As discussed in Section 2.4, the HMF at solar minimum is well approximated by a dipolar-like magnetic field with a small inclination between the magnetic and rotational axes. Consequently, the heliospheric current sheet lies close to the rotational equator, perhaps still with some small warps due to weak non-dipolar structure. Coronal holes are confined to the polar regions while helmet streamers overlie the equator, thus fast solar wind fills the high-latitude heliosphere and the ecliptic plane generally sees alternate fast and slow solar wind streams. At this time, CMEs are much less frequent and are mainly observed at low latitudes (St Cyr et al., 2000). In near-Earth space, the Parker spiral field is a very good approximation to the observed HMF, with relatively few ICMEs and, hence, few significant meridional excursions of the HMF.
As the solar cycle progresses, the complexity of the coronal magnetic field increases, with closed magnetic structures associated with streamers being found at increasingly high latitudes, allowing the HCS to extend to higher latitudes. This can also be interpreted as the underlying magnetic dipole field making a weaker contribution and becoming increasingly inclined to the rotational axis. Figure 13 shows the latitudinal extent of the HCS from PFSS extrapolations of the photospheric magnetic field and in situ observations from the Ulysses spacecraft. There is a strong solar cycle variation, from low latitudes at solar minimum, to all latitudes at solar maximum (e.g., Hoeksema et al., 1983; Riley et al., 2002).
Associated with the HCS latitudinal extent increase, the coronal magnetic field structure begins to evolve more rapidly. CMEs become more frequent and cover a greater latitudinal span (e.g., St Cyr et al., 2000; Yashiro et al., 2004). At greater number of ICMEs are encountered in the ecliptic, meaning the HMF, on average, exhibits a greater departure from an ideal Parker spiral.
If the solar magnetic field remained approximately dipolar throughout the solar cycle, Figure 13 suggests that with increasing solar activity, the HCS and associated slow solar wind band should extend to higher latitudes, while fast solar wind from the magnetic poles should be increasingly encountered in the ecliptic plane. During the rise and particularly the declining phase of the solar cycle, this picture does hold to some extent. However, around solar maximum, additional factors also come into play.
Firstly, the solar magnetic field is at its most dynamic around solar maximum. The coronal magnetic field evolves rapidly, and disturbances due to CMEs become much more frequent as a consequence. In near-Earth space, a significant fraction of the solar wind can be attributed directly to ICMEs (Cane and Richardson, 2003; Owens and Crooker, 2006). Furthermore, quadrupolar and higher order moments of the solar magnetic field become more significant (e.g., Hoeksema, 1991; Wang et al., 2000b). The increased complexity of the magnetic field structure means that while the total open solar flux increases, it occurs in smaller spatial concentrations, in particular there is a decline in polar coronal hole area and, hence, a reduction in the occurrence of fast solar wind. As can be seen in the Ulysses solar maximum fast-latitude scan (Figure 4), this results in slow solar wind becoming prevalent at all latitudes. Consequently, CIRs are rare close to solar maximum, and interplanetary shocks result primary from fast ICMEs at this time.
Around the time of solar maximum, the polarity of the polar fields reverse, though the north and south poles do not typically reverse simultaneously, often showing around 1-year delay (Babcock, 1959). This polarity reversal process, as seen in the heliosphere, is discussed in Section 5.4.
Spacecraft in near-Earth space provide a reasonably complete record of the heliospheric magnetic field since 1965. The OMNI dataset (e.g., King and Papitashvili, 2005, see also NSSDC: http://omniweb.gsfc.nasa.gov/) collates the near-Earth solar wind measurements from numerous spacecraft, mostly recently IMP8, Wind and ACE. The white line in the top panel of Figure 14 shows the 27-day average of the scalar magnetic field intensity, , in near-Earth space. The red line shows a 1-year average. The black-shaded area is international sunspot number, , scaled to fit the axis.
