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date: 27 October 2020

Solar Wind: Interaction With Planets

Abstract and Keywords

The interaction between the solar wind and planetary bodies in our solar system has been investigated since well before the space age. The study of the aurora borealis and australis was a feature of the Enlightenment and many of the biggest names in science during that period had studied the aurora. Many of the early scientific discoveries that emerged from the burgeoning space program in the 1950s and 1960s were related to the solar wind and its interaction with planets, starting with the discovery of the Van Allen radiation belts in 1958. With the advent of deep space missions, such as Venera 4, Pioneer 10, and the twin Voyager spacecraft, the interaction of the solar wind other planets was investigated and has evolved into a sub-field closely allied to planetary science. The variety in solar system objects, from rocky planets with thick atmospheres, to airless bodies, to comets, to giant planets, is reflected in the richness in the physics found in planetary magnetospheres and the solar wind interaction. Studies of the solar wind-planet interaction has become a consistent feature of more recent space missions such as Cassini-Huygens (Saturn), Juno (Jupiter), New Horizons (Pluto) and Rosetta (67/P Churyumov–Gerasimenko), as well more dedicated missions in near-Earth space, such as Cluster and Magnetosphere Multiscale. The field is now known by various terms, including space (plasma) physics and solar-terrestrial physics, but it is an interdisciplinary science involving plasma physics, electromagnetism, radiation physics, and fluid mechanics and has important links with other fields of space science, including solar physics, planetary aeronomy, and planetary geophysics. Increasingly, the field is relying on high-performance computing and methods from data science to answer important questions and to develop predictive capabilities. The article explores the origins of the field, examines discoveries made during the heyday of the space program to the late 1970s and 1980s, and other hot topics in the field.

Keywords: solar wind, space plasma physics, magnetosphere, magnetic field, aurora

1. Part One

The solar wind flows around the magnetosphere and generates a day-night asymmetry (Figure 1a), compressing the magnetic field on the “dayside” of the magnetosphere. On the “nightside” the magnetic field is extended in a “magnetotail” and is divided into two “lobes” by a current sheet that runs approximately dawn-to-dusk. The magnetosphere is coupled to the Earth’s upper atmosphere via the magnetic field. The development of theories aimed at understanding the interaction of the solar wind with the planets, and understanding this structure, predates the discovery of the solar wind and started with efforts to understand the aurora and diurnal changes in the geomagnetic field.

1.1 Connecting the Aurora and Earth’s Magnetosphere

The aurora has been studied scientifically since the 1600s, but there are earlier references to phenomena that could be aurorae in Greek literature, the Tanakh/Old Testament, and in manuscripts from ancient China. The literature is biased toward auroral displays in the northern hemisphere, yet there is literature on southern hemisphere aurorae, for example, an auroral display in 1640 described by the Chilean Jesuit Alonso de Ovalle (Willis, Vaquero, & Stephenson, 2009). Some of the earliest studies on the solar wind-Earth interaction include studies of the geomagnetic field by Edmund Halley in the late 1600s and observations of sunspots by Galileo Galilei in 1612.

Solar Wind: Interaction With Planets

Figure 1. Schematic of magnetic fields (teal lines/arrows), currents and Poynting flux (red arrows/lines) in the noon-midnight meridian of Earth’s magnetosphere from the perspective of the Earth’s dusk terminator (a), and magnetic fields and plasma flows (red arrows/lines) in the equatorial plane of Earth’s magnetosphere viewed from above the north pole (b). In both panels the Sun is off to the left-hand side and both panels show the magnetopause and bow shock boundaries (green thick lines). The beige/brown colors indicate the solar wind/foreshock, the green region is the magnetosheath, and the teal color indicates the region of closed field lines. The inset in panel (a) shows the compression of the geomagnetic field by the solar wind modeled by a mirror dipole as envisaged by Chapman and Ferraro (1930). Panel (a) is after Cowley (1980) (see also Lockwood & Davis, 1999).

In the first half of the 18th century it was discovered that the geomagnetic field varied continuously, leading to the discovery by Swedish astronomer Olaf Petrus Hiorter, working with Anders Celsius, that the geomagnetic field varied diurnally and that there was a correlation between geomagnetic variations and auroral activity. These geomagnetic perturbations are now understood as the effect of electric current systems in the ionosphere, the conducting part of Earth’s upper atmosphere which wasn’t discovered until the advent of radio in the early 1900s (Russell, Luhmann, & Strangeway, 2016). Conjugate aurora (simultaneously in the north and south) were recorded for the first time during Captain James Cook’s first voyage on HMS Endeavour (Willis et al., 2009).

Richard Christopher Carrington made extensive observations of sunspots and during the course of these daytime observations he observed a “white light” solar flare. The following day geomagnetic disturbances were accompanied by aurorae seen as far south as Puerto Rico. This large geomagnetic storm is now known as the Carrington Event and is well-cited as the case of a large storm which, if it occurred today, would cause widespread technological disruption and damage. However, at the time, Carrington’s suspicion of a causal link between the flare and the geomagnetic storm was dismissed as coincidental by Lord Kelvin (William Thomson, 1st Baron Kelvin) (Russell et al., 2016).

1.2 Birkeland and Chapman

Some of the most extensive observations of geomagnetic perturbations and aurorae were made by Norwegian scientist Olaf Kristian Bernhard Birkeland (Egeland, 2009). Between 1897 and 1903, Birkeland conducted three expeditions to northern Norway, constructed a dedicated permanent auroral observatory, and mapped the aurora and geomagnetic perturbations. Birkeland also developed laboratory experiments, with a scaled-down version of Earth and the aurora called a “Terrella.” Birkeland’s most significant contribution was the idea that electric currents flowing in the ionosphere would need to flow in and out of the ionosphere along magnetic field lines in order to couple auroral phenomena and interplanetary space. He estimated that approximately 1 MA of current flowed in the ionosphere and reasoned that the only thing that could generate currents of such magnitude was the Sun. From his observations and experiments he developed a model consisting of a two-cell global pattern of currents, fixed with respect to the Sun, which explained the aurora and the observed diurnal variations in geomagnetic perturbations. The existence of these “field-aligned” currents was hotly debated for more than 50 years and Birkeland died suddenly and mysteriously in 1917 before the importance of his work was fully realized (Egeland, 2009).

One of Birkeland’s leading opponents was Sydney Chapman, who argued that field-aligned currents were not necessary and could close entirely within the atmosphere. This view was still being promulgated in 1968 when Chapman wrote “The apparently unshakable hold on Birkeland’s mind, of his basic but invalid conception of intense electron beams, mingled error inextricably with truth in the presentation of his ideas and experiments on aurora and magnetic storms” (Potemra, 1985, and references therein), in spite of counterarguments by Naoshi Fukushima that ground-based measurements alone could not unambiguously distinguish between the physical pictures of Birkeland or Chapman (Fukushima, 1969). However, even as Chapman was writing these words, Alfred Zmuda and coworkers uncovered the first evidence that field-aligned currents existed, based on observations from a navy satellite. The interpretation of field-aligned currents was championed by Alexander Dessler and his student W. David Cummings, along with Physics Nobel Laureate Hannes Alfvén who had supported and developed Birkeland’s work in the late 1930s. In the mid-1970s substantial evidence for field-aligned currents, by then known as Birkeland currents, were presented in a series of papers by Zmuda, and also Takesi Iijima and Thomas Potemra, firmly establishing the evidence supporting Birkeland’s ideas (Potemra, 1985). Figure 2 shows the observed pattern of Birkeland currents—separated into two zones, “Region 1” and “Region 2”—and an idealized representation of the cells, similar to that which Birkeland had envisioned.

Solar Wind: Interaction With Planets

Figure 2. (a) The observed pattern of Birkeland currents (after Iijima & Potemra, 1978) and (b) an idealized schematic showing circulation over the polar cap, electric fields, and the associated Birkeland currents. Red indicates currents out of the ionosphere (downward field-aligned currents) and teal indicates currents into the ionosphere (upward field-aligned currents).

