-downwind TS distance from the Sun. This asymmetry is pronounced during solar minimum conditions because the TS propagates toward or away from the Sun with changing solar activity. The exact dependence is still unknown. Encounters with big transients in the HMF may also cause the TS position to change and even oscillate locally with interesting effects on CRs. The HP has always been considered as the heliospheric boundary from a CR modulation point of view because it supposedly separates the solar and interstellar media. Ideally, the solar wind should not propagate beyond this boundary. According to MHD models the HP is properly demarcated in the direction that the heliosphere is moving but not so in the tail direction. Some instabilities can be anticipated at the HP that may modify this picture (e.g., Zank et al., 2009). It is expected that these aspects will be studied with models in greater detail in future. The general features of the heliospheric geometry are shown in Figure 1View Image. For illustrations of these features obtained with magnetohydrodynamic (MHD) models, see, e.g., Opher et al. (2009a) and Pogorelov et al. (2009b).

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Figure 1: The basic features of the global heliospheric geometry according to the hydrodynamic (HD) models of Ferreira and Scherer (2004) in terms of the solar wind density (upper panel) and solar wind speed (lower panel). The heliosphere is moving through the interstellar medium to the right. Typical solar minimum conditions are assumed so that the solar wind speed has a strong latitudinal dependence.

The last decade witnessed the development of CR transport models based on improved HD and MHD models of the heliosphere that provide realistic geometries and detailed backgrounds (solar wind flow and corresponding magnetic field lines) to global transport models, called hybrid models. It is known that CRs exert pressure and, therefore, also modify the heliosphere (e.g., Fahr, 2004). These MHD models also predict an asymmetry in a north-south (meridional or polar) direction, making it most likely that the heliosheath is wider in the direction that Voyager 1 is moving than in the Voyager 2 direction. The local interstellar magnetic field causes the heliosphere to become tilted as featured already in earlier global simulations of the heliosphere (e.g., Ratkiewicz et al., 1998; Linde et al., 1998). Although this asymmetry seems somewhat controversial from a MHD point of view, energetic neutral particle (ENAs) observations from the IBEX mission sustain this view of the heliosphere (McComas et al., 2012b). This mission also established that the boundary where the heliosphere begins to disturb the interstellar medium, because it is moving with respect to this medium, should not be seen as a bow shock but rather as a bow wave (McComas et al., 2012a). The relative motion of the Sun with respect to the interstellar medium seems slower and also in a slightly different direction than previously thought. See also Zank et al. (2013). A schematic presentation of this new view of the geometrical shape of the heliosphere is shown in Figure 2View Image. Models of the heliosphere based on HD and MHD approaches have become very sophisticated over the past decade and many of the predicted features still have to be incorporated in the hybrid modeling approach. Whether these detailed features are contributing more than higher order effects to the global solar modulation of CRs is to be determined. For reviews on MHD modeling, see, e.g., Opher et al. (2009b) and Pogorelov et al. (2009a).

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Figure 2: A schematic view of an asymmetric heliosphere together with the directions of the interstellar magnetic field lines. The measured ENA flux at ∼ 1.1 keV is superposed on the heliopause with the bright ENA ribbon appears to correlate with where the field is most strongly curved around it. (From the Interstellar Boundary Explorer, IBEX spacecraft’s first all-sky maps of the interstellar interaction at the edge of the heliosphere.) See McComas et al. (2009) for details. Image credit: Adler Planetarium/Southwest Research Institute.

It is to be determined if the outer heliosheath, the region beyond the HP, has any effect on CRs when they enter this region from the interstellar medium. Scherer et al. (2011) presented arguments that this may be the case followed by Strauss et al. (2013bJump To The Next Citation Point) who presented numerical modeling that produces at 100 MeV a small radial intensity gradient between 0.2% to 0.4% per AU, depending on solar activity, and if the BW is assumed at 250 AU. It may also be that CRs do not enter the heliosphere completely isotropic as always been assumed (e.g., Ngobeni and Potgieter, 2011Jump To The Next Citation Point, 2012).

For informative reviews on several advanced aspects of the outer heliosphere see Jokipii (2012) and Florinski et al. (2011) and for a review on the solar cycle from a solar physics point of view, see Hathaway (2010).

The point to be made here is that the global features of the heliosphere, and in particular the variability and dynamics of the heliospheric boundary lagers, do influence the modulation and the longer-term variations of CRs, even at Earth. How important this all is, will unfold in the coming years.

