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date: 27 October 2020

# Solar Physics: Overview

## Abstract and Keywords

Solar physics is one of the liveliest branches of astrophysics at the current time, with many major advances that have been stimulated by observations from a series of space satellites and ground-based telescopes as well as theoretical models and sophisticated computational experiments.

Studying the Sun is of key importance in physics for two principal reasons. Firstly, the Sun has major effects on the Earth and on its climate and space weather, as well as other planets of the solar system. Secondly, it represents a Rosetta stone, where fundamental astrophysical processes can be investigated in great detail. Yet, there are still major unanswered questions in solar physics, such as how the magnetic field is generated in the interior by dynamo action, how magnetic flux emerges through the solar surface and interacts with the overlying atmosphere, how the chromosphere and corona are heated, how the solar wind is accelerated, how coronal mass ejections are initiated and how energy is released in solar flares and high-energy particles are accelerated. Huge progress has been made on each of these topics since the year 2000, but there is as yet no definitive answer to any of them. When the answers to such puzzles are found, they will have huge implications for similar processes elsewhere in the cosmos but under different parameter regimes.

# Introduction to the Sun

The Sun is an ordinary yellow dwarf star of spectral type G2 V in the Milky Way Galaxy with an absolute magnitude of 4.8. It is a hot ball of glowing plasma whose gravity holds it together and keeps the planets and minor bodies of the solar system in orbit around it. It was born from a contracting interstellar gas cloud about 5 billion years ago, when the core temperature became large enough that hydrogen could be fused to helium. The Sun is now about half-way through its 10-billion year hydrogen-burning phase on the main sequence. When the core hydrogen has been used up, fusion will continue in a shell around a helium core and the Sun will expand to become a red giant, which will eventually collapse to a white dwarf.

The nearness of the Sun to us makes it unique among the 100 billion stars of our galaxy, and it is of crucial importance in two respects. On the one hand, it has profound effects on the climate and space weather of the Earth and so influences us in many subtle ways as well as providing energy and warmth for life. On the other hand, it continues to act as a Rosetta stone for astronomy, since many of the fundamental cosmic processes can be well understood by studying them on the Sun in much greater detail than elsewhere and so unravelling the way they operate across the Universe.

The overall physical properties of the Sun are as follows:

• it was born 4.6×109 yr ago (only about 60 million years before the Earth);

• its mass $(M⊙)is=1.99×1030kg$, which is 330,000 times that of the Earth;

• its radius $(R⊙)$ is 695.5 Mm (= 695,500 km), where 1 Mm (megametre) = 106m, and so it is 109 times the radius (6 Mm) of the Earth;

• its mean density is 1.4×103 kg m-3, which is similar to the Earth’s mean density of 5.5×103 kg m-3;

• the pressure at the Sun’s surface is 0.2 times the Earth’s atmospheric pressure at sea-level;

• the mean distance of the Sun from Earth, called an astronomical unit (AU), is 1.496×1011 m, i.e., 149.6 million km (or 93×106 miles), which takes light 8 min to travel and is roughly 215 $R⊙$;

• the gravitational acceleration $(g⊙)$ at the surface of the Sun is 274 m s-2, which is 27 times greater than at the Earth’s surface; this gives rise to an escape velocity from the Sun’s surface of 618 km s-1;

• the radiation emitted by the Sun (i.e., its luminosity, $L⊙$) is 3.86×1026 W (= 3.86×1033 erg s-1), which amounts to about 1 kW m-2 at the surface of the Earth;

• the equatorial (synodic) rotation period is 26.24 days, giving the Sun an equatorial velocity of 2 km s-1;

• its mass-loss rate is 109 kg s-1;

• its effective temperature is 5785 K.

The Sun possesses an interior whose structure has been revealed by helioseismology. In the core of the interior the energy is being generated by thermonuclear reactions, and in the convection zone the Sun’s magnetic field is generated by dynamo action (Cameron, 2020). The atmosphere consists: of the photosphere (Chitta, Smitha, & Solanki, 2020), a thin surface layer from which most of the light is emitted; the rarer and warmer chromosphere (and the much rarer and hotter corona). The corona expands out into the heliosphere as the solar wind, with a complex origin (Cranmer, 2019), structure (Owens, 2020), and interaction with the planets (Arridge, 2020).

The Sun is not constant, but many aspects of solar activity are related to the 11-year variation in numbers of sunspots (Rempel, forthcoming), called the solar cycle (van Driel-Gesztelyi & Owens, 2020). These include:

• prominences, huge cool magnetic flux tubes suspended above the solar surface;

• solar flares, brightenings of the atmosphere, which represent enormous releases of magnetic energy (Longcope, 2020);

• and coronal mass ejections, eruptions of mass and magnetic flux out into interplanetary space.

During the late twentieth century it became clear that much of the atmospheric structure and dynamic activity is caused by the magnetic field and may be modelled using magnetohydrodynamics, as described by, e.g., Priest (2014, 2020).

## Historical Development

The Sun has long been an object of fascination to humanity. In many civilisations it was worshipped as a god, and it has often captured the hearts of poets as a source of heat and light. Solar eclipses have given a sense of awe and wonder as recorded in observations from China since 2000 bc and from Greece since 600 bc. Early observations of sunspots were made in 325 bc in Greece and in 165 bc in China, leading to systematic sunspot observations from 23 bc in China.

Although Aristarchus of Samos had in 280 bc suggested that the Earth orbits the Sun in 280 bc, Ptolemy’s belief (ad 140) that the Sun orbits the Earth was held as standard for the next 1400 years. In 1530 Copernicus proposed that the Earth orbits the Sun in a circular orbit, but in 1609 Tycho Brahe’s observations were used by Kepler to formulate his laws of planetary motion and to discover that the orbit is in fact an ellipse with the Sun at the focus. Newton’s law of universal gravitation in 1666 explained why the orbital shape is elliptical. Although the existence of sunspots had been forgotten in the West, they were rediscovered in 1610 by Thomas Harriot in England and later by Fabricius, Scheiner and Galileo using the newly invented telescope. During the Maunder minimum from 1645 to 1715, very few sunspots were present (Eddy, 1976).

