Coronal heating problem
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A corona ( coronas or coronae) is the outermost layer of a star's atmosphere. It consists of plasma. The
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
's corona lies above the chromosphere and extends millions of kilometres into outer space. It is most easily seen during a total solar eclipse, but it is also observable with a
coronagraph A coronagraph is a telescopic attachment designed to block out the direct light from a star so that nearby objects – which otherwise would be hidden in the star's bright glare – can be resolved. Most coronagraphs are intended to view t ...
.
Spectroscopic Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
measurements indicate strong
ionization Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecul ...
in the corona and a plasma temperature in excess of , much hotter than the surface of the Sun, known as the photosphere. The word ''corona'' is , in turn derived .


History

In 1724, French-Italian astronomer Giacomo F. Maraldi recognized that the aura visible during a solar eclipse belongs to the Sun, not to the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
. In 1809, Spanish astronomer José Joaquín de Ferrer coined the term 'corona'. Based in his own observations of the 1806 solar eclipse at Kinderhook (New York), de Ferrer also proposed that the corona was part of the Sun and not of the Moon. English astronomer
Norman Lockyer Sir Joseph Norman Lockyer (17 May 1836 – 16 August 1920) was an English scientist and astronomer. Along with the French scientist Pierre Janssen, he is credited with discovering the gas helium. Lockyer also is remembered for being the f ...
identified the first element unknown on Earth in the Sun's chromosphere, which was called
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
. French astronomer Jules Jenssen noted, after comparing his readings between the 1871 and 1878 eclipses, that the size and shape of the corona changes with the sunspot cycle. In 1930,
Bernard Lyot Bernard Ferdinand Lyot (27 February 1897 in Paris – 2 April 1952 in Cairo) was a French astronomer. Biography An avid reader of the works of Camille Flammarion, he became a member of the Société Astronomique de France in 1915 and made h ...
invented the
coronograph A coronagraph is a telescopic attachment designed to block out the direct light from a star so that nearby objects – which otherwise would be hidden in the star's bright glare – can be resolved. Most coronagraphs are intended to view t ...
, which allows viewing the corona without a total eclipse. In 1952, American astronomer
Eugene Parker Eugene Newman Parker (June 10, 1927 – March 15, 2022) was an American solar and plasma physicist. In the 1950s he proposed the existence of the solar wind and that the magnetic field in the outer Solar System would be in the shape of a Pa ...
proposed that the solar corona might be heated by myriad tiny 'nanoflares', miniature brightenings resembling solar flares that would occur all over the surface of the Sun.


Historical theories

The high temperature of the Sun's corona gives it unusual
spectral ''Spectral'' is a 2016 3D military science fiction, supernatural horror fantasy and action-adventure thriller war film directed by Nic Mathieu. Written by himself, Ian Fried, and George Nolfi from a story by Fried and Mathieu. The film stars ...
features, which led some in the 19th century to suggest that it contained a previously unknown element, "
coronium Coronium, also called newtonium, was the name of a suggested chemical element, hypothesised in the 19th century. The name, inspired by the solar corona, was given by Gruenwald in 1887. A new atomic thin green line in the solar corona was then con ...
". Instead, these spectral features have since been explained by highly ionized
iron Iron () is a chemical element with Symbol (chemistry), symbol Fe (from la, Wikt:ferrum, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 element, group 8 of the periodic table. It is, Abundanc ...
(Fe-XIV, or Fe13+).
Bengt Edlén Bengt Edlén (2 November 1906, Gusum – 10 February 1993, Lund) was a Swedish professor of physics and astronomer who specialized in spectroscopy. He was the first who identified the unknown coronal spectral lines in the Corona, which was u ...
, following the work of Grotrian (1939), first identified the coronal spectral lines in 1940 (observed since 1869) as transitions from low-lying
metastable In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball i ...
levels of the ground configuration of highly ionised metals (the green Fe-XIV line from Fe13+ at , but also the red Fe-X line from Fe9+ at ).


Physical features

The Sun's corona is much hotter (by a factor from 150 to 450) than the visible surface of the Sun: the photosphere's average temperature is around compared to the corona's 1 to 3 million
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...
. The corona is 10−12 times as dense as the photosphere, and so produces about one-millionth as much visible light. The corona is separated from the photosphere by the relatively shallow chromosphere. The exact mechanism by which the corona is heated is still the subject of some debate, but likely possibilities include induction by the Sun's magnetic field and magnetohydrodynamic waves from below. The outer edges of the Sun's corona are constantly being transported away due to open magnetic flux and hence generating the
solar wind The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sol ...
. The corona is not always evenly distributed across the surface of the Sun. During periods of quiet, the corona is more or less confined to the equatorial regions, with
coronal hole A coronal hole is a temporary region of relatively cool, less dense plasma in the solar corona where the Sun's magnetic field extends into interplanetary space as an open field.Freedman, Roger A., and William J. Kaufmann III. "Our Star, the Sun. ...
s covering the polar regions. However, during the Sun's active periods, the corona is evenly distributed over the equatorial and polar regions, though it is most prominent in areas with sunspot activity. The
solar cycle The solar cycle, also known as the solar magnetic activity cycle, sunspot cycle, or Schwabe cycle, is a nearly periodic 11-year change in the Sun's activity measured in terms of variations in the number of observed sunspots on the Sun's surfa ...
spans approximately 11 years, from
solar minimum Solar minimum is the regular period of least solar activity in the Sun's 11-year solar cycle. During solar minimum, sunspot and solar flare activity diminishes, and often does not occur for days at a time. On average, the solar cycle takes abou ...
to the following minimum. Since the solar magnetic field is continually wound up due to the faster rotation of mass at the Sun's equator (
differential rotation Differential rotation is seen when different parts of a rotating object move with different angular velocities (rates of rotation) at different latitudes and/or depths of the body and/or in time. This indicates that the object is not solid. In fl ...
), sunspot activity will be more pronounced at
solar maximum Solar maximum is the regular period of greatest solar activity during the Sun's 11-year solar cycle. During solar maximum, large numbers of sunspots appear, and the solar irradiance output grows by about 0.07%. On average, the solar cycle tak ...
where the magnetic field is more twisted. Associated with sunspots are
coronal loop In solar physics, a coronal loop is a well-defined arch-like structure in the Sun's atmosphere made up of relatively dense plasma confined and isolated from the surrounding medium by magnetic flux tubes. Coronal loops begin and end at two f ...
s, loops of magnetic flux, upwelling from the solar interior. The magnetic flux pushes the hotter photosphere aside, exposing the cooler plasma below, thus creating the relatively dark sun spots. Since the corona has been photographed at high resolution in the X-ray range of the spectrum by the satellite
Skylab Skylab was the first United States space station, launched by NASA, occupied for about 24 weeks between May 1973 and February 1974. It was operated by three separate three-astronaut crews: Skylab 2, Skylab 3, and Skylab 4. Major operations ...
in 1973, and then later by
Yohkoh Yohkoh (, ''Sunbeam'' in Japanese language, Japanese), known before launch as Solar-A, was a Sun, Solar observatory spacecraft of the JAXA, Institute of Space and Astronautical Science (Japan), in collaboration with space agencies in the NASA ...
and the other following space instruments, it has been seen that the structure of the corona is quite varied and complex: different zones have been immediately classified on the coronal disc. The astronomers usually distinguish several regions, as described below.


Active regions

Active regions are ensembles of loop structures connecting points of opposite magnetic polarity in the photosphere, the so-called coronal loops. They generally distribute in two zones of activity, which are parallel to the solar equator. The average temperature is between two and four million kelvin, while the density goes from 109 to 1010 particles per cm3. Active regions involve all the phenomena directly linked to the magnetic field, which occur at different heights above the Sun's surface: sunspots and
facula A facula (plural: faculae ), Latin for "little torch", is literally a "bright spot". The term has several common technical uses. It is used in planetary nomenclature for naming certain surface features of planets and moons,. and is also a type of ...
e occur in the photosphere; spicules, filaments and plages in the chromosphere; prominences in the chromosphere and transition region; and flares and
coronal mass ejection A coronal mass ejection (CME) is a significant release of plasma and accompanying magnetic field from the Sun's corona into the heliosphere. CMEs are often associated with solar flares and other forms of solar activity, but a broadly accept ...
s (CME) happen in the corona and chromosphere. If flares are very violent, they can also perturb the photosphere and generate a
Moreton wave A Moreton wave, Solar Tsunami, or Moreton-Ramsey wave is the chromospheric signature of a large-scale solar corona shock wave. Described as a kind of solar "tsunami", they are generated by solar flares. They are named for American astronomer Ga ...
. On the contrary, quiescent prominences are large, cool, dense structures which are observed as dark, "snake-like" Hα ribbons (appearing like filaments) on the solar disc. Their temperature is about –, and so they are usually considered as chromospheric features. In 2013, images from the High Resolution Coronal Imager revealed never-before-seen "magnetic braids" of plasma within the outer layers of these active regions.


Coronal loops

Coronal loops are the basic structures of the magnetic solar corona. These loops are the closed-magnetic flux cousins of the open-magnetic flux that can be found in coronal holes and the solar wind. Loops of magnetic flux well up from the solar body and fill with hot solar plasma. Due to the heightened magnetic activity in these coronal loop regions, coronal loops can often be the precursor to solar flares and CMEs. The solar plasma that feeds these structures is heated from under to well over 106 K from the photosphere, through the transition region, and into the corona. Often, the solar plasma will fill these loops from one point and drain to another, called foot points ( siphon flow due to a pressure difference, or asymmetric flow due to some other driver). When the plasma rises from the foot points towards the loop top, as always occurs during the initial phase of a compact flare, it is defined as chromospheric evaporation. When the plasma rapidly cools and falls toward the photosphere, it is called chromospheric condensation. There may also be
symmetric Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
flow from both loop foot points, causing a build-up of mass in the loop structure. The plasma may cool rapidly in this region (for a thermal instability), its dark filaments obvious against the solar disk or prominences off the Sun's limb. Coronal loops may have lifetimes in the order of seconds (in the case of flare events), minutes, hours or days. Where there is a balance in loop energy sources and sinks, coronal loops can last for long periods of time and are known as ''
steady state In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p' ...
'' or ''
quiescent Quiescence (/kwiˈɛsəns/) is a state of quietness or inactivity. It may refer to: * Quiescence search, in game tree searching (adversarial search) in artificial intelligence, a quiescent state is one in which a game is considered stable and unl ...
'' coronal loops ( example). Coronal loops are very important to our understanding of the current ''coronal heating problem''. Coronal loops are highly radiating sources of plasma and are therefore easy to observe by instruments such as ''
TRACE Trace may refer to: Arts and entertainment Music * ''Trace'' (Son Volt album), 1995 * ''Trace'' (Died Pretty album), 1993 * Trace (band), a Dutch progressive rock band * ''The Trace'' (album) Other uses in arts and entertainment * ''Trace'' ...
''. An explanation of the coronal heating problem remains as these structures are being observed remotely, where many ambiguities are present (i.e., radiation contributions along the line-of-sight propagation). '' In-situ'' measurements are required before a definitive answer can be determined, but due to the high plasma temperatures in the corona, ''in-situ'' measurements are, at present, impossible. The next mission of the NASA
Parker Solar Probe The Parker Solar Probe (PSP; previously Solar Probe, Solar Probe Plus or Solar Probe+) is a NASA space probe launched in 2018 with the mission of making observations of the outer corona of the Sun. It will approach to within 9.86 solar radii ...
will approach the Sun very closely, allowing more direct observations.


Large-scale structures

Large-scale structures are very long arcs which can cover over a quarter of the solar disk but contain plasma less dense than in the coronal loops of the active regions. They were first detected in the June 8, 1968, flare observation during a rocket flight. The large-scale structure of the corona changes over the 11-year solar cycle and becomes particularly simple during the minimum period, when the magnetic field of the Sun is almost similar to a dipolar configuration (plus a quadrupolar component).


Interconnections of active regions

The interconnections of active regions are arcs connecting zones of opposite magnetic field, of different active regions. Significant variations of these structures are often seen after a flare. Some other features of this kind are helmet streamers — large, cap-like coronal structures with long, pointed peaks that usually overlie sunspots and active regions. Coronal streamers are considered to be sources of the slow solar wind.


Filament cavities

Filament cavities are zones which look dark in the X-rays and are above the regions where Hα filaments are observed in the chromosphere. They were first observed in the two 1970 rocket flights which also detected ''coronal holes''. Filament cavities are cooler clouds of plasma suspended above the Sun's surface by magnetic forces. The regions of intense magnetic field look dark in images because they are empty of hot plasma. In fact, the sum of the
magnetic pressure In physics, magnetic pressure is an energy density associated with a magnetic field. In SI units, the energy density P_B of a magnetic field with strength B can be expressed as :P_B = \frac where \mu_0 is the vacuum permeability. Any magnetic fie ...
and plasma pressure must be constant everywhere on the
heliosphere The heliosphere is the magnetosphere, astrosphere and outermost atmospheric layer of the Sun. It takes the shape of a vast, bubble-like region of space. In plasma physics terms, it is the cavity formed by the Sun in the surrounding interstell ...
in order to have an equilibrium configuration: where the magnetic field is higher, the plasma must be cooler or less dense. The plasma pressure p can be calculated by the state equation of a perfect gas: p = n k_B T, where n is the particle number density, k_B the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
and T the plasma temperature. It is evident from the equation that the plasma pressure lowers when the plasma temperature decreases with respect to the surrounding regions or when the zone of intense magnetic field empties. The same physical effect renders sunspots apparently dark in the photosphere.


Bright points

Bright points are small active regions found on the solar disk. X-ray bright points were first detected on April 8, 1969, during a rocket flight. The fraction of the solar surface covered by bright points varies with the solar cycle. They are associated with small bipolar regions of the magnetic field. Their average temperature ranges from 1.1 MK to 3.4 MK. The variations in temperature are often correlated with changes in the X-ray emission.


Coronal holes

Coronal holes are unipolar regions which look dark in the X-rays since they do not emit much radiation. These are wide zones of the Sun where the magnetic field is unipolar and opens towards the interplanetary space. The high speed solar wind arises mainly from these regions. In the UV images of the coronal holes, some small structures, similar to elongated bubbles, are often seen as they were suspended in the solar wind. These are the coronal plumes. More precisely, they are long thin streamers that project outward from the Sun's north and south poles.


The quiet Sun

The solar regions which are not part of active regions and coronal holes are commonly identified as the quiet Sun. The equatorial region has a faster rotation speed than the polar zones. The result of the Sun's differential rotation is that the active regions always arise in two bands parallel to the equator and their extension increases during the periods of maximum of the solar cycle, while they almost disappear during each minimum. Therefore, the quiet Sun always coincides with the equatorial zone and its surface is less active during the maximum of the solar cycle. Approaching the minimum of the solar cycle (also named butterfly cycle), the extension of the quiet Sun increases until it covers the whole disk surface excluding some bright points on the hemisphere and the poles, where there are coronal holes.


Alfvén surface

The
Alfvén surface The Alfvén surface is the boundary separating the sun's corona from the solar wind defined as where the coronal plasma's Alfvén speed and the large-scale solar wind speed are equal. It is named after Hannes Alfvén, and is also called Alfvén c ...
is the boundary separating the corona from the
solar wind The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sol ...
defined as where the coronal plasma's
Alfvén speed Alfvén may refer to: People * Hannes Alfvén (1908–1995), Swedish plasma physicist and Nobel Prize in Physics laureate * Hugo Alfvén (1872–1960), Swedish composer, conductor, violinist, and painter * Marie Triepcke Krøyer Alfvén (1867–19 ...
and the large-scale solar wind speed are equal. Researchers were unsure exactly where the Alfvén critical surface of the Sun lay. Based on remote images of the corona, estimates had put it somewhere between 10 to 20 solar radii from the surface of the Sun. On April 28, 2021, during its eighth flyby of the Sun, NASA's
Parker Solar Probe The Parker Solar Probe (PSP; previously Solar Probe, Solar Probe Plus or Solar Probe+) is a NASA space probe launched in 2018 with the mission of making observations of the outer corona of the Sun. It will approach to within 9.86 solar radii ...
encountered the specific magnetic and particle conditions at 18.8 solar radii that indicated that it penetrated the Alfvén surface.


Variability of the corona

A portrait, as diversified as the one already pointed out for the coronal features, is emphasized by the analysis of the dynamics of the main structures of the corona, which evolve at differential times. Studying coronal variability in its complexity is not easy because the times of evolution of the different structures can vary considerably: from seconds to several months. The typical sizes of the regions where coronal events take place vary in the same way, as it is shown in the following table.


Flares

Flares take place in active regions and are characterized by a sudden increase of the radiative flux emitted from small regions of the corona. They are very complex phenomena, visible at different wavelengths; they involve several zones of the solar atmosphere and many physical effects, thermal and not thermal, and sometimes wide reconnections of the magnetic field lines with material expulsion. Flares are impulsive phenomena, of average duration of 15 minutes, and the most energetic events can last several hours. Flares produce a high and rapid increase of the density and temperature. An emission in white light is only seldom observed: usually, flares are only seen at extreme UV wavelengths and into the X-rays, typical of the chromospheric and coronal emission. In the corona, the morphology of flares is described by observations in the UV, soft and hard X-rays, and in Hα wavelengths, and is very complex. However, two kinds of basic structures can be distinguished: * ''Compact flares'', when each of the two arches where the event is happening maintains its morphology: only an increase of the emission is observed without significant structural variations. The emitted energy is of the order of 1022 – 1023 J. * ''Flares of long duration'', associated with eruptions of prominences, transients in white light and ''two-ribbon flares'': in this case the magnetic loops change their configuration during the event. The energies emitted during these flares are of such great proportion they can reach 1025 J. As for temporal dynamics, three different phases are generally distinguished, whose duration are not comparable. The durations of those periods depend on the range of wavelengths used to observe the event: * ''An initial impulsive phase'', whose duration is on the order of minutes, strong emissions of energy are often observed even in the microwaves, EUV wavelengths and in the hard X-ray frequencies. * ''A maximum phase'' * ''A decay phase'', which can last several hours. Sometimes also a phase preceding the flare can be observed, usually called as "pre-flare" phase.


Coronal mass ejections

Often accompanying large solar flares and prominences are coronal mass ejections (CME). These are enormous emissions of coronal material and magnetic field that travel outward from the Sun at over a million kilometers per hour, containing roughly 10 times the energy of the solar flare or prominence that accompanies them. Some larger CMEs can propel hundreds of millions of tons of material into
interplanetary space Interplanetary may refer to: * Interplanetary space, the space between the planets of the Solar System *Interplanetary spaceflight, travel between planets *The interplanetary medium, the material that exists in interplanetary space *The InterPlane ...
at roughly 1.5 million kilometers an hour.


Stellar coronae

Coronal stars are ubiquitous among the stars in the cool half of the Hertzsprung–Russell diagram. These coronae can be detected using
X-ray telescope An X-ray telescope (XRT) is a telescope that is designed to observe remote objects in the X-ray spectrum. In order to get above the Earth's atmosphere, which is opaque to X-rays, X-ray telescopes must be mounted on high altitude rockets, balloon ...
s. Some stellar coronae, particularly in young stars, are much more luminous than the Sun's. For example,
FK Comae Berenices FK Comae Berenices is a variable star that varies in apparent magnitude between 8.14 and 8.33 over a period of 2.4 days. It is the prototype for the FK Comae Berenices (FK Com) class of variable stars. The variability of FK Com stars may ...
is the prototype for the FK Com class of
variable star A variable star is a star whose brightness as seen from Earth (its apparent magnitude) changes with time. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as e ...
. These are giants of spectral types G and K with an unusually rapid rotation and signs of extreme activity. Their X-ray coronae are among the most luminous (''L''x ≥ 1032 erg·s−1 or 1025W) and the hottest known with dominant temperatures up to 40 MK. The astronomical observations planned with the
Einstein Observatory Einstein Observatory (HEAO-2) was the first fully imaging X-ray telescope put into space and the second of NASA's three High Energy Astrophysical Observatories. Named HEAO B before launch, the observatory's name was changed to honor Albert E ...
by Giuseppe Vaiana and his group showed that F-, G-, K- and M-stars have chromospheres and often coronae much like our Sun. The ''O-B stars'', which do not have surface convection zones, have a strong X-ray emission. However these stars do not have coronae, but the outer stellar envelopes emit this radiation during shocks due to thermal instabilities in rapidly moving gas blobs. Also A-stars do not have convection zones but they do not emit at the UV and X-ray wavelengths. Thus they appear to have neither chromospheres nor coronae.


Physics of the corona

The matter in the external part of the solar atmosphere is in the state of plasma, at very high temperature (a few million kelvin) and at very low density (of the order of 1015 particles/m3). According to the definition of plasma, it is a quasi-neutral ensemble of particles which exhibits a collective behaviour. The composition is similar to that in the Sun's interior, mainly hydrogen, but with much greater ionization of its heavier elements than that found in the photosphere. Heavier metals, such as iron, are partially ionized and have lost most of the external electrons. The ionization state of a chemical element depends strictly on the temperature and is regulated by the
Saha equation In physics, the Saha ionization equation is an expression that relates the ionization state of a gas in thermal equilibrium to the temperature and pressure. The equation is a result of combining ideas of quantum mechanics and statistical mechanics ...
in the lowest atmosphere, but by collisional equilibrium in the optically-thin corona. Historically, the presence of the spectral lines emitted from highly ionized states of iron allowed determination of the high temperature of the coronal plasma, revealing that the corona is much hotter than the internal layers of the chromosphere. The corona behaves like a gas which is very hot but very light at the same time: the pressure in the corona is usually only 0.1 to 0.6 Pa in active regions, while on the Earth the atmospheric pressure is about 100 kPa, approximately a million times higher than on the solar surface. However it is not properly a gas, because it is made of charged particles, basically protons and electrons, moving at different velocities. Supposing that they have the same kinetic energy on average (for the
equipartition theorem In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. T ...
), electrons have a mass roughly times smaller than protons, therefore they acquire more velocity. Metal ions are always slower. This fact has relevant physical consequences either on radiative processes (that are very different from the photospheric radiative processes), or on thermal conduction. Furthermore, the presence of electric charges induces the generation of electric currents and high magnetic fields. Magnetohydrodynamic waves (MHD waves) can also propagate in this plasma, even though it is still not clear how they can be transmitted or generated in the corona.


Radiation

Coronal plasma is optically-thin and therefore transparent to the
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) li ...
that it emits and to that coming from lower layers. The plasma is very rarefied and the
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
overcomes by far all the other length-scales, including the typical sizes of common coronal features. Electromagnetic radiation from the corona has been identified coming from three main sources, located in the same volume of space: * The K-corona (K for ''kontinuierlich'', "continuous" in German) is created by sunlight
Thomson scattering Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is the low-energy limit of Compton scattering: the particle's kinetic energy and photon frequen ...
off free
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
s;
doppler broadening In atomic physics, Doppler broadening is broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting (or absorbing) particles result in different Dop ...
of the reflected photospheric absorption lines spreads them so greatly as to completely obscure them, giving the spectral appearance of a continuum with no absorption lines. * The F-corona (F for Fraunhofer) is created by sunlight bouncing off dust particles, and is observable because its light contains the Fraunhofer absorption lines that are seen in raw sunlight; the F-corona extends to very high elongation angles from the Sun, where it is called the
zodiacal light The zodiacal light (also called false dawn when seen before sunrise) is a faint glow of diffuse sunlight scattered by interplanetary dust. Brighter around the Sun, it appears in a particularly dark night sky to extend from the Sun's direction ...
. * The E-corona (E for emission) is due to spectral emission lines produced by ions that are present in the coronal plasma; it may be observed in broad or forbidden or hot spectral emission lines and is the main source of information about the corona's composition.


Thermal conduction

In the corona thermal conduction occurs from the external hotter atmosphere towards the inner cooler layers. Responsible for the diffusion process of the heat are the electrons, which are much lighter than ions and move faster, as explained above. When there is a magnetic field the
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
of the plasma becomes higher in the direction which is parallel to the field lines rather than in the perpendicular direction. A charged particle moving in the direction perpendicular to the magnetic field line is subject to the Lorentz force which is normal to the plane individuated by the velocity and the magnetic field. This force bends the path of the particle. In general, since particles also have a velocity component along the magnetic field line, the Lorentz force constrains them to bend and move along spirals around the field lines at the
cyclotron A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. Lawrence, Ernest O. ''Method and apparatus for the acceleration of ions'', filed: Jan ...
frequency. If collisions between the particles are very frequent, they are scattered in every direction. This happens in the photosphere, where the plasma carries the magnetic field in its motion. In the corona, on the contrary, the mean free-path of the electrons is of the order of kilometres and even more, so each electron can do a helicoidal motion long before being scattered after a collision. Therefore, the heat transfer is enhanced along the magnetic field lines and inhibited in the perpendicular direction. In the direction longitudinal to the magnetic field, the thermal conductivity of the corona is : k = 20 \left(\frac\right)^\frac \approx 1.8~10^~\frac~ W m^K^ where k_B is the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...
, T is the temperature in kelvin, m_e is the electron mass, e is the electric charge of the electron, : \ln \Lambda = \ln \left(12\pi n \lambda_D^3 \right) is the Coulomb logarithm, and :\lambda_D = \sqrt is the
Debye length In plasmas and electrolytes, the Debye length \lambda_ (also called Debye radius), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each Debye length the charges are in ...
of the plasma with particle density n. The Coulomb logarithm \ln \Lambda is roughly 20 in the corona, with a mean temperature of 1 MK and a density of 1015 particles/m3, and about 10 in the chromosphere, where the temperature is approximately 10kK and the particle density is of the order of 1018 particles/m3, and in practice it can be assumed constant. Thence, if we indicate with q the heat for a volume unit, expressed in J m−3, the Fourier equation of heat transfer, to be computed only along the direction x of the field line, becomes : \frac= 0.9~10^~ \frac. Numerical calculations have shown that the thermal conductivity of the corona is comparable to that of copper.


Coronal seismology

Coronal seismology is a method of studying the plasma of the solar corona with the use of
magnetohydrodynamic Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydro­magnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magneto­fluids include plasmas, liquid metals, ...
(MHD) waves. MHD studies the dynamics of electrically conducting fluids — in this case, the fluid is the coronal plasma. Philosophically, coronal seismology is similar to the Earth's
seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
, the Sun's
helioseismology Helioseismology, a term coined by Douglas Gough, is the study of the structure and dynamics of the Sun through its oscillations. These are principally caused by sound waves that are continuously driven and damped by convection near the Sun's sur ...
, and MHD spectroscopy of laboratory plasma devices. In all these approaches, waves of various kinds are used to probe a medium. The potential of coronal seismology in the estimation of the coronal magnetic field, density
scale height In atmospheric, earth, and planetary sciences, a scale height, usually denoted by the capital letter ''H'', is a distance ( vertical or radial) over which a physical quantity decreases by a factor of e (the base of natural logarithms, approxima ...
, fine structure and heating has been demonstrated by different research groups.


Coronal heating problem

The coronal heating problem in
solar physics Solar physics is the branch of astrophysics that specializes in the study of the Sun. It deals with detailed measurements that are possible only for our closest star. It intersects with many disciplines of pure physics, astrophysics, and compu ...
relates to the question of why the temperature of the Sun's corona is millions of kelvins versus the thousands of kelvins of the surface. Several theories have been proposed to explain this phenomenon but it is still challenging to determine which of these is correct. The problem first emerged when Bengt Edlen and
Walter Grotrian Walter Robert Wilhelm Grotrian (21 April 1890 in Aachen; † 3 March 1954 in Potsdam) was a German astronomer and astrophysicist. Grotrian studied the emission line from the solar corona in the green region of the spectrum; this emission line co ...
identified Fe IX and Ca XIV lines in the solar spectrum. This led to the discovery that the emission lines seen during solar eclipses are not caused by an unknown element called "coronium" but known elements at very high stages of ionization. The comparison of the coronal and the photospheric temperatures of 6,000K, leads to the question of how the 200 times hotter coronal temperature can be maintained. The problem is primarily concerned with how the energy is transported up into the corona and then converted into heat within a few solar radii. The high temperatures require energy to be carried from the solar interior to the corona by non-thermal processes, because the
second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
prevents heat from flowing directly from the solar photosphere (surface), which is at about , to the much hotter corona at about 1 to 3 MK (parts of the corona can even reach ). Between the photosphere and the corona, the thin region through which the temperature increases is known as the transition region. It ranges from only tens to hundreds of kilometers thick. Energy cannot be transferred from the cooler photosphere to the corona by conventional heat transfer as this would violate the second law of thermodynamics. An analogy of this would be a light bulb raising the temperature of the air surrounding it to something greater than its glass surface. Hence, some other manner of energy transfer must be involved in the heating of the corona. The amount of power required to heat the solar corona can easily be calculated as the difference between coronal radiative losses and heating by thermal conduction toward the chromosphere through the transition region. It is about 1 kilowatt for every square meter of surface area on the Sun's chromosphere, or 1/ of the amount of light energy that escapes the Sun. Many coronal heating theories have been proposed, but two theories have remained as the most likely candidates: wave heating and
magnetic reconnection Magnetic reconnection is a physical process occurring in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnecti ...
(or nanoflares). Through most of the past 50 years, neither theory has been able to account for the extreme coronal temperatures. In 2012, high resolution (<0.2″)
soft X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30  ...
imaging with the High Resolution Coronal Imager aboard a sounding rocket revealed tightly wound braids in the corona. It is hypothesized that the reconnection and unravelling of braids can act as primary sources of heating of the active solar corona to temperatures of up to 4 million kelvin. The main heat source in the quiescent corona (about 1.5 million kelvin) is assumed to originate from MHD waves.
NASA The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the US federal government responsible for the civil List of government space agencies, space program ...
's
Parker Solar Probe The Parker Solar Probe (PSP; previously Solar Probe, Solar Probe Plus or Solar Probe+) is a NASA space probe launched in 2018 with the mission of making observations of the outer corona of the Sun. It will approach to within 9.86 solar radii ...
is intended to approach the Sun to a distance of approximately 9.5 solar radii to investigate coronal heating and the origin of the solar wind. It was successfully launched on August 12, 2018 and has completed the first 13 by fall of 2022 of the more than 20 planned close approaches to the Sun.


Wave heating theory

The wave heating theory, proposed in 1949 by Évry Schatzman, proposes that waves carry energy from the solar interior to the solar chromosphere and corona. The Sun is made of plasma rather than ordinary gas, so it supports several types of waves analogous to
sound waves In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
in air. The most important types of wave are magneto-acoustic waves and
Alfvén wave In plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of plasma wave in which ions oscillate in response to a restoring force provided by an effective tension on the magnetic field lines. Definition An Alfvén wave is ...
s. Magneto-acoustic waves are sound waves that have been modified by the presence of a magnetic field, and Alfvén waves are similar to
ultra low frequency Ultra low frequency (ULF) is the ITU designation for the frequency range of electromagnetic waves between 300 hertz and 3 kilohertz, corresponding to wavelengths between 1,000 to 100 km. In magnetosphere science and seismology, alternative defini ...
radio waves Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz ( GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (s ...
that have been modified by interaction with
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic part ...
in the plasma. Both types of waves can be launched by the turbulence of granulation and super granulation at the solar photosphere, and both types of waves can carry energy for some distance through the solar atmosphere before turning into
shock waves In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a med ...
that dissipate their energy as heat. One problem with wave heating is delivery of the heat to the appropriate place. Magneto-acoustic waves cannot carry sufficient energy upward through the chromosphere to the corona, both because of the low pressure present in the chromosphere and because they tend to be reflected back to the photosphere. Alfvén waves can carry enough energy, but do not dissipate that energy rapidly enough once they enter the corona. Waves in plasmas are notoriously difficult to understand and describe analytically, but computer simulations, carried out by Thomas Bogdan and colleagues in 2003, seem to show that Alfvén waves can transmute into other wave modes at the base of the corona, providing a pathway that can carry large amounts of energy from the photosphere through the chromosphere and transition region and finally into the corona where it dissipates it as heat. Another problem with wave heating has been the complete absence, until the late 1990s, of any direct evidence of waves propagating through the solar corona. The first direct observation of waves propagating into and through the solar corona was made in 1997 with the
Solar and Heliospheric Observatory The Solar and Heliospheric Observatory (SOHO) is a European Space Agency (ESA) spacecraft built by a European industrial consortium led by Matra Marconi Space (now Airbus Defence and Space) that was launched on a Lockheed Martin Atlas IIAS lau ...
space-borne solar observatory, the first platform capable of observing the Sun in the
extreme ultraviolet Extreme ultraviolet radiation (EUV or XUV) or high-energy ultraviolet radiation is electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths from 124  nm down to 10 nm, and therefore (by the Planck–E ...
(EUV) for long periods of time with stable
photometry Photometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electro ...
. Those were magneto-acoustic waves with a frequency of about 1 millihertz (mHz, corresponding to a wave period), that carry only about 10% of the energy required to heat the corona. Many observations exist of localized wave phenomena, such as Alfvén waves launched by solar flares, but those events are transient and cannot explain the uniform coronal heat. It is not yet known exactly how much wave energy is available to heat the corona. Results published in 2004 using data from the
TRACE Trace may refer to: Arts and entertainment Music * ''Trace'' (Son Volt album), 1995 * ''Trace'' (Died Pretty album), 1993 * Trace (band), a Dutch progressive rock band * ''The Trace'' (album) Other uses in arts and entertainment * ''Trace'' ...
spacecraft seem to indicate that there are waves in the solar atmosphere at frequencies as high as (10 second period). Measurements of the temperature of different
ions An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...
in the solar wind with the UVCS instrument aboard
SOHO Soho is an area of the City of Westminster, part of the West End of London. Originally a fashionable district for the aristocracy, it has been one of the main entertainment districts in the capital since the 19th century. The area was develo ...
give strong indirect evidence that there are waves at frequencies as high as , well into the range of human hearing. These waves are very difficult to detect under normal circumstances, but evidence collected during solar eclipses by teams from
Williams College Williams College is a private liberal arts college in Williamstown, Massachusetts. It was established as a men's college in 1793 with funds from the estate of Ephraim Williams, a colonist from the Province of Massachusetts Bay who was kill ...
suggest the presences of such waves in the 1– range. Recently, Alfvénic motions have been found in the lower solar atmosphere and also in the quiet Sun, in coronal holes and in active regions using observations with AIA on board the
Solar Dynamics Observatory The Solar Dynamics Observatory (SDO) is a NASA mission which has been observing the Sun since 2010. Launched on 11 February 2010, the observatory is part of the Living With a Star (LWS) program. The goal of the LWS program is to develop the ...
. These Alfvénic oscillations have significant power, and seem to be connected to the chromospheric Alfvénic oscillations previously reported with the Hinode spacecraft. Solar wind observations with the ''Wind'' spacecraft have recently shown evidence to support theories of Alfvén-cyclotron dissipation, leading to local ion heating.


Magnetic reconnection theory

The magnetic reconnection theory relies on the solar magnetic field to induce electric currents in the solar corona. The currents then collapse suddenly, releasing energy as heat and wave energy in the corona. This process is called "reconnection" because of the peculiar way that magnetic fields behave in plasma (or any electrically conductive fluid such as mercury or
seawater Seawater, or salt water, is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% (35 g/L, 35 ppt, 600 mM). This means that every kilogram (roughly one liter by volume) of seawater has appr ...
). In a plasma,
magnetic field lines A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
are normally tied to individual pieces of matter, so that the
topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
of the magnetic field remains the same: if a particular north and south magnetic pole are connected by a single field line, then even if the plasma is stirred or if the magnets are moved around, that field line will continue to connect those particular poles. The connection is maintained by electric currents that are induced in the plasma. Under certain conditions, the electric currents can collapse, allowing the magnetic field to "reconnect" to other magnetic poles and release heat and wave energy in the process. Magnetic reconnection is hypothesized to be the mechanism behind solar flares, the largest explosions in the Solar System. Furthermore, the surface of the Sun is covered with millions of small magnetized regions 50– across. These small magnetic poles are buffeted and churned by the constant granulation. The magnetic field in the solar corona must undergo nearly constant reconnection to match the motion of this "magnetic carpet", so the energy released by the reconnection is a natural candidate for the coronal heat, perhaps as a series of "microflares" that individually provide very little energy but together account for the required energy. The idea that nanoflares might heat the corona was proposed by Eugene Parker in the 1980s but is still controversial. In particular,
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30  PHz) to 400 nm (750  THz), shorter than that of visible light, but longer than X-rays. UV radiation ...
telescopes such as
TRACE Trace may refer to: Arts and entertainment Music * ''Trace'' (Son Volt album), 1995 * ''Trace'' (Died Pretty album), 1993 * Trace (band), a Dutch progressive rock band * ''The Trace'' (album) Other uses in arts and entertainment * ''Trace'' ...
and
SOHO Soho is an area of the City of Westminster, part of the West End of London. Originally a fashionable district for the aristocracy, it has been one of the main entertainment districts in the capital since the 19th century. The area was develo ...
/EIT can observe individual micro-flares as small brightenings in extreme ultraviolet light, but there seem to be too few of these small events to account for the energy released into the corona. The additional energy not accounted for could be made up by wave energy, or by gradual magnetic reconnection that releases energy more smoothly than micro-flares and therefore doesn't appear well in the TRACE data. