The solar corona is a low beta, high conductivity plasma. Thus, coronal dynamics are dominated by the evolution of the coronal magnetic field, which in turn is driven by plasma motions in the photosphere. The coronal plasma is heated to around 1 – 2 million Kelvin, by processes which are still under debate (e.g., Cranmer, 2008; McComas et al., 2007), though it must involve the coronal magnetic field as it is the only source of sufficient energy density. The high coronal temperature leads to the formation of the solar wind, which becomes super-Alfvénic within 10 – 20 solar radii. The solar wind drags the coronal magnetic field out into the heliosphere, forming the HMF. Thus, the large scale structure and dynamics of the HMF is governed by the solar wind flow, which in turn has its origin in the magnetic structure of the corona. The simplest steady-state picture is observed under solar minimum conditions when the coronal magnetic field is closest to dipolar, typically with the magnetic dipole axis tilted by a few degrees to the solar rotation axis. The corona is observed to be organised into a belt of dense bright streamers around the magnetic equator with darker polar coronal holes in the high latitude regions. At this time fast solar wind (typical speeds 750 km s–1) fills most of the heliosphere, flowing outwards from the Sun from the regions of open magnetic field lines originating in the polar coronal holes. However, a belt of slower solar wind (typical speeds 300 – 400 km s–1) of about 20° latitudinal width originates from the streamer belt region corresponding to the magnetic equator. The magnetic field boundary separating oppositely directed magnetic field lines originating from the northern and southern polar coronal holes is carried out by this slower solar wind to form the heliospheric current sheet (HCS), a large scale magnetic boundary which extends throughout the heliosphere. The heliospheric magnetic field structure which arises under these conditions is described in more detail in Sections 2.3 and 2.4 and the evolution into a more complex field structure under solar maximum conditions in Section 5.2.
Remote observations of the photospheric magnetic field have the potential to give us a valuable synoptic picture of the coronal magnetic field which is vital in understanding the global structure of the HMF. The line-of-sight component of the photopsheric magnetic field can be routinely imaged using ground- and space-based magnetographs (e.g., Hoeksema and Scherrer, 1986). Most of this photospheric flux is “closed” solar flux, meaning it forms chromospheric or coronal loops below the height at which gas pressure exceeds magnetic pressure and, thus, does not contribute to the heliospheric magnetic field carried by the solar wind (e.g., Wang and Sheeley Jr, 2003). A fraction of these loops ( 10 to 50%, e.g., Arge et al., 2002) do extend high enough to be dragged out by the solar wind, as detailed below. This flux is often termed “open,” as it extends out to form the HMF (note that flux open to the corona may still form closed loops within the heliosphere. See Section 3.1). From photospheric observations alone, it is not possible to discern between open and closed solar magnetic flux and, thus, estimate the magnitude and configuration of the HMF. The observed photospheric magnetic field can, however, be used as a boundary condition to coronal models. Extrapolation of the photospheric magnetic field requires a complete map of the photospheric field. As all past and present magnetograph instruments are either ground based or in near-Earth space, this means the solar rotation poles are poorly viewed and accruing complete longitudinal coverage requires a full synodic solar rotation, 27.27 days. Thus, photospheric extrapolation is best suited to reconstruction of the steady-state corona and HMF and, consequently, is generally more applicable to solar minimum conditions than the rapidly evolving structures at solar maximum.
The Potential-Field Source-Surface model (PFSS, Schatten et al., 1969; Altschuler and Newkirk Jr, 1969) is the most widely used photospheric extrapolation technique, owing to its simplicity and low computational overhead. It assumes zero current density in the corona, meaning PFSS solutions approximate the minimum energy state of the corona for a given photospheric boundary condition. The inner boundary is the observed photospheric magnetic field, while the outer boundary is the “source surface” where the field is assumed to be radial, typically placed around in order to best match spacecraft observations (e.g., Hoeksema et al., 1982; Lee et al., 2011). Open solar flux, and hence the HMF, is then defined as any magnetic loop threading the source surface. While the PFSS model has proven invaluable for understanding the solar cycle evolution of the HMF (e.g., see Section 5.4), it should be noted that it does not provide perfect agreement with in situ spacecraft observations of HMF intensity or sector structure, and many features are ad hoc, rather than based on first principles. On the basis of the Ulysses observation of a latitudinal invariance in the strength of the radial HMF (see Section 2.3), a thin current sheet model Schatten (1971) is sometimes added to the PFSS model in order to create a more uniform radial field strength at the source surface (e.g., Wang and Sheeley Jr, 1995).
Photospheric magnetograms can also be used to constrain 3-dimensional magnetohydrodynamic (MHD) models of the corona, such as Magnetohydrodynamics Around a Sphere (MAS) (Linker et al., 1999; Mikić et al., 1999, see also http://www.imhd.net) and the Space Weather Modeling Framework (SWMF) (Tóth et al., 2005). Initial conditions are typically derived using the PFSS model and the time-dependent MHD equations then solved to allow the solution to relax to steady state. In general, this produces qualitatively similar results for the heliospheric magnetic field configuration and magnitude to PFSS solutions (Riley et al., 2006a). In principle, the MHD approach allows for a time-dependent inner boundary condition, though at present this involves an ad-hoc manipulation of the photospheric magnetic field and has only been possible for specific event studies (e.g., Linker et al., 2003).
Both PFSS and MHD extrapolations find that open solar flux, the foot points of heliospheric field lines, usually map to dark regions in soft X-ray and EUV images known as coronal holes (e.g., Levine et al., 1977; Wang et al., 1996), which are predominantly confined to the poles at solar minimum (see also Cranmer, 2009). Regions determined to have closed solar magnetic fields are closely associated with the observed locations of coronal bright regions such as helmet streamers, which are confined to the equatorial regions near solar minimum. (Note that alternative interpretations of the source of open solar flux do exist, e.g., Woo (2005).) This pattern was somewhat disrupted during the most recent solar minimum between solar cycles 23 and 24, due to the decreased strength of the polar fields allowing weak equatorial field regions to generate low-latitude coronal holes (Luhmann et al., 2009; Abramenko et al., 2010).
The underlying geometry of the HMF can be understood by considering a completely steady state idealised solar wind with an exactly radial outflow of constant speed, independent of radial and latitudinal position. The footpoints of the magnetic field lines are assumed to be fixed in the photosphere and, hence, to rotate with the Sun. The magnetic field is assumed to be frozen in to solar wind plasma, but to exert no force on it. Under such conditions, the heliospheric magnetic field becomes twisted into an Archimedean spiral in the solar equatorial plane, as predicted by Parker (1958), and shown schematically in Figure 1.
In a constant solar wind flow, magnetic flux conservation requires the radial component of the HMF, , to fall off as the inverse square of the heliocentric distance, . Thus, in a spherical polar coordinate system defined by distance , colatitude and longitude , we can write1) and (2) it can be shown that the azimuthal component of the magnetic field then exhibits a behaviour with distance:
For completeness, the assumption of an exactly radial solar wind flow gives:
These equations show that at colatitude , field lines can be viewed as wrapped around the surface of a cone of half angle or, alternatively, that the field lines gradually become less tightly wound with latitude until a field line originating from the Sun’s rotational pole should be purely radial. In the inertial frame the velocity streamline is radial but the field line remains the same.
Taking a solar wind speed of 400 km s–1, typical of 1 AU near the ecliptic, the angle that the heliospheric magnetic field line makes with the radial direction is approximately 45° in the vicinity of the Earth. Early spacecraft observations of the HMF confirmed that the field lines lay approximately in the solar equatorial plane (Coleman Jr et al., 1962) and that the predicted spiral direction was obtained on average (Ness and Wilcox, 1964; Davis Jr et al., 1966). Figure 2 shows magnetic field angle to the radial direction as a function of solar wind speed (after, e.g., Borovsky, 2010). Solid lines show the probability distribution functions calculated from the OMNI dataset, covering 1965 – 2012. The HMF unwinds at higher speeds, as expected. The vertical dashed lines show the equivalent ideal Parker spiral values, in agreement with the observations. This figure also illustrates the large variability in the HMF direction on the hourly averaged time scale plotted, an important and persistent feature of the HMF over a wide range of time scales.
The discovery from early observations (e.g., Wilcox and Ness, 1965) that the in-ecliptic HMF is divided into just a few magnetic field polarity sectors in each solar rotation indicates that the HMF structure in the heliosphere is much simpler than the complexes of activity seen in the photosphere and corona, as indicated schematically in Figure 1. This phenomenon was interpreted (Schulz, 1973) as the dominant dipole and weaker higher order components of the solar field being carried out into the heliosphere by the solar wind, the two polarities of the dipole being separated by the warped heliospheric current sheet (HCS), shown as the green dashed line in Figure 1. The polarity pattern in the heliosphere is discussed in more detail in Section 2.4.
The in-ecliptic HMF, in particular around 1 AU, is well sampled, and the Parker model has been shown to well describe the HMF to a good approximation over a wide range of heliocentric distances: from Helios observations in the inner heliosphere (e.g., Bruno and Bavassano, 1997), Pioneer and Voyager observations out to about 8 AU (Thomas and Smith, 1980; Burlaga et al., 1982), and in the more distant outer heliosphere (Burlaga and Ness, 1993). On the other hand, observations of the high latitude HMF are limited to measurements made by the Ulysses spacecraft (Wenzel et al., 1992), which made three polar orbits of the Sun between launch in 1990 and the end of mission in 2009. At all latitudes, the angle of the HMF to the radial direction was found to closely follow that predicted by Parker, with a general unwinding of the spiral at higher latitudes (Forsyth et al., 2002). Similarly, the HMF, on average, lies on a cone of constant latitude, resulting in no net component. Figure 3 illustrates ideal Parker spiral magnetic fields at latitudes of 0, 30 and 60 degrees (shown as black, blue, and red lines, respectively). However, see Section 4.1 for discussion of deviations from the ideal Parker spiral model.
At both solar minimum and solar maximum polar passes, Ulysses observations showed to be invariant with latitude (Smith and Balogh, 1995, 2003), contrary to the expectations of PFSS model fields, which approximate a dipolar field at solar minimum. This suggests that close to the Sun (i.e., well within ), the coronal magnetic field undergoes significant non-radial expansion so as to equilibrate tangential magnetic pressure, and hence , on the solar wind source surface (Suess and Smith, 1996). Consequently, the degree of non-radial expansion undergone by coronal flux tubes can vary considerably depending on the location of the photospheric foot point within a coronal hole. Using a PFSS model of the corona, Wang and Sheeley Jr (1990) found an anticorrelation between flux-tube expansion and resulting solar wind speed, discussed further in Section 2.4. The “Ulysses result” of invariance with latitude also means that a measurement of at any point in the heliosphere is, in principle, sufficient to estimate the total magnetic flux threading a heliocentric sphere at the point of observation, which is directly related to the magnetic flux threading the solar wind source surface, usually referred to as the total unsigned open solar flux (OSF; e.g., Smith and Balogh, 1995; Lockwood et al., 2004, see also Section 5).
For much of the solar cycle, particularly around solar minimum, the Sun’s magnetic field is dominated by its dipolar component, as evidenced by both PFSS solutions to the observed photospheric magnetic field and in situ measurements of the HMF. However, remaining quadrupole distortions are sufficient to induce more complex HMF sector patterns in the ecliptic. The in situ measurements of the Ulysses spacecraft are summarised by Figure 4. The white line in the left-hand panel shows the heliographic latitude of Ulysses overlaid on the sunspot number, shown in black. The dashed white lines bound Ulysses’s three fast latitude scans, which each take approximately one year to complete. During these intervals, Ulysses observes solar latitudes between 80° S and 80° N and all solar longitudes owing to solar rotation. The centre column shows the magnetic field polarity observed by Ulysses (red/blue are outward/inward, respecively), mapped back to the source surface and plotted as a function of heliographic latitude and longitude (Jones et al., 2002). The two solar minimum maps show the heliospheric magnetic field is split into two large regions of opposite polarity, approximately aligned with the north and south rotational solar hemispheres. This is the expected signature of nearly rotationally aligned dipolar coronal field, dragged out by the radial solar wind. A weak quadrupolar component can be seen in the slight warping of the HCS and slow solar wind band away from the solar equator. At solar maximum, an approximately dipolar signature is still present, though with a very high tilt to the rotation axis. However, it must be noted that at solar maximum the coronal magnetic field is evolving rapidly, on time scales well below 1-year, the time taken for Ulysses to sample the full solar latitude range. A combination of near-Earth spacecraft observations and PFSS solutions at this time suggest a significant quadrupolar component and that the apparent dipole observed by Ulysses is a result of fortuitous sampling of different latitudes.
At solar minimum, open solar flux and, therefore, the HMF largely maps to polar coronal holes. Thus, assuming the Wang and Sheeley Jr (1990) framework, fast solar wind would be expected from the large-scale unipolar regions over the poles, where the field undergoes little non-radial expansion at high latitudes in comparison to nearer the edges of the streamer belt. Conversely, slower solar wind is expected nearer the solar equator, where opposite magnetic polarities converge to produce helmet streamers and significant non-radial expansion is needed to equalise over the source surface. This solar wind structure was observed by Ulysses (McComas et al., 2003) and is shown in the right-hand column of Figure 4. Note, however, that while flux-tube expansion is extremely useful for identifying the location of slow solar wind, it is unlikely to be the actual mechanism by which it is formed (e.g., McComas et al., 2007, and references therein). At solar maximum, slow solar wind fills much of the heliosphere, as discussed in Section 5.2. In general the sources of the fast wind are better understood than those of the slow wind.
As noted above the large-scale regions of opposite HMF polarity are separated by the heliospheric current sheet (HCS). Near solar minimum, the HCS encircles the Sun close to the rotational equator and hence lies close to the ecliptic plane. Thus, spacecraft in near-Earth space will generally be close in heliolatitude to the HCS and will sample HMF polarities from both polar coronal holes as the Sun rotates, as shown in Figure 6. For a purely dipolar magnetic field typically with at least a small tilt to the rotation axis, a two-sector structure would be expected in the ecliptic plane, as sketched in Figure 1. As the quadrupolar component of the field increases, a more complex sector structure should be observed. Figure 5 shows the observed (top) and PFSS-reconstructed (middle) HMF polarity in near-Earth space as a function of Carrington longitude and time (after, e.g., Wilcox and Ness, 1965; Hoeksema et al., 1982). The bottom panel shows the sunspot cycle. Polarities of OSF estimated by the PFSS extrapolation of the observed photospheric magnetic field agree well with the large-scale magnetic sector structure seen in the heliosphere, throughout the solar cycle. Periods of both two- and four-sector structures are seen. As the HCS is formed by OSF of opposite polarities coming into contact by the non-radial expansion of separate coronal holes, the HCS maps to helmet streamers and is typically located within slow solar wind (e.g., Figure 4). The two- and four-sector structure have been observed to rotate at different rates: sampled at the Earth the four-sector structure generally follows the 27 day equatorial rotation period while the two-sector structure is often seen to rotate more slowly, at about 28 day period (Svalgaard and Wilcox, 1975).
Inclination of the solar magnetic axis to the solar rotation axis, as well as warps in the streamer belt, combined with the rotation of solar wind sources with the Sun, results in fast and slow solar wind successively entering the heliosphere at a fixed longitude in heliospheric coordinates, as shown in Figure 7. In such instances, fast wind (red) will catch up with slow wind ahead of it (blue) and the stream interface (SI) will take the form of a spiral front (black). The region of solar wind compression and deflection is referred to as the stream interaction region (SIR). In the quasi-steady state regime, SIRs will corotate with the Sun, and are thus referred to as corotating interaction regions (CIRs, Smith and Wolfe, 1976; Pizzo, 1991; Gosling and Pizzo, 1999; Crooker et al., 1999). In near-Earth space, CIRs are most commonly observed during the declining phase of the solar cycle, when there is typically a quasi-stable dipolar corona with significantly inclination to the rotational axis.
In the rest frame of the solar wind, both fast and slow wind flow in toward the SI. As the HMF is frozen to the plasma flow, neither fast nor slow wind can pass through the SI and are defected along it. This is achieved by disturbance waves propagating anti-sunward into the slow solar wind and sunward (in the plasma rest frame) into the fast wind. Figure 8 shows a CIR observed by Ulysses at 5.1 AU, just below to the ecliptic plane. The forward and reverse waves, shown as blue and red vertical lines, respectively, have steepened into shock fronts, which typically occurs at heliocentric distances larger than 2 AU (Smith and Wolfe, 1976). Within the interaction region, bounded by the red and blue lines, the magnetic field intensity and plasma density are enhanced by compression. Figure 7, based on the model of Pizzo (1991), shows how inclination of the stream interface means solar wind flow is systematically deflected along the SI, with fast (slow) solar wind deflected in the direction counter to (along) the solar rotation direction and poleward (equatorward) with respect to the heliographic equator. The poleward and equatorward deflections being confirmed observationally from Ulysses data by Gosling et al. (1993b).
As the HMF is frozen to the solar wind flow, it should be dragged in the same sense as the deflected flow within an interaction region. Clack et al. (2000) found that this expected large scale correlation between the flow and the magnetic field was hard to extract from the general variability of the magnetic field direction. However, due to the compression of the HMF within the interaction region, the varying magnetic field is forced to lie in a plane approximately parallel to the SI. As a consequence of the relationship between the HCS and the coronal streamer belt, the HCS is located at the centre of the slow solar wind band near the Sun. Indeed, the HCS is often observed to be embedded within SIRs and CIRs (Gosling and Pizzo, 1999). As the forward wave/shock propagates into the slow solar wind ahead of a CIR it can eventually overtake the HCS boundary, making it more likely for the HCS to be embedded within a CIR with increasing distance from the Sun (Thomas and Smith, 1981). In Figure 8, the location of the HCS is shown by the green dashed line. Behind the compressed interaction region, at the trailing end of the high-speed stream the fast solar wind runs away from the slow solar wind behind it, creating a rarefaction region in which the magnetic field intensity and plasma density are reduced, and the solar wind speed monotonically declines. Behind the SI and within the rarefaction region it is often noticed that the magnetic field components have higher variance. This is because the presence of large amplitude Alfvén waves is a typical property of the fast solar wind (e.g., Belcher and Davis Jr, 1971).
With the Voyager 1 spacecraft having recently passed the heliopause (Gurnett et al., 2013) and Voyager 2 close behind, our understanding of the outer heliosphere is evolving rapidly. This section contains a very brief summary of the outer heliosphere magnetic field. For a more comprehensive discussion of these topics, Zank (1999) and Linsky (2009) provide excellent, in-depth reviews of the distant heliospheric structure, while Balogh and Jokipii (2009) review the heliospheric magnetic field in the heliosheath.
The global-scale structure of the heliosphere and its interaction with the local interstellar medium (LISM) can be largely understood through magnetohydrodynamic simulations (e.g., Zank, 1999, and references therein), though they must include the effect of heliospheric pickup ions, produced by the photoionisation of neutral atoms (see Section 3), as they dominate the solar wind momentum flux past 10 AU. A sketch of the expected plasma and magnetic field boundaries is shown in Figure 9. The motion of the Sun and heliosphere relative to the LISM is 23 km s–1 (Linsky et al., 1995). Given the uncertainty in the LISM magnetic field strength and orientation, there is still some debate about whether this motion is super Alfvénic and, thus, results in a standing bow shock within the LISM. Recent observations from the IBEX mission (see Section 3), however, argue that the orientation of the LISM magnetic field is such that the interaction is sub-magnetosonic (McComas et al., 2012). Much like the interaction of the Earth’s magnetosphere with the solar wind, the heliopause is expected to be compressed on the LISM inflow side and extended on the downflow side. Unlike the magnetopause, however, the super Alfvénic solar wind outflow produces a standing termination shock inside the heliopause, which compresses, slows and deflects the solar wind flow. The Voyager 1 spacecraft crossed the termination shock in December 2004 at 94 AU (Stone et al., 2005), with Voyager 2 making its entry into the heliosheath in August 2007 at 84 AU (Stone et al., 2008). Voyager 2 started seeing enhancements in energetic particles at 76 AU, suggesting the termination shock is non-spherical, which allows particles to escape from the shock, back down the Parker spiral HMF (McComas and Schwadron, 2006). Inclination in the magnetic field of the local interstellar medium relative to that of the heliosphere may lead to further asymmetries near the heliopause (Schwadron et al., 2011). Voyager 1 recently encountered a region of flow stagnation, where the solar wind speed reached zero (Krimigis et al., 2011), before measuring an electron density enhancement consistent with the interstellar medium in April 2013 (Gurnett et al., 2013). The full implications of these observations are still being assessed and will be included in a future revision of this review.
Inside the termination shock, the HMF is generally well described by the Parker spiral model, however, there is some debate about whether the fall-off in magnetic field intensity is faster than predicted. Note that the radial magnetic field, , decreases as the square of the heliocentric distance [Equation (1)] and can be both positive and negative, meaning it is technically challenging to make measurements of the outer-heliosphere with sufficient accuracy to test the Parker model. The magnetic field intensity, , is a scalar quantity, so can be averaged over long time periods. Analysis of the Pioneer 10 and 11 data suggested decreases by approximately 1% per AU more than predicted by the Parker model (Winterhalter et al., 1990). The existence of such a “flux deficit” (Thomas et al., 1986) is disputed by Burlaga et al. (2002), who argue that the Voyager observations are consistent with the Parker model within observational uncertainty, if both the solar cycle variation of the solar source and time/latitude variations in solar wind speed are accounted for.
Assuming the observed latitudinal invariance in in the inner heliosphere, the term in [Equation (3)] means in the outer heliosphere should be stronger near the equator than the poles. Pioneer and Voyager spacecraft, however, did not find strong evidence of latitudinal gradients in (Winterhalter et al., 1990). There are a number of possible explanations for these observations. The confinement of SIRs to low latitudes at solar minimum means that the HMF has a tendency to become more radial than the Parker model predicts. Furthermore, the excess plasma pressure produced by heating at the SIR forward/reverse shocks could lead to a meridional expansion of the HMF, transporting flux to higher latitudes, in agreement with the small poleward plasma flows detected by Voyager (e.g., Richardson and Paularena, 1996). Alternatively, at solar minimum, the Kelvin–Helmholtz instability could act between the high-latitude fast wind and the low-latitude slow wind to generate a channel of vortices to drive such plasma flows and, hence, transport HMF (Burlaga and Richardson, 2000).
The shorter time-scale dynamics of the outer heliospheric HMF are dominated by merged interaction regions (MIRs, e.g., Burlaga et al., 2003; Hanlon et al., 2004); huge structures of compressed magnetic field and plasma which form from coalescing solar wind structures such as CIRs and ICMEs. The early formation of these structures can be observed even at 1 AU, where they can result in prolonged and severe geomagnetic effects. In the outer heliosphere, they can produce significant (if transient) deviations to the Parker spiral magnetic field. (See also Section 4.2.) MIRs also provide strong barriers to galactic cosmic ray propagation and in extreme cases may produce a significant disturbance to the structure of the heliopause and termination shock.