The nineteenth century saw huge advances in solar physics, partly because of the use of photography and spectroscopy. Fraunhofer discovered many lines in the solar spectrum (1814). Prominences were rediscovered at a solar eclipse (1842), having previously been mentioned in Russian chronicles. The 11-year cycle of sunspots was discovered by Schwabe (1843). Later, the sunspot cycle was found to be related to geomagnetic substorms, and Spörer’s law for the equatorward drift during the sunspot cycle in the appearance of sunspots was discovered (1858). The corona was photographed for the first time (1851), and the emission line of a new element, helium, was discovered during the eclipse of 1868.

The first solar flare was recorded by Carrington (1859) and had major terrestrial consequences, which are particularly relevant in view of the vulnerability of modern high-technology-based societies to space weather. The 1859 event was unusually powerful and was followed the next day by a worldwide disturbance of telegraph systems resulting from a major geomagnetic storm. This storm was associated with sparkling bright auroras that could be seen even at latitudes as low as England, France, and Italy. The next Carrington type event occurred on March 6, 1989, which again resulted in strong fluctuations of the Earth’s magnetic field and this time with serious power failure in Quebec.

The early twentieth century continued this age of discovery. Hale, Ellerman, Nicholson, and Joy (1919) used their newly invented spectroheliograph and found that sunspots possess a strong magnetic field. They also discovered laws of sunspot polarity, namely, that sunspot pairs have opposite polarity and leading sunspots have opposite polarity in the two hemispheres. Also, in the 1920s and 1930s, it was realised that hydrogen and helium dominate in the atmosphere and interior. The coronagraph was invented by Lyot in order to observe the corona without waiting for an eclipse (1930). Edlén built on work by Grotrian to show that the corona has a temperature of a million degrees Kelvin, since coronal emission lines are produced by highly ionised elements (1941). The magnetograph was invented by Babcock and Babcock (1952) and used to discover properties of the photospheric solar magnetic field. Global five-minute oscillations of the photosphere were discovered by Leighton (1960).

Early space satellites and rocket flights led to the discovery of coronal mass ejections (1972) and (on soft X-ray images) to coronal loops, coronal holes and X-ray bright points (1973). In the photosphere, kilogauss magnetic fields were discovered by Stenflo (1973) in the Quiet Sun. The 1990s and 2000s saw major observational developments from a series of space satellites, these include:

• Yohkoh (which revealed the dynamic nature of the corona),

• SoHO (the Solar and Heliospheric Observatory, which deduced the rotational structure of the solar interior and the properties of coronal mass ejections),

• TRACE (the Transition Region and Coronal Explorer, which gave a high-resolution view of the corona),

• RHESSI (the Reuven Ramaty High Energy Solar Spectroscopic Imager, which transformed our understanding of solar flares),

• STEREO A and STEREO B (which viewed coronal mass ejections in three dimensions simultaneously from two separate view angles), and

• SDO (the Solar Dynamics Observatory, which advanced our knowledge of solar activity and the solar interior).

At the same time, there were many advances in theoretical understanding. Cowling put forward a theory for sunspots and an anti-dynamo theorem (1934). Bethe proposed the carbon-nitrogen and proton-proton chains to explain the source of the Sun’s energy (1938). Biermann realised that the coolness of sunspots is created by the magnetic inhibition of convection (1941). Alfvén developed a theory for magnetic waves (1942). Parker produced major works on the dynamo and magnetic buoyancy (1955) and also proposed a model for the solar wind (1958), whose existence was later confirmed observationally (1959). The 1980s saw key advances in the theory of waves, instabilities, and the process of magnetic reconnection, whereby magnetic energy is converted into other forms. More recently, detailed models for many aspects of solar activity have been produced, and new surprises have come from the latest space satellites and ground-based telescopes.

# Structure of the Sun

A brief summary is given of the solar interior, helioseismology, the solar dynamo, the photosphere, the chromosphere, and the corona. There follows accounts of the different aspects of solar activity, namely, sunspots, the solar cycle, solar prominences, coronal mass ejections, and solar flares, as well as various aspects of the solar wind. More detailed accounts can be found in other articles of this Encyclopedia.

## Solar Interior

The Sun is a roughly spherical ball of plasma held together by gravity and consisting of mainly hydrogen (92% by number of atoms) and helium (8%) as well as the other elements such as carbon, nitrogen, and oxygen (totalling 0.1%). The solar interior is hidden from direct view, but its structure is being revealed by a new range of helioseismology techniques that analyze the properties of wave motions. It consists of three regions (Figure 1), namely, the core, the radiative zone, and the convection zone, where energy is transported outward by convection.

Figure 1. The structure of the Sun’s interior, indicating the sizes of the various regions and their temperatures (in K) and densities (in kg m-3), where $1R⊙=696$ Mm and distances are not drawn to scale.

The core acts like a giant thermonuclear reactor converting hydrogen into helium and generating 99% of the Sun’s energy mainly by the proton-proton chain. Five million tonnes of hydrogen are converted every second and, for every kilogram that is fused, 0.007 kg is converted into energy. The effect is to convert 4 protons (1H) into a helium nucleus (4He) by the reaction

$Display mathematics$

The helium nucleus is smaller in mass by 3% than the four protons, and the energy appears in two high-frequency γ‎-rays (26.2MeV) and two electron neutrinos (0.5 MeV). Due to their small non-zero mass, two-thirds of the electron neutrinos are converted into muon and tau neutrinos during their journey to the Earth, but the remaining one-third have been detected in observations from underground observatories such as Sudbury.

The core has a radius of 150,000 km and contains half of the Sun’s mass. The central temperature and density are 15 million K and 1.6 ×105 kg m-3, the latter being 13 times that of solid lead and producing a central pressure that is 230 billion times the Earth’s sea-level atmospheric pressure.

A standard model for the solar interior has been set up by assuming that the pressure $[p(r)]$, density $[ρ(r)]$, and temperature $[T(r)]$ depend only on radial distance $(r)$ from the center, and that the plasma is in hydrostatic and thermal equilibrium. One such model (Model S) due to Christensen-Dalsgaard et al. (1996) is shown in Figure 2.

Figure 2. A standard model (Model S) for the solar interior, showing the sound speed $(cs)$, temperature $((r/R⊙))$, density $(ρ)$ and pressure $(p)$ as functions of radius $(r/R⊙)$ in terms of their values at the solar center ($cs0=5.05×105ms−1$, $T0=1.57×107K$, $ρ0=1.54×105kgm−3$ and $p0=2.35×1016Nm−2$) (courtesy Jörgen Christensen-Dalsgaard).

In the radiative zone, the energy generated in the core leaks very slowly outward by radiative diffusion. An unimpeded photon travelling at the speed of light would take only two seconds to travel from the solar center to its surface. However, the solar interior is so incredibly opaque and there are so many absorptions and emissions of a photon that it takes instead 170,000 yr for the journey. In the process, the wavelength is increased from that of $γ$-rays to visible light at the solar surface.

At the convection zone, the temperature gradient becomes so large that the plasma becomes convectively unstable, and convection replaces radiative diffusion as the main mechanism for transporting the energy outward. Convection is able to transport heat because rising blobs of plasma are hotter than falling blobs. At the lower boundary of the convection zone there exists a strong shear layer, called the tachocline, where the Sun’s large-scale magnetic field is probably generated. Convective instability occurs due to the effect of buoyancy when the density in a rising blob of plasma is less than the ambient density, the condition for which is the Schwarzschild criterion, namely,

$Display mathematics$
(1)

where $γ$ is the ratio of specific heats, $g$ is the acceleration due to gravity, $m$ is the mean particle mass, and $kB$ is the Boltzmann constant.

The Sun does not rotate as a solid body but exhibits differential rotation, with the surface rotating faster at the equator (once every 26 days at a speed of 1.9 km s-1) than at the polar regions (once every 36 or 37 days). Also, there is a much weaker meridional flow of about 20 m s-1 directed from equator to poles at the solar surface, but the way this continues into the solar interior is unknown.

### Helioseismology

Our knowledge of the solar interior has been revolutionised by deductions from observed solar oscillations using helioseismology. Before that, our understanding of the solar interior was based on models that used the solar mass, radius, and luminosity, together with an assumed solar age and an initial helium abundance. Five-minute oscillations of the photosphere were discovered by Leighton, Noyes, and Simon (1962). Later they were realised to be standing acoustic waves formed within the convection zone (Frazier, 1968) and a rich spectrum of overtones was observed for high-degree modes and small wavelengths (Deubner, 1975). Also, low-degree modes that penetrate much deeper into the interior were discovered (Claverie, Isaak, McLeod, van der Raay, & Cortes, 1979). The way in which they could be used to deduce properties of the solar interior was soon recognised and were used to improve the estimate of the convection zone depth from 150 Mm to 200 Mm (Gough, 1977). Since then, improved observations have come from ground-based networks such as BiSON and GONG and from spacecraft such as SoHO.

The main oscillations are acoustic waves (called p-modes) around five-minutes period which propagate many times around the Sun and are refracted as they propagate into the solar interior, eventually being turned back toward the surface at a depth that depends on the wavelength, being deeper for longer wavelengths. The sound speed is about 7 km s-1 at the photosphere and 500 km s-1 at the solar center, giving a sound-travel time through the Sun of about two hours.

As well as give the internal temperature structure, a new discovery from helioseismology has been surprising maps of the internal rotation rate (Figure 3). It was expected that an extrapolation from the surface values would give a rotation that is constant on cylinders, but instead it was found to be constant on cones through the convection zone at mid-latitudes (Schou et al. 1998). The radiative zone is rotating at a roughly constant rate equal to the surface value at a latitude of 40°, which produces a strong shear layer (the tachocline) at the base of the convection zone. Another shear layer exists just below the photosphere.

Figure 3. A meridional cut through the solar interior, showing the rotation rate deduced from rotational splitting of normal modes. Rotation times are indicated on three thick curves (after Schou et al., 1998).

Local helioseismology refers to a series of techniques that complement the methods of global seismology. Whereas the latter treats disturbances as global normal modes, local helioseismology regards them as propagating modes (Duvall et al., 1997) and has been used to determine the properties just below the surface. For example, time-distance seismology determines the travel time between pairs of points on the solar surface and has detected meridional flows below the surface and inflows toward active regions.

### Solar Dynamo

The magnetic field of the Sun as a whole would diffuse away through the plasma by ohmic diffusion on a time-scale that is similar to the age of the Sun, and so most of the magnetic field that was present when the Sun was formed would by now have decayed away. It is therefore thought that the presently observed cyclic magnetic field of the Sun is generated somehow by dynamo action. Many observed aspects of the magnetic field need to be explained such as: the 11-year cycle in sunspot number; the fact that sunspots are restricted to two belts of latitude that migrate toward the equator during the cycle; a leading spot always has the same polarity as others in the northern hemisphere during one cycle and is opposite to those in the southern hemisphere; a leading spot is closer to the equator than a following spot; northern polar fields are opposite to southern polar fields and reverse in sign near sunspot maximum.

The first major step in the theory of dynamos was the anti-dynamo theorem of Cowling (1934), which ruled out a wide class of configurations by stating that a steady axisymmetric magnetic field cannot be maintained by dynamo action. If one considers separately the toroidal and poloidal magnetic field of the solar interior, it was clear that differential rotation would stretch out poloidal magnetic flux and so generate new toroidal flux by the so-called $ω$-effect (Figure 4), but the main problem was to understand how the poloidal flux can be generated.

Figure 4. The generation of poloidal magnetic field by the $ω$-effect, namely, the effect of differential rotation on the toroidal magnetic field. Light arrows indicate magnetic field lines and dark ones the shear flow.

Parker made two ground-breaking steps in the 1950s. First of all, he suggested that magnetic buoyancy would cause magnetic flux tubes to rise through the convection zone and form pairs of oppositely directed sunspots when they break through the solar surface (Figure 5; Parker, 1955a). Then he suggested that many small cyclonic motions would create poloidal flux from toroidal flux by the so-called $α$-effect (Parker, 1955a), which could be modelled by the addition of a term $[∇×(αB)]$ to the mean induction equation, where $α$ is constant (Figure 6).

Figure 5. The effect of magnetic buoyancy in causing a magnetic flux tube to rise through the convection zone and create a pair of oppositely directed sunspots where it breaks through the solar surface.

Figure 6. The $α$-effect, whereby rising, twisting motions create poloidal flux from toroidal flux.

A more systematic treatment of Parker’s ideas was presented by Steenbeck, Krause, and Rädler (1966), who developed a mean field formalism for the effect on the mean magnetic field of small-scale turbulent flows that are not mirror symmetric, such as when the Coriolis force produces a mean helicity. Their resulting mean induction equation for the poloidal magnetic field $〈B〉$ has the form

$Display mathematics$

where $η$ is the magnetic diffusivity, $β$ is a turbulent magnetic diffusivity and $α$ represents Parker’s $α$-effect.

In contrast to this mathematical treatment, a more qualitative and observationally motivated approach was proposed to generate the poloidal field by Babcock (1961) and Leighton (1969). They suggested that when sunspot fields decay, their tilt (Joy’s law) implies that they provide a new large-scale poloidal field.

In the 1970s, a host of kinetic $α−ω$ dynamos was created that solved the induction equation alone. The general belief was that the dynamo was acting throughout the convection zone and that any sufficiently rapid complex motions would tend to produce kinematic dynamo action. However, the 1980s saw a re-assessment of $α−ω$ dynamos due to several developments: it was realised that the required strength for the fields (>104G) meant that they are too strong to be acted on by turbulence throughout the convection zone and they rise too quickly through the convection zone; the measurements of internal rotation $Ω(R)$ from helioseismology disagreed with the expectation from dynamo models that $dΩ/dR<0$; and doubts were expressed about the derivation of $α$.

As a result of these doubts, two possibilities were proposed for a large-scale dynamo, with the poloidal field generated either in the tachocline or near the solar surface. The first was a tachocline dynamo operating at the base of the convection zone (Parker, 1993; Spiegel & Weiss, 1980) and the second was a flux transport dynamo as a development of the Babcock–Leighton ideas in which an $ω$-effect operates in the tachocline and an $α$-effect near the photosphere (Dikpati & Choudhuri, 1994). Recently, the flux-transport ideas have been put on a firm foundation by Cameron and Schüssler (2015, 2017), who set up a quantitative model and proved a theorem that evaluates the rate of change of toroidal flux in terms of an integral over the solar surface; the theory predicts that the strength of one solar cycle correlates with the polar fields at the end of the previous cycle, in agreement with observations.

## Solar Atmosphere

The surface layer of the Sun from which most of the light is emitted is a few 100 km thick and is called the photosphere. It represents the top of the convection zone and has a temperature of around 6,000 K. The density falls exponentially with distance from the base of the photosphere and the temperature decreases from 6,600 K to a minimum value of 4,400 K at a height of 500 km and then increases (Figure 7). This increase continues through the chromosphere, slowly rising to around 10,000 K, and subsequently suddenly increasing to 1 MK or more in the corona.

Figure 7. A schematic for the mean value of temperature and density as a function of height in the solar atmosphere according to the VAL model (courtesy Eugene Avrett). Note, however, that in practice the atmosphere is highly inhomogenous, dynamic and time-varying.

The region at intermediate temperatures of 100,000 K is called the transition region, but it is not a static layer at all: rather, it represents the small amount of plasma that is dynamically increasing or decreasing its temperature as it passes rapidly between chromospheric and coronal values. Indeed, the whole atmosphere is not a series of static plane-parallel layers, but is highly inhomogeneous and is continually moving and changing its temperature and density.

The outer corona is expanding outward as the solar wind, which fills the heliosphere. Typical plasma densities decrease from 1023m-3 in the photosphere to 1019m-3 in the chromosphere, 1015m-3 in the transition region, 1012m-3 at a height of 1 $R⊙$ in the corona, and 107m-3 at 1 AU.

The photosphere emits a continuous spectrum with many superimposed dark absorption lines, formed at specific wavelengths when light is absorbed by the overlying atmosphere. Some absorption lines come from the chromosphere and most of the spectral lines from the transition region and corona are emission lines, often in the UV and EUV region. Spectral lines are invaluable in providing information on the physical properties of the atmosphere, such as the temperature and density (from the intensity), the velocity (from Doppler shifts), the unresolved turbulent motions (from the line width), and the magnetic field (from Zeeman and Hanle effects).

### Photosphere

Several kinds of convective motion are seen in the photosphere with different length and time scales, namely, granulation, mesogranulation, supergranulation, and giant cells. Superimposed on these are five-minute oscillations and large-scale differential rotation and meridional flow.

Several million granules cover the solar surface and consist of bright hot rising (0.5–1.5 km s-1) plasma in the centers of small convection cells and dark cool falling plasma around their boundaries. They are typically 1 Mm across with a typical lifetime of 5–10 min. Supergranules show up best as a pattern of horizontal motions (350 m s-1) with typical sizes of 30 Mm and lifetimes of one to two days. Mesogranules have parameters intermediate between granules and supergranules. Faculae are small patches brighter than normal near the limb, which represent the edges of granules seen obliquely. Outside active regions they form a network along supergranule boundaries.

Figure 8. A typical line-of-sight photospheric magnetic field map, with bright and dark areas representing positive and negative fields, respectively. Label (1) points to polar field, (2) a large-scale unipolar field, (3) an active region, (4) an ephemeral region and normal network, (5) a remnant active region, (6) enhanced network field (from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO), courtesy of NASA/SDO and the HMI science team).