2.2 Solar wind and heliospheric magnetic field

2.2.1 Global magnetic field geometry

Parker (2001) reviewed how the expansion of the solar corona provides the solar wind with an embedded solar magnetic field that develops into the HMF. He had predicted a well-defined spiral structure for the HMF (Parker, 1958). Over the years modifications to this field have been proposed but the realization of Fisk (1996Jump To The Next Citation Point) that the differential rotation of the Sun and the rigid rotation of polar coronal holes has a significant effect on the structure of the HMF, led to second generation global HMF models that are much more complex and controversial and as such not yet fully appreciated of what it may imply for CR modulation (e.g., Sternal et al., 2011Jump To The Next Citation Point, and references therein). These specific features will have to be studied with MHD modeling to resolve the dispute. The Parker-type field and moderate modification thereof (e.g., Smith and Bieber, 1991Jump To The Next Citation Point) are still widely used in CR modeling. See also the review by Heber and Potgieter (2006Jump To The Next Citation Point).

A straightforward equation for the spiral HMF is

( r )2 B = Bo -0 (er − tan ψeϕ ), (1 ) r
with unit vector components er and eϕ in the radial and azimuthal direction respectively; r0 = 1 AU for dimensional purposes and ψ is the (spiral) angle between the radial and the average HMF direction at a certain position. It is given by
Ω(r − r⊙ )sin 𝜃 tan ψ = --------------, (2 ) V
and indicates how tightly wound the HMF is, with Ω the angular speed of the Sun, and with r⊙ = 0.005 AU the radius of the solar surface. A typical value at Earth is ψ ≈ 45∘, increasing to ∼ 90∘ with increasing radial distance r beyond 10 AU in the equatorial plane. The solar wind speed is V and 𝜃 is the polar angle so that the magnitude of the HMF is
( r0)2 ∘ ------------ B = Bo -- 1 + (tanψ )2, (3 ) r
with an average value of 5 nT at Earth or as determined by Bo.

The main attribute of the HMF is that it follows a 22-year cycle with a reversal about every ∼ 11 years at the time of extreme solar activity (e.g., Petrovay and Christensen, 2010). It exhibits many distinct shorter scale features (e.g., Balogh and Jokipii, 2009), also associated with the TS and the heliosheath region (Burlaga et al., 2005; Burlaga and Ness, 2011). One of the largest of these magnetic structures was encountered by Voyager 1 in 2009.7 when it already was ∼ 17 AU beyond the TS when the shock had been observed at 94 AU. At this time the field direction suddenly changed indicating a sector crossing. This means that these features, which are well-known in the inner heliosphere, are also occurring in some evolved form in the inner heliosheath. For a review, see Richardson and Burlaga (2011Jump To The Next Citation Point). In this context, it is expected that more interesting and surprising observations and subsequent modeling will follow from the Voyager mission.

A major corotating structure of the HMF of important to CR modulation is the heliospheric current sheet (HCS), which divides the solar magnetic field into hemispheres of opposite polarity. The ∼ 11-year period when it is directed outwards in the northern hemisphere has become known as A > 0 epochs, such as during the 1970s and 1990s, while the 1980s and the period 2002 – 2014 are known as A < 0 cycles. The HCS has a wavy structure, parameterized by using its tilt angle α (Hoeksema, 1992Jump To The Next Citation Point) and is well correlated to solar activity. During high levels of activity α = 75°, but then becomes undetermined during times of extreme solar activity, while during minimum activity α = 3° – 10°. The waviness of the HCS plays an important role in CR modulation (Smith, 2001). It is still the best proxy for solar activity from this point of view. It is widely used in numerical modeling and some aspects are discussed below. A disadvantage is that it is not known how the waviness is preserved as it moves into the outer heliosphere, and especially what happens to it in the heliosheath. The waviness becomes compressed in the inner heliosheath as the outward flow decreases across the TS. It should also spread in latitudinal and azimuthal directions in the nose of the heliosphere. A schematic presentation of how the waviness of the HCS could differ from the nose to the tail regions of the heliosphere is shown in Figure 3View Image. The dynamics of the HCS in the inner heliosheath was investigated by Borovikov et al. (2011Jump To The Next Citation Point) amongst others.

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Figure 3: A schematic presentation of how the waviness of the HCS could differ ideally from the nose to the tail regions of the heliosphere. The waviness depicted here corresponds to moderate solar activity. For an elaborate illustration of the dynamics of the HCS obtained with MHD models, see, e.g., Borovikov et al. (2011Jump To The Next Citation Point). Image reproduced by permission from Kóta (2012Jump To The Next Citation Point), copyright by Springer.