Contemporaneous with the development of ideas on the origins of geomagnetic perturbations and the aurora were ideas about how the solar wind interacted with the geomagnetic field. In 1918, Chapman had proposed that an intermittent singly charged beam from the Sun, referred to as “corpuscular radiation,” was the source of geomagnetic perturbations. Frederick Lindemann, a divisive character who was to become one of Winston Churchill’s closest advisers, criticized Chapman’s theory on the basis of the mutual repulsion of single charges and suggested that the solar wind must be an electrically neutral mixture of positive and negative charges. This ultimately led Chapman and his student, Vincenzo Consolato Antonino Ferraro, to develop a theory of magnetic storms in 1930. Chapman and Ferraro argued that corpuscular radiation would be a very good electrical conductor, and so as the plasma approached the Earth it would see Earth as a mirror dipole and would compress the geomagnetic field (inset in Figure 1a) to form a cavity (Chapman & Ferraro, 1930). This cavity was termed the “magnetosphere” by Thomas Gold in 1959.

The clue that corpuscular radiation—the solar wind—was a more permanent stream came from the study of comets in the 1940s (Ahnert, 1943; Biermann, 1951; Hoffmeister, 1943). Around the same time, Alfvén had proposed the existence of hydrodynamic waves in plasmas and introduced the idea that, in the limit of infinite conductivity, magnetic flux and plasma could be coupled or tied together (Alfvén, 1942). This theorem would become known as Alfvén’s theorem, or the “frozen-in-flux” theorem, and resembles the Helmholtz-Kelvin theorem (e.g., Lighthill, 1986) in ideal fluids. Alfvén used the idea of frozen-in-flux to complete Biermann’s picture, arguing that the magnetic field of the Sun should be “frozen” into the solar-wind plasma (Alfvén, 1956, 1957) to form the interplanetary magnetic field (IMF). Eugene Newman Parker also demonstrated that this implied that the IMF would be wrapped up into an Archimedean spiral (Parker, 1958a). He theoretically showed how the solar wind could be a supersonic hydrodynamic expansion of the corona (Parker, 1960), and that this could apply to all main-sequence stars later than spectral class F, with clear implications for the stellar wind-exoplanet interaction. Parker’s supersonic solar wind was not accepted at first; in particular, Joseph W. Chamberlain challenged Parker’s ideas and instead advocated a “solar breeze” that was subsonic (Chamberlain, 1960), based on his interest in the escape of planetary atmospheres. Ultimately Parker was vindicated, but the dialogue between the two scientists advanced our understanding of outflows from celestial bodies (Hunten, 2005). The supersonic solar wind was detected in 1959 by the USSR’s Luna 2/Luna 3 probes, led by Konstantin Iosifovich Gringauz (Gringauz, Bezrukikh, Ozerov, & Rybchinskii, 1960), who also designed the radio transmitter on Sputnik I. These observations were corroborated in 1961 by observations made by NASA’s Explorer 10 probe, led by Herbert Bridge, and in more detail in 1962 with NASA’s Mariner 2 spacecraft by Marcia Neugebauer and Conway W. Snyder (Bridge et al., 1962; Neugebauer & Snyder, 1962).

These ideas have important implications for the environment in which the planets are immersed. The IMF field strength, B, and solar-wind density, ρ‎, decrease approximately as the inverse square of the heliocentric distance, whereas the speed, v, is approximately constant. As a consequence, the solar-wind dynamic pressure, ½ρv2, falls with radial distance from the Sun. The two wave modes of direct relevance for the solar-wind interaction are the “Alfvén mode,” vA2=B2/μ0ρ, and the “Fast mode,” vF=vs2+vA2, where vs=γpth/ρ, where νs=γpth/ρ is the thermal pressure in the solar wind, and γ is the ratio of specific heats. Both the Alfvén and fast-mode Mach numbers generally increase with heliocentric distance. These variations have consequences for the interaction of the solar wind with the planets.

1.3 When the Solar Wind Meets a Planet

As the solar wind reaches Earth, or any magnetized planet, currents are induced in the solar wind to oppose the penetration of the geomagnetic field through the solar wind—an application of Lenz’s law. In terms of the solar wind-planet interaction, this means that geomagnetic field is an obstacle to the solar wind and the solar wind must flow around the Earth. Since the solar wind is both supersonic and super-Alfvénic, the plasma must be slowed to subsonic speeds in order to flow around the obstacle. The existence of astrophysical shocks had been proposed by Gold in 1955 but it wasn’t until 1962 that Sir William Ian Axford and Paul J. Kellogg independently proposed that a shock wave would “stand” in the solar wind, upstream of Earth, slowing down the solar wind (Axford, 1962; Kellogg, 1962). This shock wave is now known as the bow shock and was discovered by the OGO spacecraft in 1966. Particles reflected from the bow shock can move upstream along the magnetic field in a region known as the “foreshock.” The region downstream of the shock consists of heated and compressed plasma and is referred to as the magnetosheath (Figure 1b). The final boundary, separating the plasma and magnetic fields of solar and terrestrial origin, is known as the magnetopause, by approximate analogy with the tropopause in Earth’s lower atmosphere (Hines, 1963; Siscoe, 1987) (Figure 1a). The magnetopause was first encountered by Explorer 10 in 1961. The basic investigation of the magnetospheres of other planets, including their bow shock and magnetopause (for magnetized planets), started with the USSR’s Venera 4 at Venus in 1967. See Table 1 for a list of early missions and milestone missions in the modern era.

Table 1. Summary of Major Milestones in the Study of Solar-Wind Interactions With Various Solar-System Bodies

Mercury

1974

Mariner 10 (USA)

2011

MESSENGER (USA)

Venus

1967

Venera 4 (USSR); Mariner 5 (USA)

1975

Venera 9/10 (USSR)

1978

Pioneer Venus Orbiter (USA)

Mars

1964

Mariner 4 (USA)

1971

Mars 2 and Mars 3 (USSR)

1974

Mars 5 (USSR)

1989

Phobos 2 (USSR)

1997

Mars Global Surveyor (USA)

Jupiter

1973

Pioneer 10 (USA)

1974

Pioneer 11 (USA)

1979

Voyager 1 and 2 (USA)

1992

Ulysses (Europe/USA)

1995

Galileo (USA)

Saturn

1979

Pioneer 11 (USA)

1980

Voyager 1 (USA)

1981

Voyager 2 (USA)

2004

Cassini-Huygens (USA/Europe/Italy)

Uranus

1986

Voyager 2 (USA)

Neptune

1989

Voyager 2 (USA)

Pluto

2015

New Horizons

The Moon

1959–1976

Luna 1-24 (USSR)

1967–1973

Explorer 35 (USA)

1969–1977

Apollo Lunar Surface Experiments and sub-satellites (USA)

Comets

1/P Halley

1986

Vega 1 and 2 (USSR/France); Suisei (Japan); Sakigake (Japan); Giotto (Europe); ICE (USA)

67/P Churyumov–Gerasimenko

2014

Rosetta (Europe/France)

Asteroids

951 Gaspra

1991

Galileo (USA)

243 Ida

1993

Galileo (USA)

253 Mathilde

1997

NEAR Shoemaker (USA)

433 Eros

2000

NEAR Shoemaker (USA)

John R. Spreiter, an engineer with a background in aerodynamics and high-speed flight, conducted some of the most comprehensive studies of this interaction. He applied these ideas to the supersonic flow around the planets. Spreiter later collaborated with Stephen S. Stahara to develop computational models that were applied to study the supersonic solar wind-planet interaction at almost every planet in the solar system (Stahara, 2000).

The interaction which Chapman and Ferraro had described in 1930, known as the “Chapman-Ferraro problem,” was solved analytically in the 1960s by James E. Midgley and Leverett Davis Jr., and independently by Gilbert Dunbar Mead and David Breed Beard (Mead & Beard, 1964; Midgley & Davis, 1963). The Chapman-Ferraro currents that flow on the magnetopause are illustrated in Figure 1a and in 3D in Figure 3. To a first approximation, the location of the magnetopause can be determined by an equilibrium between the solar-wind dynamic pressure and the magnetic pressure of the geomagnetic field (1),

k12ρv2cos2Ψ+pthsin2Ψ=(fB)22μ0
(1)

Where ψ is the angle between the local normal to the magnetopause and the flowing solar wind, B is the magnetic-field strength inside the magnetosphere, μ0 is the permeability of free space, and f is a factor of order unity which accounts for the additional field of the magnetopause (Chapman-Ferraro) currents. Equation (1) assumes that the flow undergoes no deflection between the solar wind and magnetopause, known as the “Newtonian approximation.” The factor of k accounts for the conversion of solar-wind dynamic pressure into thermal pressure at the bow shock and asymptotically approaches 0.881 for high Mach-number shocks (Petrinec & Russell, 1997).

Solar Wind: Interaction With Planets

Figure 3. The coupled magnetopause-magnetotail current system found when solving the Chapman-Ferraro problem. Teal lines are magnetic field lines within the magnetosphere and brown lines are current density streamlines. At the nose of the magnetopause, the current flows from dawn-to-dusk (in the terrestrial magnetosphere) but dusk-to-dawn over the north/south flanks of the magnetopause before closing partly via the magnetotail current sheet, and partly via the nose of the magnetopause. The green wireframe is the magnetopause.

Assuming a dipole magnetic field perpendicular to the solar wind, the magnetic field strength at the nose of the magnetopause, a distance rMP from the planet (in units of planetary radius), can be written as B=B0rMP3, where B0 is the surface equatorial magnetic field strength. Also using the fact that ψ=0 at the nose, equation (1) can be rewritten to give the distance of the magnetopause:

rMP=(f2B022μ0k)1/6(12ρv2)1/6
(2)

As expected, the magnetopause is further away under lower dynamic pressure and is fairly “rigid” in that it varies only with the 1/6th power of the dynamic pressure. For Earth, RMP is around 10 Earth radii, or ~64000 km, whereas at Jupiter it is at 50–100 Jupiter radii, or ~3–7 million km. In the 1980s, James A. Slavin, working with Spreiter, Stahara, and Edward J. Smith (who had been involved in the early detections of the magnetopause and bow shock), had shown that Jupiter’s magnetosphere was more compressible, later also shown to be the case for Saturn (Arridge, Achilleos, Dougherty, Khurana, & Russell, 2006), which is a consequence of internal forces in the magnetosphere. In contrast, Mercury’s magnetosphere is less compressible due to the effect of electromagnetic induction in Mercury’s conducting interior (Hood & Schubert, 1979; Slavin & Holzer, 1979; Suess & Goldstein, 1979). In this compressional (normal stress) mode of interaction, the force required to deflect the solar wind around the magnetosphere must ultimately be applied by and on the Earth, and ultimately this force is transmitted to Earth’s interior via the geomagnetic field (Siscoe, 1966). An order of magnitude calculation with a dynamic pressure of 1 nPa applied uniformly over a circular cross section of radius 64000 km gives a force of 107 N. Although this is orders of magnitude smaller than the gravitational force of the Sun on the Earth, this may not be the case in some exoplanetary systems.

The solar wind can also interact via drag forces (tangential stress) which can extract energy and momentum from the solar wind, essential for driving aurorae and geomagnetic activity. Forces are principally applied to the atmosphere via the action of Birkeland’s field-aligned currents which enable the transport of momentum from one location to another. In the case of Region 1 currents (Figure 2b), they exert a drag force on the solar wind and a force on Earth’s neutral atmosphere (via friction between the ionosphere and the neutral thermosphere) in a direction away from the Sun. Region 1 currents flow into the ionosphere on the dusk flank and away from the ionosphere on the dawn flank. Current systems in the magnetosphere also close via Birkeland currents and form the Region 2 current system, which is coupled in the ionosphere. In general, the picture is more complex because of additional forces applied to the atmosphere by an interaction of the ionospheric currents with the Earth’s magnetic field, which involves additional forces being applied to the interior of the Earth (Siscoe, 1966; Vasyliūnas, 2007), and in extreme storms the Region 1 currents play a more important role than the normal stress of the Chapman-Ferraro mechanism in mediating the coupling between the solar wind and the magnetosphere (Siscoe, 2006). The final ingredient in Figure 1a is the flow of electromagnetic energy, the Poynting flux, S=E×B/μ0. Only a small fraction of the energy of the solar wind that passes the magnetosphere crosses the magnetopause to enter the magnetosphere. In a non-steady situation, some of this energy can be stored in the magnetotail, ASds=WB/t, and can be released during periods of enhanced geomagnetic activity.

1.4 Drag on the Magnetosphere: Reconnection and the Viscous Interaction

As discussed in Priest (“Magnetohydrodynamics—overview”), the magnetic Reynolds number, Rm, is a dimensionless quantity used to characterize the balance of advection (frozen-in-flux) and diffusion in the evolution of the magnetic field. In the limit Rm1, frozen-in-flux applies, and Ohm’s law takes the form E+v×B=0. This implies that magnetic field lines are equipotentials and that flows in the ionosphere are also present in the magnetosphere, and vice versa. Birkeland’s two-cell global pattern of field-aligned currents implied a circulation or “stirring” of the upper atmosphere that must also imply a stirring of the magnetosphere. Figure 4 shows a simplified version of the accepted flows in the terrestrial magnetosphere, from the perspective of the ionosphere (Figure 4a) and magnetosphere (Figure 4b). The basic pattern of the flows is a sunward flow across the polar cap, with a return flow via the dawn and dusk flanks of the magnetosphere. The potential drop associated with this flow across the polar cap is generally 50–100 kV. These ionospheric flows can be opposed by ohmic losses and the viscosity of the atmosphere. The ionosphere can also stir the magnetosphere. In the ionosphere, ion-neutral collisions can drive the ionosphere to move with the neutral atmosphere, at a velocity vn, leading to a motional electric field, E=vn×B, that is mapped along equipotential field lines to the magnetosphere. This is important close to Earth but is unimportant beyond geostationary orbit (the closed streamlines in Figure 4b); this simple argument depends on details of the magnetosphere-ionosphere coupling. Although frozen-in-flux is widely applied, it is worth noting that in the “F” region of the ionosphere, frozen-in-flux applies to a good degree, although collisions in the “E” region mean that the ions are not “frozen-in” at those altitudes.

Around the mid-1960s there were two competing ideas to explain how tangential drag with the solar wind could stir the magnetosphere and thus the ionosphere. One was a “magnetic reconnection” model which permitted magnetic-field lines anchored on Earth to merge or “reconnect” with those in the solar wind, thus “opening” the magnetosphere to the solar wind. The other was that a “viscous” interaction would occur on the boundaries of the magnetosphere.

Solar Wind: Interaction With Planets

Figure 4. Circulation in the ionosphere (a) and in the magnetosphere (b). In the equatorial plane the magnetosphere corotates with the ionosphere, but this maps to lower latitudes than are visible in panel (a). The streamlines that cross the polar cap in panel (a) are on open field lines out of the plane of (b), but the sunward return flows at dawn and dusk in (a) relation to the sunward flows in (b). The teal color in (b) corresponds to the closed field region in Figure 1.

1.5 Birth of the Open Model

James Wynne Dungey laid the foundations for the magnetic reconnection model in the late 1940s and early 1950s in his doctoral studies, supervised by Sir Fred Hoyle. Hoyle had been inspired by Ronald Gordon Giovanelli’s ideas that solar flares could be generated by “neutral” sheets—surfaces that divide oppositely directed magnetic fields and which magnetic field lines cannot cross. Hoyle thought that the presence of such neutral sheets on the nightside of Earth’s magnetosphere might be related to the aurora and directed Dungey to investigate (Southwood, 2016). Dungey concluded that under certain conditions these neutral sheets could accelerate particles toward the Earth in a process that is now known as “magnetic reconnection.”