The photospheric magnetic field is shown in Figure 7, indicating the different types of field, which exist over a wide range of strengths and scales, and showing two sunspot bands north and south of the equator. At small scales, there is a strong kilogauss component that is vertical and occupies less than 5% of the surface and is located mainly along supergranule boundaries. It consists of tiny magnetic elements or intense flux tubes that have field strengths of 1 kG, fluxes of 3×1017 Mx and diameters of 100 km. In addition, weaker, more horizontal internetwork fields are present in the interior of supergranule cells with field strengths of 100–300 G. Recently, it has been discovered from the Sunrise Mission that kG fields are also present inside supergranule cells at the boundaries of granules (Lagg et al., 2010; Solanki, 2017; Solanki et al., 2011).

There are several large-scale patterns of magnetic field. At the boundaries of supergranule cells, a supergranular network consists of a mixture of weak and strong fields, which concentrate especially at the junctions between several supergranule cells. Ephemeral regions are small bipolar regions of flux emergence which last for half a day and are carried toward the network where they contribute a majority of the flux. They have a typical flux of 1019 Mx and often give rise to X-ray bright points in the corona.

Active Regions are large-scale regions of flux emergence with a mean field of a few 100 G and fluxes of 1019–1023 Mx that surround sunspot groups. Like sunspots, they form two bands north and south of the equator. Large-scale unipolar areas extend over several 100 Mm in latitude and each possess a dominant polarity; many of them are formed when active regions decay, spread out and drift toward the poles. Coronal holes exist in the corona above some large photospheric unipolar regions, such as near the poles.

### Chromosphere and Transition Region

The chromosphere consists of plasma that is being continually accelerated, heated, and cooled as cool jets are accelerated upwards at 104K at the network in such a way that some of the plasma continues to transition-region temperatures and most flows back down to the surface. An even smaller fraction of the plasma is heated up to coronal temperatures, some of which flows out as the solar wind in regions that are magnetically open. The magnetic field of the photospheric network spreads out to fill the whole chromosphere and corona.

At the solar limb spicules show up with the chromosphere in the $Hα$ line consisting of a forest of at least 100,000 cool rising jets. Type I spicules reach speeds of 10–50 km s-1 and heights 3–5 Mm before falling back down. They possess lifetimes of 3–10 min, diameters 120–700 km, temperatures 10,000–15,000 K and densities 1017m-3. Type II spicules are more dynamic (30–150 km s-1), longer (2–10 Mm), have shorter lifetimes (10–180 sec), and they fade from view rather than fall. Type II’s dominate in coronal holes and the quiet Sun, whereas both type I’s and type II’s are present in active regions.

On the solar disc, however, the chromosphere in $Hα$ is dominated by long dark thin structures called fibrils, arching over supergranules or extending from sunspots. The disc counterparts of type I spicules are dynamic fibrils or dark mottles at supergranule junctions, whereas those of type II’s are faint bright waving straws or rapid blue-shift events.

### Corona

The corona may be observed in white light only during a solar eclipse (Figure 9a), since it is a million times weaker than the dazzling brightness of the solar disc. It shows up as a faint halo, about as bright as the full Moon, caused by scattering of photospheric light off electrons (the K-corona) and dust (the F-corona). The K-corona, which dominates within 2.3 $R⊙$, is proportional to electron density and so is brighter where there is more plasma. There is only one total solar eclipse per year lasting about three minutes, observed in a narrow strip across the Earth’s surface only about 100 km wide, and so in 1930 Lyot invented the coronagraph to create artificial eclipses using a telescope with an occulting disc to blot out the photosphere. Coronagraphs were subsequently used in ground-based observatories and space missions such as Skylab and STEREO and have been invaluable in giving detailed understanding of the corona.

Figure 9. Images of the solar corona seen (a) in photospheric white light that is scattered mainly off electrons during a solar eclipse near solar maximum [courtesy High Altitude Observatory (HAO), University Corporation for Atmospheric Research (UCAR), Boulder, Colorado. UCAR is sponsored by the National Science Foundation] and (b) direct in soft X-rays from the Yohkoh satellite (courtesy Saku Tsuneta), which was a Japanese solar mission, developed and launched by ISAS/JAXA, Japan, with NASA and SERC/PPARC (UK) as international partners.

It was realised in the late 1930s by Grotrian and Edlén that many coronal emission lines are due to highly ionized states of known elements such as iron and that they imply the coronal temperature is roughly 106K. The corona therefore emits thermally in the X-ray region and may be imaged from space directly in soft X-rays or EUV (Figure 9b).

The structure of the corona is dominated by the magnetic field and possesses three types of structure: coronal loops, which are bright in soft X-rays and magnetically closed, connecting magnetic regions of the photosphere that have opposite polarity; coronal holes, which are relatively dark in soft X-rays and are magnetically open, allowing the fast solar wind to escape outward; and X-ray bright points, which are tiny features scattered over the whole disc.

Coronal loops vary in their size and properties, from large loops that interconnect different active regions down to tiny loops that are seen to make up X-ray bright points at high resolution. X-ray bright points have typical lifetimes of eight hours: they are caused by magnetic reconnection and are driven either by emerging flux in bipolar ephemeral regions or by flux cancellation between photospheric magnetic fragments of opposite polarity. One also sees coronal jets accelerated above magnetic flux concentrations by magnetic reconnection up to speeds of 200 km s-1, especially in coronal holes.

Coronal streamers are large bright structures seen in eclipse images which lie above prominences or active regions and consist of a large arcade of closed magnetic fields topped by a fan of open fields that are stretched open by the solar wind. The large-scale shape and brightness of the corona vary with the solar cycle such that in eclipse images at solar minimum there are large coronal holes near the North and South Poles and large streamers about the equator, whereas at solar maximum holes and streamers extend out in all directions.

Coronal holes are cooler and less dense than the surrounding corona. Polar holes may last for seven to eight years around solar minimum and possess a flux of 1023Mx and a field strength of 5–10 G. They also possess ray-like structures called polar plumes which arise from network magnetic flux concentrations. Coronal holes at lower latitudes are shorter lived and transient coronal holes may show up after coronal mass ejections for only a few hours or a day. Coronal holes lie above unipolar magnetic regions where there is a significant flux imbalance.

The corona loses energy by: heat conduction away from the temperature maximum toward the solar surface and interplanetary space; radiation; and mass outflow as the solar wind, giving total losses of about 1021W, which is a small fraction (0.001%) of the solar luminosity. The cause of the heating of the corona (as well as the chromosphere) is likely to be magnetic, but the mechanisms have still not been identified. Two main classes of heating mechanism have been proposed: magnetohydrodynamic waves generated in the convection zone, propagating out and dumping their energy either by resonant absorption or phase mixing; and magnetic reconnection in many small current sheets. Coronal magnetic field strengths lie between a few G and several 100 G, and may be obtained by extrapolating from observed photospheric values and assuming a potential, force-free or magnetohydrostatic field.

# Solar Activity

All aspects of solar activity depend on the Sun’s magnetic field. Active regions are regions of enhanced magnetic flux with fields of a few 100 Gauss, formed by flux emergence and occupying two bands north and south of the equator and within $±30o$ of it. In the chromosphere, as viewed in $Hα$, active regions show up as bright plages. Within a mature active region, one usually finds dark regions in the photosphere of extremely strong magnetic field called sunspots. In the corona, an active region appears bright in X-rays and is both hotter and denser than the surroundings. The boundary between one polarity and the other is known as the polarity inversion line, which may be highly contorted for a complicated active region with many sunspots, but is less complex for a simple bipolar region.

Polarity inversion lines are an essential characteristic of the distribution of magnetic flux on the solar surface, which appear to wrap around the Sun’s surface much like the seams on a tennis ball. Their importance lies in the fact that coronal loops arch across them, and prominences lie along them, while eruptive solar flares and coronal mass ejections are associated with such prominences when they erupt.

Looking from the Earth, the right side of an active region is known as the preceding part and often contains a large sunspot (the p-spot), whereas the main spot in the left side, if it exists, is called a follower-spot (or f-spot). As an active region decays, its magnetic flux declines and its magnetic field becomes simpler and weaker, giving a remnant active region, showing up in the corona as a simple arcade of coronal loops joining one polarity to the other across the polarity inversion line.

Within or on the edge of an active region, or far from it, one finds cool, thin, dark ribbons in $Hα$ images called filaments when viewed from above or prominences when viewed on the limb. They represent cool dense plasma suspended in large-scale twisted magnetic flux tubes and located up in the corona, but with chromospheric temperatures. Occasionally, they will erupt and give rise to a huge ejection of magnetic flux and plasma known as a coronal mass ejection. When such eruptions take place from active regions they produce large solar flares.

Active regions exhibit many dynamic processes. Cool $Hα$ surges may be ejected upwards at speeds of 20–60 km s-1, lasting for 10–20 min, and either returning back along the same curved path or fading from view as it is heated. Coronal rain is cool plasma flowing down along magnetic field lines, whereas active-region transient brightenings are localised impulsive events in X-rays or EUV.

## Sunspots and the Solar Cycle

In the photosphere sunspots are cooler and darker than their environment because their strong magnetic fields inhibit convection (Figure 10a). They have typical diameters 3.5–60 Mm and possess a central dark umbra surrounded by a filamentary and less-dark penumbra. The umbra has 40% of the spot radius, 30% of the photospheric brightness and is 1,000–1,900 K cooler than the photosphere, whereas the penumbra has 80% of the photospheric brightness and is 250–400 K cooler than the photosphere. Spots of diameter 10 Mm (or 60 Mm) tend to last 2–3 (or 80–90) days.

Figure 10. (a) An image of a sunspot and (b) the overlying chromospheric superpenumbra with tick marks every 5 Mm from the Swedish Solar Telescope (courtesy Luc Rouppe van der Voort).

The magnetic field in the umbra is typically 2.8 kG, while the magnetic flux of a large spot is 1021Mx and of a large sunspot group is 2×1022Mx. 46% of sunspots are unipolar, 53% bipolar, and 1% complex. In $Hα$ around a mature spot one sees superpenumbral fibrils stretching out way beyond the penumbra, usually radial though sometimes spiralling (Figure 10b).

Sunspots exhibit different kinds of flow and fine-scale structure. Evershed flow is a radial outflow in the penumbra of 2.5 km s-1, which reverses its direction and becomes an inflow at chromospheric heights. A steady annular convection cell, called a moat exists around a mature sunspot, with a diameter 15–100 Mm and containing outflowing moving magnetic features at 1.5–1.8 km s-1. The umbra contains tiny bright features called umbral dots lasting 10 min–2 hr and having upflows of 1 km s-1, as well as a spectrum of umbral oscillations with periods of five and three min, respectively. The penumbral field has an interlocking comb structure, with bright filaments that are more vertical and become magnetic loops extending far from a sunspot, as well as dark filaments, some of which are low-lying and dip down to the surface within the penumbra, while others are slightly higher and reach to twice the spot radius.

The 11-year variation in sunspot number and in many aspects of solar activity is called the sunspot (or solar) cycle (Figure 11). This oscillation was discovered in 1843 by Schwabe but has now been extended back before modern sunspot records by using 14C proxy data from tree rings (back 26,000 yr) and 10Be from ice cores (back 50,000 yr). The incidence of Galactic cosmic rays on Earth is affected by solar activity and forms radioactive isotopes of these elements, which decay with half lives of 5730 and 1.5×106yr, respectively.

Figure 11. The 11-year cycle in sunspot number (yearly averaged) from 1610 to 2018. The Maunder minimum had very few sunspots (courtesy David Hathaway).

The cycle in sunspot numbers varies in period and in maximum value, the period varying between 7.3 and 17.1 yr (with an average of 10.9 yr), while the maximum varies between 49 and 201 (average 108). During the Maunder minimum from 1645 to 1715 (one of many grand minima that show up in proxy data) there were very few sunspots, and northern Europe was cooler than normal.

The Hale–Nicholson laws of polarity, obeyed by 97% of sunspot groups are:

• the polarity of leading spots remains the same for each 11-year cycle;

• every 11 years, the polarity reverses at the start of each new cycle;

• in the North and South Hemispheres, leading spots have the opposite polarity;

• the leading spots are closer to the equator.

Together, these laws suggest that active regions arise from a strong toroidal flux tube below the photosphere.

## Prominences

Prominences are suspended in the corona in huge magnetic flux tubes containing plasma that is 100 times denser and 100 times cooler than the surrounding corona. Outside active regions, they are large quiescent prominences, which consist of huge vertical sheets of plasma of temperature 7,500–9,000 K, density 1015–1017m-3, length 6–600 Mm, height 10–100 Mm and thickness 3–10 Mm. They also occur within active regions where the magnetic field is much stronger and the prominences are shorter, thinner and lower.

Quiescent prominences are highly filamentary and dynamic on small scales, consisting of fine-scale threads. The magnetic field is mainly horizontal with fields of 8–15 G, which increases with height and is inclined at a small angle (20–30°) to the prominence axis. They are located in highly sheared or weakly twisted magnetic fields above polarity inversion lines. At some time in its life, a prominence may become unstable or lose equilibrium and erupt from the Sun (Figure 12), often showing substantial twist in the process, much of which may be produced by reconnection during the eruption. Large quiescent prominences, on the one hand, may erupt slowly over the course of several hours and are accompanied by a coronal mass ejection as the whole of the overlying magnetic arcade and coronal streamer also erupts. Active-region prominences, on the other hand, tend to erupt much more rapidly, presumably because the magnetic forces are much stronger, and they are accompanied by two-ribbon solar flares.

Figure 12. An erupting prominence in He II 304, with the size of the Earth indicated, from AIA (Atmospheric Imaging Assembly) on SDO (Solar Dynamics Observatory) (courtesy of NASA/SDO and the AIA science team).

Prominences have potential wider importance for other areas of astrophysics as locations that can be studied in great detail, where radiative thermal instability or non-equilibrium is leading to their formation and where magnetic instability on non-equilibrium is later giving rise to eruptive behaviour.

## Coronal Mass Ejections and Solar Flares

Coronal mass ejections (CMEs) are eruptions of coronal streamers, driven by the magnetic field and with erupting prominences at their cores (Figure 13). When the prominence is in an active region a large two-ribbon flare accompanies it. The main difference between those from outside active regions and within active regions lies in the strength of the magnetic field, and so active-region eruptions are usually faster and often have more high-energy phenomena associated with them. In interplanetary space, CMEs show up as magnetic clouds or interplanetary coronal mass ejections and, when they head toward the Earth and interact with its magnetosphere, they often give rise to severe space weather effects. An Earthward directed CME takes two to five days to reach Earth, depending on its speed, but high-energy particles can make the journey in an hour or so.

Figure 13. Coronal mass ejection observed by LASCO (Large Angle and Spectrometric Coronagraph) on SoHO (Solar and Heliospheric Observatory) (courtesy of the LASCO consortium on SOHO, which is a project of international cooperation between ESA and NASA).

The frequency of CMEs varies with the solar cycle, from 0.5 per day during solar minimum to 6 per day during solar maximum. The magnetic flux of a CME is 1020–1022Mx, while its mass is 1011–4×1013kg and its kinetic energy is 1029–1032erg, about the same as a solar flare. The speed ranges between 20 km s-1 and 2,000 km s-1, with a mean of 300 km s-1 during solar minimum and 500 km s-1 at solar maximum.

Magnetic reconnection is likely to be key in the initiation of CMEs, since disconnected concave-upward structures are often observed in them and a thin bright ray often appears in their wake and lying above a set of hot coronal loops (called flare loops when a flare is present). The presence of supra-thermal counter-streaming electrons in interplanetary CMEs implies the magnetic field is still closed down to the Sun, but, by the time CMEs reach 5 AU, 50% of them have become disconnected from the Sun. It is also clear from energy considerations that only the coronal magnetic field possesses enough energy to explain the kinetic energy, heating and work done against gravity in a CME.

Large two-ribbon solar flares are highly complex and occur when a prominence and coronal mass ejection are ejected from an active region. They represent the most violent events in the solar system, and used to be defined as a brightening in chromospheric $Hα$, but they are now realised to be a rapid energy release in the corona of active regions, with subsequent effects in other parts of the electromagnetic spectrum such as chromospheric $Hα$.

During the preflare phase, the soft X-ray emission slowly increases in intensity, and an active-region prominence starts to rise. At the impulsive phase, which may last 102–103 sec, the intensity in soft X-rays and $Hα$ increases rapidly as the prominence rise suddenly speeds up, and high-energy effects appear such as a microwave and a hard X-ray burst associated with the acceleration of high-energy particles. The rise phase lasts for five minutes to one hour, with a rapid increase in intensity and the formation of two $Hα$ ribbons of emission on both sides of the polarity inversion line at the feet of a 107K coronal arcade glowing in soft X-rays. Finally, in the main phase, the coronal and chromospheric intensity declines over the course of an hour or sometimes more than a day, as the arcade of hot coronal loops rise and the $Hα$ ribbons separate, quickly at first and more slowly as the flare progresses.

During the rise phase, high-energy particles accelerated in the corona propagate outward and also downward, where they heat the footpoints of coronal loops and cause heated plasma to “evaporate” upwards and fill the coronal loops with hot dense plasma. During the main phase, this plasma subsequently cools and falls back down to the solar surface.

The energy conversion from magnetic to other forms (kinetic energy, heat, fast particles) varies in total from 1022 J (1029 erg) in a subflare to 6×1025J (6×1032erg) in a large event. The division into different forms varies, since some are more nonthermal than others and some have coronal mass ejections, when typically half the energy appears as radiant energy and half as the coronal mass ejection.

The overall scenario for what is happening in a large flare is that magnetic energy is stored in a highly sheared and twisted magnetic field until it goes unstable or loses equilibrium and erupts, which drives magnetic reconnection below a large rising magnetic flux rope around an erupting active-region prominence. As the reconnection continues, the flux and twist of the flux rope increase, and leave behind a rising arcade of very hot coronal loops with separating flare ribbons at their foot-points. Indeed, many observational features of flares are consistent with this widely accepted reconnection paradigm.

# Solar Wind

The outer solar corona is continously expanding outward as the solar wind, which was predicted by Parker and has been observed in situ by a range of spacecraft, starting with Luna I in 1959. The dominant energy loss from coronal holes is outward transport by the solar wind (600 W m-2) rather than downward conductive flux. Much of the solar wind is thought to originate at supergranule and granule boundaries, showing up as blueshifts of 3 km s-1 in the network. The Ulysses satellite revealed a two-fold nature of slow solar wind and fast solar wind, but the mass flux is the same in both (1012 m-2s-1).

At 1AU, the slow solar wind has a speed of 300–400 km s-1, while the electron density is 7×106 m-3 and the electron temperature is 2×105K. It is highly variable and comes from the boundaries of coronal holes and streamers near the equator at solar minimum but from small coronal holes and active regions at all latitudes at solar maximum. It originates in the corona rather than the photosphere. From the cusps of coronal streamers, faint blobs of plasma are continually released. The heliospheric current sheet that stretches from the top of a coronal streamer is warped and inclined at about 7° to the Earth’s orbit. Viewed from a spacecraft, it is known as a sector boundary and the whole pattern as sector structure, which delineates high-speed and low-speed streams that are continually interacting.

At 1AU, the fast solar wind is relatively steady and has a speed of 700–750 km s-1, which is less dense (2.5×106 m-3) than the slow wind. It originates low down in the photosphere of coronal holes and accelerates rapidly to half its terminal speed at 2–4 $R⊙$. At solar minimum, this is from polar regions, but at solar maximum it arises from narrow, slightly slower streams at all latitudes. The proton temperature is hotter than the slow solar wind but the electron temperature is the same. There is a preferential heating of heavy ions and of ions perpendicular to the magnetic field.

The solar wind is time-varying on many scales and consists mainly of electrons, protons, and $α$-particles (3–4%), while the magnetic field forms a spiral pattern. On large scales, coronal mass ejections involve the eruption of coronal arcades and streamers and make up 16% of the mass flux at solar maximum. On small scales, outwardly propagating magnetic fluctuations are continually present and tangential and rotational discontinuities are frequent.

At 1AU, the wind speed and density are 30% lower at solar minimum than solar maximum, while the magnetic field remains the same. Normal fast solar wind takes about five days to reach the Earth from the Sun, whereas a coronal mass ejection can make the journey in one or two days and sunlight takes only eight minutes. The solar wind interacts with the magnetospheres of the planets in complex and varied ways. At the Earth, on the front side of the magnetopause, this can involve flux transfer events, while in the geomagnetic tail reconnection leads to geomagnetic substorms and enhanced aurora. A wide variety of space weather effects occur in the Earth’s space environment, which are greatly enhanced by coronal mass ejections. Beyond the Earth’s orbit, the solar wind continues out to a heliospheric boundary with the interstellar medium at 50–100 AU.

## Models of Solar Wind

Parker (1958) considered a steady, isothermal, spherically symmetric expansion of the solar atmosphere and discovered solar wind solutions that pass through a sonic point (where the flow speed equals the isothermal sound speed) and join subsonic flows at the Sun with supersonic flows at large distances. Later, the solutions were generalized to include: polytropic solutions (where $p/ρα$ = constant, with $α>1$ a constant); an energy equation; the rotation of the Sun; a magnetic field (for which there are three critical points in place of the sonic point); and a nonradial expansion to model a coronal hole. Since the 2000s, the focus has been on developing models in two or three dimensions and on including kinetic effects (see, e.g., Priest, 2014).

As far as the mechanism for accelerating the wind, for the fast solar wind, wave turbulence models have been set up by Cranmer, van Ballegooijen, and Edgar (2007), and Cranmer and van Ballegooijen (2012). Convective motions in the photosphere generate MHD disturbances that propagate into the corona and develop into turbulence. A single-fluid model for propagation along an expanding flux tube was set up in which the waves are partially reflected, and the counter-propagating waves generate a turbulent cascade, in which energy is transferred from large to small scales where it dissipates. It was applied to a stretched dipole model for solar minimum and the heating rate was proportional to magnetic field strength. Later, the model was generalized to include a three-fluid model of electrons, protons, and heavy ions.

For the slow solar wind, the mechanism is not so clear. One possibility is the same as the fast solar wind but in many small transient coronal holes. Another is the continual reconnection of the small-scale complex solar magnetic field in transferring momentum and energy from closed field lines onto open ones or interchange reconnection between the large-scale open field of coronal holes and the closed field of coronal streamers. Furthermore, an S-Web model (Antiochos, DeVore, Karpen, & Mikić, 2007) suggests three-dimensional reconnection at a complex set of separators in the streamer belt (Titov, Mikic, Török, Linker, & Panasenco, 2012).

# Conclusion

Studying the Sun is a highly complex endeavor, involving a wide range of different specialities. Observationally, there is a wide range of different instrumentation on ground-based and space-based telescopes, which in turn leads to sophisticated data analysis techniques. In addition, creative applications of atomic physics and spectroscopy are central, as are the complementary disciplines of fluid mechanics, magnetohydrodynamics and collisionless plasma physics.

At present solar physics is in a vibrant state as great advances are being made in each of these areas in order to fathom the greatest mysteries of the subject. Indeed, at present many of the fundamental questions about the nature of the Sun have not yet been answered although huge progress has taken place since the late 2000s. These unresolved questions include: the nature of the solar dynamo and solar cycle; the way in which magnetic flux emerges through the solar surface and interacts with the overlying magnetized atmosphere; the magnetic heating of the corona to millions of degrees Kelvin; the acceleration of the slow and fast solar wind; the cause of coronal mass ejections and eruptive solar flares; and the acceleration of high-energy particles in solar flares.

Once answers to these major puzzles have been obtained, they will have profound implications for many other areas of astronomy, where magnetic field generation, heating of coronae, acceleration of winds, the nature of eruptions, and particle acceleration are occurring in a wide range of environments under different parameter regimes.

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