The bottom panel shows the 27-day averages of the total unsigned heliospheric flux threading the 1-AU sphere, , using a 1-day modulus of 1-hour measurements of (Owens et al., 2008a). Extrapolation from a single-point measurement of to a global measure of total unsigned heliospheric flux is possible because of the Ulysses result of the latitude invariance in (Smith and Balogh, 2003; Lockwood et al., 2004). Interpreting in terms of the coronal source-surface open solar flux is not trivial: As the 1-AU -averaging interval is increased, e.g., from 1 hour to 1 day, the estimate of will decrease as more in/out flux is canceled (Lockwood and Owens, 2009). A value of 1 day gives the best match between in situ and PFSS estimates of coronal source surface OSF (Wang et al., 2000a). The choice of this averaging interval is equivalent to defining a minimum size for structures at 1 AU which originate at the coronal source surface, as opposed to forming between the source surface and 1 AU by kinematic effects, waves, turbulence, inverted HMF intervals, etc. There are currently a number of different approaches to dealing with this issue (Smith and Balogh, 2003; Owens et al., 2008a; Lockwood et al., 2009a; Erdős and Balogh, 2012) which yield slightly different absolute values for the coronal source-surface OSF, but result in very similar solar cycle trends, discussed here.
Both and show similar trends, with clear solar cycle variations in phase with the variation (e.g., Slavin and Smith, 1983; Richardson et al., 2000; Smith and Balogh, 2003; Owens et al., 2008a; Zhou and Smith, 2009; Lockwood et al., 2009a). However, the Gnevyshev gap, the small drop in solar magnetic activity at the time of solar maximum (Gnevyshev, 1977; Richardson et al., 2002), is much more pronounced in and than it is in sunspot number.While ICMEs are strongly associated with short-term enhancements in and ICME rates are known to vary in phase with the solar cycle (Cane and Richardson, 2003; Riley et al., 2006b), Richardson et al. (2000) concluded that the solar cycle variation in was not a direct result of spacecraft being increasingly immersed in identifiable ICME material. See Section 5.4 for further discussion.
Cycle-to-cycle variations are discussed as part of long-term records of HMF in Section 5.5. However, we note here that the most recent solar minimum between the end of solar cycle 23 and the start of cycle 24, centred around 2008 – 2009, has been longest and deepest of the space age, with the lowest and directly observed (Smith and Balogh, 2008; Lockwood et al., 2009a,b). This has been accompanied by a significant reduction in the solar wind momentum flux (McComas et al., 2008). At the photosphere, this minimum was manifest in the largest number of consecutive sunspot-free days since 1913 and the lowest polar magnetic field strength since routine observations began in 1975, which is likely the continuation of a decline in magnetic field strength which began several years previously(Wang et al., 2009, see also the Wilcox Solar Observatory (WSO) long-term polar magnetic field observations). As of early 2013, the photospheric magnetic field suggests the North pole has changed polarity, while the southern polar field is slowly weakening prior to reversal (Shiota et al., 2012). This suggests the Sun is presently very close to, if not just past, solar maximum, despite and being at comparable levels to the 1996 solar minimum. Thus, cycle 24 is likely to be the weakest of the space age in terms of HMF strength and sunspot number (e.g., Svalgaard et al., 2005). Section 5.5 puts these observations in a longer-term context.
Over the solar cycle, the total unsigned OSF varies by approximately a factor two, roughly in phase with the sunspot variation. The large-scale solar polarity reversal means the structure of the heliospheric field varies from approximately a rotationally-aligned dipolar-like field at solar minimum, through increasing inclination and warping of the heliospheric current sheet towards solar maximum, before a return to rotationally-aligned dipolar field of opposite polarity the following minimum (Section 2.4). A number of theoretical constraints can be placed on the mechanism(s) by which this heliospheric evolution takes place. As the solar wind is super Alfvénic, the total OSF can only be increased by transporting a closed coronal loop out past the source surface so that it is dragged out into the heliosphere. As magnetic flux can not be transported back towards the Sun through the source surface, the only way to reduce the total OSF is by “disconnecting” open flux by magnetic reconfiguration below the source surface (though these open field lines may form closed loops in the heliosphere, so that flux is not truly disconnected from the Sun). There does, however, remain some debate about the magnetic flux systems and topologies involved in HMF creation and loss, and whether this process occurs in quasi-steady state or as a series of transient events.
The solar cycle evolution of photospheric magnetic flux has been well characterised by three complete cycles of observation (Schrijver and DeRosa, 2003; Hathaway, 2010). As predicted by Babcock (1959, 1961), existing polar fields are “eroded” by opposite polarity flux within emerging bipoles, such as sunspots, before being repopulated by flux of the opposite polarity. Wang and Sheeley Jr (2003) used a series of PFSS solutions to show that emerging mid-latitude bipoles cause pre-existing closed coronal loops to rise and destroy/create open flux. This process both increases the total open solar flux, and creates/destroys open flux in the manner required for the polarity reversal. Over the solar cycle, the rise to solar maximum sees the axial dipole component of the Sun’s field weaken, while the quadrupolar component strengthens, as observed (Hoeksema, 1991; Wang et al., 2000a). While the polar fields are expected to reverse polarity around solar maximum, this model does not explicitly require the poles to flip simultaneously.
However, despite the success of such quasi-steady state models in capturing the large-scale evolution of the HMF, it is important to remember that PFSS models do not contain any time evolution and cannot account for transient structures such as CMEs. The location of newly opening solar magnetic flux between successive PFSS solutions correlates well with the timing and location of CMEs observed by coronagraphs (Luhmann et al., 1998, 1999; Yeates et al., 2010). Thus, in this “dynamic” picture, emerging active regions do not directly open new magnetic flux themselves, but act as source regions for CMEs, which provide the mechanism by which new magnetic loops are added to the heliosphere (see also Low, 2001). Indeed, in situ suprathermal electron observations clearly indicate that ICMEs carry new magnetic flux into the heliosphere (Gosling et al., 1987, see also Section 3.1). The remaining question is the relative contribution to new HMF from CMEs compared with that from rising ambient loops. Coronagraph estimates of CME rates (St Cyr et al., 2000; Yashiro et al., 2004) coupled with in situ estimates of typical ICME magnetic flux content (Lynch et al., 2005; Owens, 2008) suggest that CMEs potentially carry sufficient closed magnetic flux to account for the solar cycle variation of the OSF (Owens and Crooker, 2006, 2007; Connick et al., 2011). Similarly, CMEs may act as important sinks of newly emerging magnetic helicity, by bodily removing it from the corona (Low, 2001; Lynch et al., 2005). CMEs also project the Hale cycle of sunspot polarities out into the heliosphere. Gopalswamy et al. (2003) noted a correspondence between the cessation of high latitude CMEs and the polar field reversal. Low (2001); Low and Zhang (2004) suggested that CMEs play the role of emerging loops in the model of Wang and Sheeley Jr (2003), bodily removing old open solar flux from the corona for replacement by new open flux of opposite polarity, thus bringing about the global polarity reversal. More recently, Owens et al. (2007) suggested that the addition and removal of CME loops provides open flux transport, rather than open flux destruction, which agrees with suprathermal electron observations (McComas et al., 1992; Pagel et al., 2005), particularly within magnetic clouds (Crooker et al., 2008; Lavraud et al., 2011, see also Section 4.2.1).
In the Fisk model of coronal evolution, described in section 4.1, the solar cycle reversal of the HMF polarity can proceed as a rotation of the HCS (Fisk et al., 1999), as suggested by Ulysses observations of the magnetic sector structure throughout the solar cycle (Jones et al., 2003). Such a rotation would require “preferential” longitudes for the dipole axis as it approaches the solar equator, which have been suggested from observations of the HMF polarity (Neugebauer et al., 2000). Fisk and Schwadron (2001) suggest HCS rotation is driven by a diffusive process involving reconnection between open and closed flux (interchange reconnection, Crooker et al., 2002), which is thought to continually operate at the coronal hole boundaries (Nash et al., 1988; Wang and Sheeley Jr, 2004). Unlike the potential-field corona, where open flux is confined to the interiors of coronal holes, this allows the foot points of the HMF to move through the streamer belt by reconnection with, and subsequent opening of, closed coronal loops. This could provide the mechanism for the release of the slow solar wind (Fisk and Schwadron, 2001) and explain the difference in first ionisation potential (FIP, Geiss et al., 1995) between fast and slow streams (Zurbuchen et al., 1998; Schwadron et al., 1999), which is not accounted for by steady state models. However, there are theoretical issues with open solar flux existing within closed field regions (Antiochos et al., 2007) and the MHD-simulated coronal response to evolving photospheric magnetic flux shows limited evidence of this behaviour (Lionello et al., 2006; Linker et al., 2011).
There are a number of sources of proxy data for the heliospheric magnetic field hundreds to thousands of years into the past, allowing insight into long-term solar variability. This section contains a very brief summary of the long-term evolution of the HMF.
Records of geomagnetic variations can be used to infer the near-Earth solar wind conditions, primarily magnetic sector structure (Svalgaard, 1972), the magnetic field intensity and solar wind speed (e.g., Lockwood et al., 1999; Svalgaard and Cliver, 2005, 2010). A complete review of the methods and techniques is presented by Lockwood (2013), but we note here that annual averages are typically estimated in order to avoid effects of the inclination of the ecliptic and terrestrial dipole relative to the solar rotation axis, and that the uncertainty in the solar wind reconstructions increases prior ro 1880 as the number and quality of geomagnetic station records decreases significantly. For the 20th century, however, there is good agreement in HMF reconstructions from different geomagnetic records (Lockwood and Owens, 2011). Figure 15 shows the Lockwood et al. (2013a,b) (white) and Svalgaard and Cliver (2010) (yellow) reconstructions of near-Earth heliospheric magnetic field intensity, B (top). This has been converted to total unsigned OSF using the observationally constrained non-linear relation between B and OSF (Lockwood and Owens, 2011). OMNI spacecraft observations are shown in red and scaled sunspot number as dark background. The solar cycle variation is immediately obvious, but there is also a clear long-term variation, with the total OSF rising by nearly a factor 2 through the first half of the 20th century (Lockwood et al., 1999).
While there are issues with the intercalibration of sunspot records, the near-contiguous observations from 1610 to present (e.g., Hoyt and Schatten, 1998) are invaluable for understanding the evolution of the solar magnetic field. While the geomagnetic and cosmogenic isotope proxies relate directly to the HMF, sunspot records are related to large-scale magnetic features on the photosphere. In order to relate the two data sets, Solanki et al. (2000) proposed a continuity model of the OSF. The OSF source term must describe the rate at which new closed loops are added to the heliosphere and, thus, can be approximated by sunspot number. The loss term is more difficult to quantify. One approach is to assume various OSF contributions decay with different timescales (Krivova et al., 2007; Vieira and Solanki, 2010). Owens and Lockwood (2012) instead assume that the OSF source term follow the CME rate, which is linked to the sunspot number (Webb and Howard, 1994), and that the OSF loss term follows the HCS tilt, owing to reconnection driven by differential rotation (Owens et al., 2011a).
The green line in Figure 16 shows a reconstruction of total OSF based upon group sunspot number records (Owens and Lockwood, 2012). Obviously, prominent features from the sunspot spot record, such as the Dalton minimum around 1800 – 1820 and the Maunder minimum around 1650 – 1710, are also present in HMF reconstructions (Owens et al., 2012). General agreement with the geomagnetic reconstructions for the 20th century, shown in white, is good, with both showing a rise and fall in the total OSF.
Ground-based neutron monitor counts, a proxy for the galactic cosmic ray flux at the top of the Earth’s atmosphere, show a strong solar cycle variation in anti-phase with sunspot number. At solar maximum, the increase in OSF, coupled with the increased latitudinal extent of the HCS/CIRs, provides a more effective barrier to cosmic rays reaching the inner heliosphere (e.g., Usoskin et al., 2005, and references therein). Cosmogenic isotope abundances, e.g., in ice-core records, can provide proxies for GCR flux and, hence, the HMF, over 10 000 years (e.g., McCracken, 2007; Usoskin, 2013; Steinhilber et al., 2010; Solanki et al., 2004). The red and blue lines in Figure 16 show 22-year running averages of OSF inferred from heliospheric modulation potentials consistent with the 10Be and 14C abundances, respectively, since 1610 and extended to the space age using neutron monitor records (see Muscheler et al., 2007; Lockwood and Fröhlich, 2008, and references therein for more detail). The long-term features such as the Dalton and Maunder minima, as well as the 20th century trends, are clearly present. The full record suggests that the HMF has been as strong as that of the space age on 24 previous occasions in the last 9300 years, though this grand solar maximum (GSM) is the longest in the record (Abreu et al., 2008). Two of the 24 previous ends of GSMs have resulted in Maunder minimum-like conditions within 50 years (Barnard et al., 2011).