Generally, Rm1 in most regions of the magnetosphere and thus the solar-wind plasma and field is separated from the magnetospheric plasma and field by a current sheet (the Chapman-Ferraro currents, e.g., Figure 1a). It is within these current sheets, where Rm1, due to short-length scales and slow plasma flows, that the magnetic field diffuses at a neutral or “X-point” (Figure 5a), mixing plasma and magnetic flux of differing origins. Dungey envisaged two neutral points, one on the dayside and one on the nightside, with flows away from the dayside neutral point north and south, flowing anti-sunward over the poles, and then toward the equatorial plane at the nightside neutral point, as illustrated in Figure 5a. The flows from this neutral point would return the flux back toward the dayside, thus completing a “convection” cycle (“stirring”), now referred to as the Dungey cycle.

Solar Wind: Interaction With Planets

Figure 5. (a) Circulation in the magnetosphere produced by the Dungey cycle, (b) circulation in the magnetosphere produced by a viscous interaction at the boundaries of the magnetosphere. Note that (a) is drawn from the perspective of the noon-midnight meridian (dusk) whereas (b) is from above the North Pole, but in both diagrams the Sun is off to the left. Red arrows and curves indicate flows of plasma and streamlines respectively, teal lines are magnetic field lines, and the thick green line is the magnetopause boundary.

The efficiency of magnetic reconnection, ξ, is defined as the ratio of the electric field across the magnetosphere, Em=ψLm, to the electric field just downstream of the bow shock, Esw=ψL0, where L0 and Lm are the distance between the two central streamlines in Figure 1b at the shock and magnetosphere, respectively, and ψ is the potential drop between the two field lines. We can estimate this quantity using some simple assumptions. The speed, density, and magnetic-field strength “jump” by a factor Z~3–4 across the shock, with the speed decreasing and the density/field strength increasing from upstream to downstream. Assuming incompressible flow between the shock and magnetosphere, the continuity equation implies that v0L02=vswZL02~vmLm2, hence:

ξ=EmE0=ψmLmL0ψ0=L0Lm=vmv0=vmZvsw
(3)

We can replace the speeds with v=MACA, where MA is the Alfvén Mach number and CA is the Alfvén speed. Setting CA,m=Z1/2CA,sw from the definition of Z and the CA gives (4), which is dependent on Z,MA,sw, and MA,m.

ξ=MA,mCA,mZMA,swCA,sw=MA,mZ3/2MA,sw=Z3/4MA,mMA,sw
(4)

Priest (“Magnetohydrodynamics—overview”) shows that the maximum Mach number outside the reconnection inflow is inversely proportionate to ln(Rm); with some assumptions on the form of the magnetic Reynolds number, the maximum Mach number can be written as a transcendental function of a scale size, d, and a gyroradius, rg (Cravens, 2004), which gives a Mach number of 0.04 for d=64000 km and rg=100km.

MA,m=π81lndrglnMA,m
(5)

Using this Mach number with MA,sw=8 and Z=4 in (4) gives ξ=0.2. When used with a solar-wind electric field of 2 mV/m and a length scale of 30 Earth radii across the magnetopause, we obtain a cross-polar cap potential of ~80 kV, which compares favorably to the typical values of 50–100 kV.

Although the basic ideas were present in Dungey’s (1950) doctoral thesis, they proved difficult to publish in their entirety. Dungey continued to develop his ideas through the 1950s, working with Giovanelli as a postdoctoral fellow in Sydney, at Pennsylvania State University, and at Meudon Observatory in Paris. His main breakthrough came while in a street café in Montparnasse in Paris. Watching milk being stirred into coffee reminded Dungey of the two-cell ionospheric current system and gave Dungey the final piece of the puzzle leading to his seminal 1961 article (Dungey, 1961; Southwood, 2016) that launched the open model of the magnetosphere. One of the major predictions from this model was that the orientation of the IMF would play a role in determining the level of geomagnetic activity, determining the electric field in (2). Ideally, it should be opposite to the geomagnetic field (southward) at the subsolar point of the magnetopause for reconnection to take place (Dungey, 1961). Dungey’s ideas were slow to gain acceptance through the 1960s and 1970s, even though scientists such as Donald H. Fairfield, Larry J. Cahill Jr., Roger Arnoldy, and Joan Hirshberg had presented mounting evidence though the 1960s showing that the orientation of the magnetic field in the solar wind was important in controlling geomagnetic activity. It wasn’t until the launch of the International Sun Earth Explorers (ISEE) dual-spacecraft mission ISEE 1 (also known as Explorer 56) and ISEE 2 in 1977 that direct evidence for magnetic reconnection at the magnetopause was found. ISEE 1 and 2 were joined in 1978 by ISEE 3 (Explorer 59), which would eventually go into a heliocentric orbit and visit comets Giacobini-Zinner in 1985 and Halley in 1986.

1.6 Viscous Interaction

The main alternative to Dungey’s open model invoked a viscous interaction at the boundary of the magnetosphere to produce a circulation like that in a falling raindrop. Axford and Colin O. Hines presented their theory of a viscous solar wind-magnetosphere interaction in 1961, building on earlier work by Hines in 1959. A viscous transfer of momentum across the boundary of the magnetosphere, from the solar wind into the magnetosphere, would then cause magnetospheric plasma to convect into the tail region, subsequently requiring some return flow to avoid a build-up of plasma on the nightside of the Earth. Figure 5b shows such a circulation as envisaged by Axford and Hines (1961). Similar to Dungey’s picture, the application of frozen-in-flux implies that plasma circulates in the ionosphere. Axford and Hines also speculatively added an inner convection system, possibly driven by a separate viscous interaction close to Earth at a separate boundary near four Earth radii. Axford and Hines were not specifically focused on the precise mechanism that generated the viscous interaction at the magnetopause. Ideas at the time included turbulent mixing at the magnetopause, molecular diffusion, sound waves at a shear layer, and some sort of instability at the boundary followed by inward transport of momentum by eddy viscosity. Although the reconnection model is now understood as the main driver of dynamics in the terrestrial magnetosphere, various lines of evidence show that viscous interactions are important, from cross-polar cap potentials during northward IMF to solar-wind entry into a magnetospheric boundary layer (also known as the Low Latitude Boundary Layer, LLBL) adjacent to the magnetopause (Eastman, Hones, Bame, & Asbridge, 1976).

1.7 The Magnetotail

The theories of Dungey (1961) and Axford and Hines (1961) explicitly included a “magnetospheric tail” to the magnetosphere, known simply as the “magnetotail,” but both Parker (1958b) and Jack Hobart Piddington (1960) had predicted the existence of a tail a few years earlier. These ideas were further developed in the early 1960s, for example, extending the viscous model (Axford, Petschek, & Siscoe, 1965), but the study of the magnetotail accelerated with its observational detection in data from the IMP 1 satellite in 1963 and 1964 (Ness, 1965), suggesting a magnetotail extending beyond the Moon. Since then, the magnetotail has been studied in great detail by a large number of space missions, some of which have been specifically focused on the tail, such as the Japanese Geotail mission. Magnetic reconnection in the magnetotail is a key element of Dungey’s theory and a great deal of work has been carried out regarding the dynamical behavior of the magnetotail. The equilibrium structure of the tail has continued to receive attention in theoretical studies (Rich, Vasyliūnas, & Wolf, 1972; Schindler & Birn, 1986). The magnetotail on the nightside of the magnetosphere also exerts forces on the Earth, but the exact details of the global force balance are currently an unsolved problem (Siscoe, 1966; Vasyliūnas, 2015).

1.8 Summary

Ultimately, Dungey’s reconnection model became the dominant paradigm in understanding the magnetosphere, aurorae, and magnetic perturbations. Mercury’s magnetosphere is an extreme example of a magnetosphere driven by the Dungey cycle. Its proximity to the Sun provides an intense solar-wind environment; at times the solar wind impinges directly on Mercury’s surface. Also, due to the small-scale size of Mercury’s magnetosphere, the circulation time for the Dungey cycle is measured in minutes, compared to hours at Earth.

However, the viscous interaction is recognized as an important method of solar wind-magnetosphere coupling at Earth, and other planets, and many observations of the formation of K-H vortices at the magnetopause have been presented. Making direct observations at the magnetopause has been revealed as very important in understanding the modes of interaction with the solar wind, rather than just relying on system-wide estimates. These observations tell us that the viscous interaction is important as well as system-wide information such as the presence of a long magnetotail and that the cross-polar cap potential is 10s of kV during northward IMF.

It is important to highlight that these models (and the derivation of equation (3)) describe a more-or-less steady process of convection. However, explosive releases of energy in the magnetosphere known as “auroral substorms” (Akasofu, 1964) and “flux transfer events,” where transient localized bundles of magnetic flux are reconnected and peel off the magnetopause during unsteady reconnection (Russell & Elphic, 1979), demonstrate that convection is not a steady process (Axford, 1969) and must be kept in mind when understanding solar wind-magnetosphere coupling.

The development of these theories was intimately tied to explaining aurorae, magnetic deviations, and other polar geophysical phenomena, but now have more wide-reaching implications, for example, on the development and maintenance of radiation belts. Figure 6 shows a system diagram of the energy sources/sinks, interactions leading to flows of energy, and reservoirs within the Earth-magnetosphere system (see, for example, Baumjohann & Paschmann, 1987). Some of the Poynting flux that crosses the magnetopause is directly transferred to the ionosphere via heating and Region 1 currents, and some is stored in the magnetotail lobes (as indicated in Figure 1a). The rest is converted to wave energy stored within the magnetospheric cavity (e.g., Kelvin-Helmholtz waves radiating wave energy into the magnetosphere; Kivelson & Pu, 1984). From the magnetotail there are further magnetosphere-ionosphere interactions that can deposit energy in the ionosphere, or it can be lost via outflows and closed magnetic field structures known as plasmoids that exit the magnetotail, or the energy can be transferred to the ring current via injections of energized plasma and energetic particles. Losses from the ring current include precipitation of energized plasma into the ionosphere.

Solar Wind: Interaction With Planets

Figure 6. System diagram showing energy flows in the terrestrial magnetosphere (after Baumjohann & Paschmann, 1987). Acronyms: FLR: field-line resonances; FAC: field-aligned currents (including Birkeland currents); WPI: wave-particle interactions.

2. Part Two

Modern research into the solar wind-planet interaction is very broad, yet there are several areas that have seen a great deal of attention and which have some threads that go back to the earliest days of the field. In part two we examine the viscous interaction as an important factor in understanding the response of Earth’s magnetosphere to the solar wind, but also, asa potential dominant mode of interaction further out in the solar system (2.1/2.4), system-level coupling of the solar wind and magnetosphere and the science of Space Weather (2.2), the interaction of the solar wind with bodies that do not possess a strong internally-generated magnetic field (2.3), and the application of the ideas in this article for exoplanetary systems around other stars (2.5).

2.1 Viscous Magnetospheric Interactions

The Kelvin-Helmholtz instability (KHI) is one of the main focuses of contemporary research into the viscous interaction. Named after Lord Kelvin and Hermann Ludwig Ferdinand von Helmholtz, the KHI can develop in fluids where there is a velocity shear, either within the body of the fluid or at an interface between two different fluids. In the magnetosphere, these velocity shears act at the flanks of the magnetopause where there is a velocity shear between the magnetosheath and magnetospheric plasma. Contemporary research is also focused on the viscous interaction across multiple length scales in the plasma, from the fluid scale to the electron scale.

In inviscid fluids, a velocity shear is always unstable to the KHI with viscosity stabilizing the instability. In a collisionless plasma, magnetic stresses and the compressibility have a stabilizing effect. Equation (6) is the instability criterion for the KHI in a magnetized plasma, where the subscripts indicate different sides of a boundary and k is the wave vector. When B||k, magnetic tension stabilizes the KHI but no such stabilizing influence is exerted if the Bk (Chandrasekhar, 1961). For purely northward/southward IMF, the growth rate for the KHI should be equal, however, KHI waves are seen more frequently under northward IMF. This is resolved by understanding that during northward IMF the LLBL has a higher density, which reduces the density gradient across the magnetopause, and so the KHI condition can be more easily met.

[k(v1v2)]2>(ρ1+ρ2ρ1ρ2)[(kB1)2+(kB2)2]
(6)

An important element of contemporary research is the realization that during the nonlinear evolution of the KHI, complex vortices form that enhance the transport of momentum across the magnetopause. It has also been recognized that additional mechanisms (e.g., diffusion) are required to provide mass as well as momentum transport. The formation of KH vortices was found to be a possible trigger for magnetic reconnection in the narrow current sheets within the vortices (Nykyri & Otto, 2001), thus enabling additional mass transport (Hasegawa et al., 2004). Contemporary work also investigates how KH waves and vortices can launch magnetosonic waves inside the magnetosphere that can deposit energy, convert to Alfvén waves, and couple to the ionosphere via field-aligned currents.

2.2 Space Weather and Solar Wind-Magnetosphere Coupling Functions

The modern applied science of Space Weather focuses on understanding and forecasting the effects of geomagnetic activity on humans and human systems, such as power networks, satellite infrastructure, global positioning, and radiation risks for airline passengers and staff. Although a relatively modern discipline, the field has its roots in attempts to understand geomagnetic and auroral phenomena and their relationship to the solar wind, indeed the term “Space Weather” first appeared in the late 1950s, although variants were in use as early as 1847 (Cade & Chan-Park, 2015).

One major element of Space Weather is understanding how solar-wind parameters control the state of the magnetosphere. The principal mass source for the Earth’s magnetosphere is the solar-wind mass flux (ρv), and the principal energy sources that drive geomagnetic activity are the solar-wind kinetic-energy flux (ρv3/2) and Poynting flux (vBz2/μ0). At Earth, the mass, kinetic energy, and Poynting fluxes are 1012 protons m-2 s-1, 0.4 mW m-2, and 0.009 mW m-2, respectively, with totals of 50 kg s-1, 5 TW, and 0.1 TW over the cross section of the magnetopause. Although these mass and kinetic energy fluxes are smaller at Jupiter by a factor of 25 (the squared ratio of the heliocentric distances of Jupiter and Earth), their totals are much larger (104 kg s-1, 103 TW, and 10 TW) due to the much larger scale size of the Jovian magnetosphere, caused by a combination of a smaller dynamic pressure and larger magnetic field strength in equation (1). The kinetic-energy flux impinging on the magnetosphere is converted into electromagnetic energy at the bow shock and magnetopause, which then drives geomagnetic activity. The efficiency of this conversion depends on further properties of the upstream medium, including the solar-wind Mach number, which affects energy conversion at the bow shock, and the upstream interplanetary-magnetic-field orientation, which affects reconnection at the magnetopause. In Earth’s magnetosphere, this energy is extracted and stored, and can be instantaneously/spontaneously released during events known as substorms.

Geomagnetic activity is often captured using a number of different indices that measure the state of different parts of the system. For example, the Disturbance Storm Time (Dst) index measures the strength of Earth’s ring current, and the planetarische Kennziffer (planetary index) Kp introduced by Julius Bartels (1899–1965) measures the strength of auroral current systems. Early attempts to understand the state of the magnetosphere via geomagnetic indices, in terms of the energy and mass input into the system, gave way to the idea of coupling functions that relate solar-wind parameters to values of geomagnetic indices.

Snyder, Neugebauer, and Rao (1963) were the first to study a correlation between geomagnetic indices and solar wind, finding a positive correlation between the Kp index and the speed of the solar wind. Hirshberg and Colburn (1969) found a correlation with the north-south (Bz) component of the IMF. Reflecting Dungey’s ideas about southward IMF and dayside reconnection, Arnoldy (1971) introduced the so-called half-wave rectifier function, instead of the full Bz in correlating solar-wind parameters and geomagnetic activity, where Bz=Bz for Bz<0, and zero otherwise. These early correlations gave way to the idea of coupling functions, with various combinations of upstream parameters. Burton, McPherron, and Russell (1975) derived such an empirical relationship between ρ,ν, and IMF Bz, and the Dst index. Since then, other authors have examined various combinations of ρ,ν, and IMF Bz, some of which equate to physical quantities such as the solar-wind motional electric field, vBz. The “Akasofu epsilon” parameter equation (7) is one coupling function involving the Poynting flux and a continuous, sin2θ2, approximation to the half-wave rectifier (Perreault & Akasofu, 1978), where θ is the “clock angle” of the magnetic field, zero when orientated northward, and 180° when southward.

ϵ=vswB2sin4θ2
(7)

Vasyliūnas et al. (1982) presented a theoretically derived power-transfer function based on three elements: the size of the magnetospheric obstacle, the kinetic-energy flux, and a dimensionless transfer function. Vasyliūnas et al. chose a transfer function of the form MA2αsin4θ2, where MA is the Alfvén Mach number of the solar wind and α‎ is an empirical parameter to be determined through a fit to data. Two interesting limits for this coupling function are α=0, where the magnetic field is unimportant (kinetic-energy flux is the primary energy source), and α=1 where we recover a version of Akasofu’s epsilon parameter. Finch and Lockwood (2007) evaluated a variety of these coupling functions on different time scales from a day to a year, and show that the formulation of Vasyliūnas et al. (1982) offers the best correlation with α‎~0.4–0.3.

Increasingly, forecasting methods are using techniques and methodologies from nonlinear systems and machine learning, including the use of neural networks (Munsami, 2000), linear filters (McPherron, Hsu, & Chu, 2015), NARMAX (nonlinear autoregressive moving average with exogenous inputs) models (Boynton, Balikhin, & Billings, 2015), and autoregressive Gaussian processes (Chandorkar, Camporeale, & Wing, 2017) in an attempt to develop forecast models that can adapt to noisy and/or incomplete inputs. Although these methods do not include a rigorous physical basis (e.g., Vasyliūnas et al., 1982), they have proven effective at forecasting and play roles in space-weather prediction systems. In addition to forecasting geomagnetic indices, the fluxes of radiation-belt particles near geostationary orbit are a strong focus for forecasting using both nonlinear methods and more physically motivated models. One difficulty is that energy may be stored for a variable length of time, and possibly released randomly, leading to a “waiting-time distribution” (Borovsky, Nemzek, & Belian, 1993). Coupling models are beginning to include such time-history effects where the magnetosphere does not respond instantaneously. In a similar vein, the efficacy of coupling functions can be considered over differing timescales, from instantaneous values to those averaged over days to years (e.g., Finch & Lockwood, 2007).

While these studies are insightful into the solar wind-magnetosphere interaction and provide important forecasts, a full understanding of this interaction requires a clear understanding of the physical processes operating at the magnetopause, for example, the details of magnetic reconnection under different parameter regimes. While a great deal of effort is currently focused on forecasting the effects of large coronal mass ejections on geomagnetic activity, however, an important future growth area is also in the long-term effects of the background solar wind.

2.3 Induced Magnetospheres

Many bodies in the solar system that do not have strong internally generated magnetic fields, including Venus, Pluto, comets, and Saturn’s largest moon Titan, interact differently with the solar wind. The basic physics also applies to the interaction of natural satellites with their parent magnetospheres; the required ingredient is a flowing magnetized plasma. Examples of such moon-magnetosphere interactions include most of the natural satellites at the giant planets. The interaction of the solar wind (or a flowing magnetized plasma) with a planetary body that lacks an internally generated magnetic field can also be broadly split into interactions with airless bodies; for example, many of Saturn’s icy moons are essentially airless bodies and bodies with thick atmospheres, as are Venus and Saturn’s moon Titan. It should be noted that although Mars and the Moon lack a global magnetic field, regions of their crust do have remnant crustal magnetic fields that add further structure to their solar-wind interaction. The nature of the interaction is also crucially dependent on the upstream environment. For example, Mars and Venus are usually immersed in the supersonic solar wind, whereas the majority of the major satellites at the giant planets are usually inside their parent-planet’s magnetospheres. Exceptions include Titan, which has been seen in the solar wind (e.g., Bertucci et al., 2015) and the magnetosheath of Saturn, and Oberon at Uranus. The upstream environment inside the magnetosphere is different from that in the solar wind; the magnetic field strength is usually higher, the Mach numbers of the plasma are usually subsonic and sub-Alfvénic, although Callisto and Triton are sometimes in a trans- or super-Alfvénic flow, and Io is sometimes in a supersonic flow (Arridge et al., 2011; Kivelson et al., 2004). The partitioning of pressure between dynamic pressure, thermal pressure, and magnetic pressure is also usually different.

At the Moon, and other airless bodies, the incident solar wind is absorbed by the lunar soil (regolith) and a wake forms downstream, gradually refilling with distance from the Moon (Figure 7a). Absorption of solar-wind ions into the regolith was suspected as early as the mid-1960s from the analysis of meteorites and was confirmed in preliminary analyses of Apollo 11 samples that showed high abundances of noble gases (Pillinger, 1979). Although solar-wind ions only penetrate several 10s of nm (up to around 100 nm, dependent on energy) into lunar materials, it is thought that the regolith may contain a record of the solar-wind flow over geological timescales. Such surface modification is also active in natural satellites at both Jupiter and Saturn, for example, Europa (Paranicas, Carlson, & Johnson, 2001) and Mimas and Tethys (e.g., Howett, Spencer, Hurford, Verbiscer, & Segura, 2012).

Solar Wind: Interaction With Planets

Figure 7. Interactions of the solar wind (or other flowing magnetized plasmas—indicated by beige regions) with (a) inert bodies with no atmosphere producing a plasma wake (pink), (b) bodies with an ionosphere (e.g., Venus, Mars, and Titan) (after Saunders & Russell, 1986) with the formation of a bow shock and magnetopause (green lines) with a magnetosheath in-between (light green), (c) formation of Alfvén wings (indicated in pink) in subsonic flow (after Neubauer, 1980). In each figure, thin red lines and arrows indicate plasma flows, teal lines and arrows indicate magnetic field lines, and the thick red lines and arrows in (c) indicate Alfvén and MHD slow mode wave characteristics.

This interaction is modified by the presence of a conducting interior. For a body with a low conductivity, the magnetic field simply diffuses through the interior, but when the conductivity is high, eddy currents are induced in the interior which exclude the external magnetic field. The induced magnetic field from those eddy currents then modifies the interaction. At the Moon, the induced field was measurable on the surface by the Apollo missions. When combined with the magnetic field in lunar orbit (the inducing field) measured by Explorer 35, an estimate of the size of the conducting lunar core could be made (Sonett, 1982). Induction also played an important role in one of the key discoveries in planetary science in the mid-to-late 1990s and early 2000s, that of conducting subsurface oceans inside the natural satellites at Jupiter detected by their induced magnetic fields (e.g., Khurana et al., 2009).

An induced magnetosphere forms around bodies with a substantial atmosphere and ionosphere (Figure 7b). In this situation, the ionosphere acts as a barrier to the external flow and a bow shock forms between the solar wind and the planet; the barrier between the magnetosheath and the induced magnetosphere is called the ionopause and lies just above the ionosphere. A further barrier also exists above the ionopause where magnetic flux accumulates and magnetic-field lines drape around the ionosphere more strongly, which is known as the Induced Magnetic Boundary, or sometimes Magnetic Pileup Boundary. On the nightside, an induced magnetotail is formed by the magnetic-field lines “draping” around the obstacle. Venus’s induced magnetosphere has been studied in great detail by a range of missions that have visited the Cytherian system, including Soviet Venera and U.S. Mariner and Pioneer Venus missions. For these induced magnetospheres, the pressure-balance relation (1) is modified to a balance between the solar-wind dynamic pressure and the thermal pressure in the ionosphere, with the thermal pressure and magnetic pressure in the solar wind playing smaller roles. Under high levels of solar-wind driving, the magnetic field can be pushed through the topside ionosphere and potentially down into the insulating neutral atmosphere below. When trapped in the ionosphere, the interplanetary magnetic-field lines are tied into the ionosphere, forming a “memory” of previous solar-wind conditions, where they may diffuse away over a period of time. But during that time they may also participate in the pressure balance with the solar wind.

The solar wind-planet interaction at Mars and Venus has received special attention due to the role of the solar-wind interaction in driving atmospheric escape via “non-thermal” processes, both at the present epoch and over geological timescales, which may be important in studying hydrological processes on Mars. One such process is the escape of ions that are produced outside the induced magnetosphere when a molecule or atom from the neutral atmosphere is ionized. This process is known as pickup. Charged particles gyrate around magnetic-field lines and the size of the gyration (“gyroradius”) depends on the magnetic-field strength, the mass and charge of the particle, and its speed. At Mars and Venus, the gyroradius is of the same order as the radius of the planet, so particles can gyrate around the planet and be lost to the solar wind. At other planets, the gyration is much smaller and the particles remain trapped. Reconnection is another process that can occur, which contributes to the mass-loss rate. Current estimates for the non-thermal mass-loss rate are of the order of 2–3 kg/s at Mars (Jakosky et al., 2018) and ~0.1 kg/s at Venus (Futaana, Wieser, Barabash, & Luhmann, 2017), although these loss rates are solar-cycle dependent and have considerable uncertainty.

The cometary interaction is an extreme case of an atmosphere-type interaction. In contrast to Mars or Venus, the atmosphere is not gravitationally bound to the nucleus. Gas produced from the nucleus flows outward, and by conservation of mass should lead to a density profile that falls as 1/r2 as appropriate for spherical outflow from a point-like source. However, these particles are also subjected to ionization processes that act as a loss term, and so the actual density profile takes the form,

n(r)=Q4πr2vexp[rτv]
(8)

where v is the expansion rate of the gas, Q is the production rate of gas, and τ‎ is the ionization or loss rate of the particles. The production rate Q depends on both the comet and its distance to the Sun, but ranged from 3 kg/s at 3 AU to 103 kg/s at perihelion (1.24 AU) for comet 67P/Churyumov–Gerasimenko (Hansen et al., 2016). The outflowing gas produces a very extended region around the comet and a large ionosphere. Apart from a bow shock, there are two boundaries between the solar wind and the comet. The first is a “contact surface” boundary, where the dynamic pressure of the solar wind is balanced by the dynamic pressure of the outflowing cometary gas, but the comet atmosphere still extends beyond the contact surface and can be ionized by the solar wind and other processes. The additional boundary is where the composition of the plasma changes from cometary (dominated by water and its dissociation products) to solar wind and is known as the cometopause.

Alfvén wings (Figure 7c) are nonlinear standing (in the rest frame of the body) Alfvén waves generated by an interaction with a conducting obstacle, and are most noticeable in interactions at lower Mach numbers, especially subsonic environments such as the Galilean moons. Alfvén waves travel away from the interaction region along characteristics (CA+ and CA in Figure 7c) at an angle to the local magnetic field, which is equal to tan1MA for the special case of perpendicular flow; thus, smaller Mach numbers have larger angles between the Alfvén wings and the magnetic field (Neubauer, 1980). Although mostly discussed in the interactions of the Galilean satellites and Titan with the Jovian and Saturnian magnetosphere, Alfvén wings have also been observed in the solar wind at Earth when MA is small (Chané, Saur, Neubauer, Raeder, & Poedts, 2012) and corresponded to a period of very quiet geomagnetic activity, in spite of southward IMF conditions. This suggests a very different mode of solar wind-planet interaction.

2.4 Giant Planet-Solar Wind Interaction

The role of the solar wind in driving the giant-planet magnetospheres is not as clear as the terrestrial magnetosphere for three main reasons: (a) magnetospheres of the giant planets have significant internal plasma and energy sources; (b) solar-wind properties are different at large heliocentric distances and magnetopause processes may operate in a different parameter regime; and (c) generally the upstream solar-wind conditions are not routinely measured.

As at Earth, Jupiter and Saturn impose corotation on their parent magnetospheres; however, because Jupiter and Saturn rotate more rapidly and magnetospheric motions driven by the solar wind are weaker, the region of corotation is much more extended compared to Earth’s magnetosphere. For example, at Jupiter the region of closed streamlines in Figure 4b dominates most of the magnetosphere, with a superimposed region of circulation driven by the Dungey cycle thought to play a minor role. Although the magnetospheres of Jupiter and Saturn are thought to be mainly internally driven, coincident observations of the magnetosphere, solar wind, and aurorae of Jupiter and Saturn have revealed that solar wind-planet coupling is at work; in particular, the variation of the size and brightness of Saturn’s main aurorae is known to change with solar-wind conditions (Crary et al., 2005). Coupling functions, as used in terrestrial research, are used to study the solar wind–planet interaction, although study of the outer planets is limited since simultaneous measurements inside the magnetosphere and inside the solar wind are very limited; 12ρv2 and vBz are thought to be the most directly important quantities in determining the influence of the solar wind on Saturn’s magnetosphere (Crary et al., 2005).

One main debate that exists in the literature centers on the Dungey cycle and the role of magnetic reconnection versus viscous and rotational effects; of particular debate is the efficiency of reconnection, which decreases as MA increases equation (4). Detailed theory and simulations show two effects act to suppress or reduce the rate of reconnection: diamagnetic suppression due to a difference in plasma beta across the magnetopause (Swisdak, Rogers, Drake, & Shay, 2003), and flow shear suppression due to flow shears adjacent to the magnetopause (Cassak & Otto, 2011). Diamagnetic suppression is an important consideration at the outer planets because MA increases with heliocentric distance and magnetosheath plasma beta is strongly affected by the Mach number of the bow shock. Although the efficiency has been debated in the literature, evidence for magnetic reconnection at the magnetopause of Jupiter and Saturn has been presented in numerous studies, both directly at the magnetopause (e.g., Huddleston, Russell, Le, & Szabo, 1997; Jasinski et al., 2016; McAndrews et al., 2008) and remotely in the cusp at high latitudes (e.g., Jasinksi et al., 2014). Masters (2015) used a detailed analysis of the reconnection process at the magnetopause to show that the half-wave rectifier was a reasonable coupling function at Saturn. If reconnection is operating, the question remains: what is its dynamical influence compared to rapid planetary rotation? McComas and Bagenal (2007) proposed an alternative method of interaction with the solar wind, suggesting that true regions of open flux at Jupiter would be very small and that closure would be via reconnection on the magnetopause rather than in the magnetotail, although this view has been challenged.

Another area of debate is the role of the viscous interaction at the giant planets. A number of authors have investigated which regions of the magnetopause are unstable to the KHI and which regions can undergo magnetic reconnection (e.g., Desroche, Bagenal, Delamere, & Erkaev, 2012) and reveal that large regions of the magnetopause are not able to reconnect unless the fields are completely anti-parallel, whereas there are large regions that are unstable to the KHI. The flattened shape of the Jovian magnetosphere also affects the flow of the solar wind around the magnetosphere and affects the conditions for reconnection at the magnetopause. This has led some to suggest that the coupling between the solar wind and giant-planet magnetospheres may be more strongly driven by a viscous interaction than a Dungey-type interaction, with reconnection playing a role in KH vortices.