Drake et al. (2010Jump To The Next Citation Point) suggested the compacted HCS could lead to magnetic reconnection, otherwise, it could become so densely wrapped that the distance between the wavy layers becomes less than the gyro-radius of the CRs, which may lead to different transport-effects. The behaviour of the HCS in the nose and tail directions of the heliosheath, and its role in transporting CRs, is a study in progress (e.g., Florinski, 2011). It appears that the heliosheath may even require additional transport physics to be included in the next generation of transport models. What happens to the HMF closer to the HP, in the sense of is it still embedded in the solar wind as the HP is approached, is another study in progress.

2.2.2 Global solar wind features

A well reported feature of the global solar wind velocity is that it can be considered basically as radially directed from close to the Sun, across the TS and deep into the inner heliosheath. However, during periods of minimum solar activity this radial flow becomes distinctively latitude dependent, changing easily from an average of 450 km s–1 in the equatorial plane to 800 km s–1 in the polar regions as observed by the Ulysses mission (see the reviews by Heber and Potgieter, 2006Jump To The Next Citation Point, 2008Jump To The Next Citation Point, and reference therein). This aspect is also illustrated in the bottom panel of Figure 1View Image. This significant effect disappears with increasing solar activity. These features are incorporated in most CR modulation models.

The solar wind gradually evolves as it moves outward from the Sun. Its speed is, on average, constant out to ∼ 30 AU, then starts a slow decrease caused by the pickup of interstellar neutrals, which reduces its by ∼ 20% before the TS is reached. These pickup ions heat the thermal plasma so that the solar wind temperature increases outside ∼ 25 AU. The solar wind pressure changes by a factor of 2 over a solar cycle and the structure of the solar wind is modified by interplanetary coronal mass ejections (ICMEs) near solar maximum. The first direct evidence of the TS was the observation of streaming energetic particles by both Voyager 1 and 2 beginning ∼ 2 years before their respective TS crossings. The second evidence was a decrease in the solar wind speed commencing 80 days before Voyager 2 crossed the TS. The TS seems to be a weak, quasi-perpendicular shock, which transferred the solar wind flow energy mainly to the pickup ions (Richardson and Stone, 2009Jump To The Next Citation Point).

Across the TS, the radial solar wind speed slowed down from an average of ∼ 400 km s–1 to ∼ 130 km s–1. It then had decreased essentially to zero as Voyager 1 approached the HP but based on non-plasma observations (Krimigis et al., 2011). This appears to happen differently at Voyager 2 and will certainly be different in the tail direction of the heliosphere. Voyager 2, with a working plasma detector, has observed heliosheath plasma since August 2007, which indicates how it has evolved across the inner heliosheath. The radial speed slowly decreased as the plasma flow slowly turned tailward but remained above 100 km s–1, which implies that Voyager 2 was still a substantial distance from the HP in 2012 and that its approach towards the HP is also developing differently from a solar wind point of view (Richardson et al., 2008Jump To The Next Citation Point; Richardson and Wang, 2011). The inner heliosheath is clearly a highly variable region.

The magnitude of the radial component of the solar wind velocity in terms of polar angle and radial distance in AU, as is typically used in numerical models, up to just beyond the TS, is given by

[ ( ( ) )] V (r,𝜃) = V 1 − exp 13.33 r⊙ −-r- 0 r0 [ ( ( π )) ] 1.475 ∓ 0.4tanh 6.8 𝜃 − --± 𝜃 [( ) ( ) ( 2 )] s +-1 − s-−-1 tanh r-−-rTS- , (4 ) 2s 2s L
where V 0 = 400 km s–1, s = 2.5 and L = 1.2 AU. The TS is positioned at rTS, L is the TS scale length, and s is the compression ratio of the TS, which changes position over a solar cycle. The top and bottom signs respectively correspond to the northern (0 ≤ 𝜃 ≤ π ∕2) and southern hemisphere (π∕2 ≤ 𝜃 ≤ π) of the heliosphere, with 𝜃T = α + 15π∕180. This determines at which polar angle the solar wind speed changes from a slow to a fast region during solar minimum activity conditions. This equation is only for such conditions and must also be modified if the solar wind velocity obtains a strong latitudinal and azimuthal component when approaching the HP.

For reviews on observations and interpretations of the solar wind in the outer heliosphere, see Richardson and Stone (2009) and Richardson and Burlaga (2011).

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