Uranus and Neptune are poorly explored but are expected to be highly variable with a non-steady solar-wind interaction. This variability is driven by their asymmetrical internal magnetic fields (e.g., the magnetic poles are closer to the equator than at other planets) and they have large obliquities. This produces large changes in the orientation of the magnetic field, relative to the solar wind, over diurnal and seasonal cycles and, in general, the simplified sketches presented in Figures 1 and 3 do not apply. These asymmetries have a number of broad consequences: (a) the competition between corotation and solar-wind convection is not as straightforward; they may not necessarily work against one another; (b) solar wind-magnetosphere coupling might occur in a pulsed/variable fashion over a rotation of the planet because of the changing orientation of the magnetic field; and (c) sources of gas from natural satellites and rings do not necessarily lie in the same plane as the plasma, which can affect the internal sources of plasma. The importance of the viscous interaction and the lower efficiency of magnetic reconnection are also being applied to understand the interaction of the solar wind with these Ice Giants. These magnetospheres are poorly understood, but some of these ideas were examined using the Voyager 2 flybys in 1986 and 1989, and work continues with computational simulations and remote observations of the aurorae.

2.5 Stellar Wind-Exoplanet Interaction

The exploration of solar wind-planetary interactions in our own solar system and the detection of exoplanets has stimulated interest in the structure of exoplanetary magnetospheres and how they interact with stellar winds. Jupiter’s magnetic field was first detected by its auroral radio emissions in the 1950s and so the possibility for detecting and characterizing exoplanets from their auroral radio emissions has gained much attention. The auroral radio emissions themselves are thought to be generated by a plasma instability known as the Electron Cyclotron Maser Instability (e-CMI) which generates radio emissions with a particular polarization and at a frequency dependent on the strength of the magnetic field where the radio emissions are generated. Thus, the detection of auroral radio emissions from an exoplanet can give an estimate of the magnetic-field strength of the planet and insight into its stellar-wind interaction. An advantage of radio is that auroral radio emissions from magnetized exoplanets are expected at kilometer and decameter wavelengths (~300 kHz–30 MHz) which are bright against a stellar radio spectrum (Zarka, 1998).

The exploration of Jupiter and Saturn by Voyager’s Grand Tour allowed an estimation of the efficiency of conversion of solar-wind kinetic energy flux into auroral radio power. Desch and Kaiser (1984) showed that the efficiency was quite low, of the order 10-6, but that this conversion was remarkably uniform between Earth, Jupiter, and Saturn when accounting for the different scale sizes of each magnetosphere and the magnetic-field strength of each planet. Desch and Kaiser (1984) used these results to construct a Radiometric Bode Law relating solar-wind energy input into auroral radio power—drawing an analogy with Bode’s law for planetary magnetic fields. Searches for auroral exoplanet radio emissions started with Bastian, Dulk, and Leblanc (2000) and at the time of writing only one positive detection has been made (Vedantham et al., 2020). Part of the difficulty lies in the very weak (at distances of 10s of light years) expected radio power and the ability to detect these radio emissions through the frequency cutoff imposed by Earth’s ionosphere.

This paucity of detections has also provided scope for more detailed consideration of the physics of stellar wind-exoplanet interaction mechanisms, much of which is borrowed from our understanding of solar-system environments, particularly moon-magnetosphere interactions. The star-exoplanet interaction has been broadly described using two main modes of interaction: reconnection with the stellar wind, and a homopolar generator/unipolar inductor. Magnetic reconnection in the stellar-wind interaction with close-in exoplanets has been discussed by a number of authors as a method for driving magnetospheric dynamics and also for producing hotspots in the stellar envelope that might be evidence for an unseen magnetized exoplanet (e.g., Ip, Kopp, & Hu, 2004; Jardine & Cameron, 2008; Nichols & Milan, 2016). Goldreich and Lynden-Bell (1969) considered the interaction of Io with Jupiter’s magnetosphere using a unipolar inductor model. In the context of a star-exoplanet interaction, it is assumed that the exoplanet is a good conductor (through the presence of an ionosphere or conducting interior, for example), and as such, the electric field in the exoplanet’s rest frame is zero. If the field lines are equipotentials, then the field lines connecting the exoplanet back to the star will slip relative to the planet. In the stellar reference frame, there will be an electric field directed across the exoplanet’s flux tube, driving current in the stellar atmosphere that must be closed via field-aligned currents and the exoplanet in its Alfvén wings. The Vedantham et al. (2020) detection appears to be a case of this type of interaction. Such stellar-exoplanet interactions may produce hotspots in the envelope of the star, may significantly heat the exoplanet interior through induction heating (Kislyakova et al., 2017), and may alter the orbits of exoplanets (Laine & Lin, 2012).

In all of these discussions, the size of the magnetosphere is an important factor, calculated in the usual manner by balancing the dynamic pressure of the stellar wind with the magnetic pressure of the planet. However, it is important to recognize that this may not apply in a close-in exoplanet where the stellar magnetic-field pressure may be larger than the dynamic pressure in the upstream flow, for example, additional terms are required in equation (1). Magnetic reconnection might be suppressed, similar to that argued at the giant planets, and this might be a function of spectral class and age. Bow shocks may also be detectable during transits that could provide constraints on planetary magnetic-field strengths, permitting a more detailed consideration of the stellar wind-magnetosphere interaction (Vidotto, Jardine, & Helling, 2011).

The position of the planet and the stellar-wind regime in which it is immersed is crucial. For example, it has been argued that the e-CMI might not be able to operate efficiently in the dense magnetosphere of a “hot Jupiter” close to its parent star (Daley-Yates & Stevens, 2018) or the Radiometric Bode Law scaling might not apply when inside a stellar corona with a subsonic regime (Jardine & Cameron, 2008), or the scaling may saturate when a hot Jupiter is driven very strongly by a stellar wind (Nichols & Milan, 2016). Some work has been done to try to understand these effects, but more work remains.

2.6 Conclusions

Planetary magnetospheres are complex systems with many interacting elements. Great progress has been made in the last 50 years due to combinations of ground- and space-based observatories together with monitors of the solar wind that allow us to more uniquely understand various processes. This integration of heterogeneous datasets is one of the field’s strengths, but also one of its challenges in an era of Big Data.

At a systems level, there is a slow movement toward a more detailed consideration of the time history of solar-wind parameters, energy storage and release, and statistical distributions of release times. However, the coupling physics is generally poorly understood, especially the details of viscous interaction mechanisms. Most studies rely on two-dimensional conceptual sketches of magnetic reconnection, whereas more detailed three-dimensional theories are required, especially at the outer planets. Detailed understanding of these magnetopause processes is essential in detailed modeling at the system level, but it is difficult to apply this when different mechanisms may be operating in different locations on the magnetopause, a surface area in excess of 1010 km2 at Earth and 1014 km2 at Jupiter. Yet these challenges are important when trying to understand the physics of the near-Earth space environment which has an impact on our technologically advanced civilization. Comparisons between magnetospheres where reconnection is very important (e.g., Mercury and Earth vs. Jupiter and Saturn), where viscous processes are important (e.g., Jupiter and Saturn), where internal driving is important (e.g., Jupiter and Saturn), and across different length scales (e.g., Mercury vs. Earth vs. Saturn vs. Ganymede) allow us to try to unpick the physical dependencies on the various parameters (e.g., field strength, external environment, rotation rate). Comparisons of more symmetrical magnetospheres (e.g., Earth and Saturn) with Uranus and Neptune enable us to understand the effects of large asymmetries.

The field has made important connections to other fields in considering the interaction between the solar wind, magnetosphere, and planetary atmospheres, surfaces, and interiors. Specific examples of areas of study include the effect of oxygen outflow into Earth’s magnetosphere during geomagnetic storms, the heating of planetary atmospheres by magnetosphere-ionosphere coupling and its effects on climate, the escape of volatiles on geological timescales, and the effect on planetary interiors.

Although a number of studies consider stellar wind-exoplanet interactions with a more first-principles approach, many studies involve relatively crude scaling from solar-system contexts without modification to account for the varying environments at different exoplanets. More meaningful theoretical development is required to make more definite contributions to exoplanet detection and characterization.

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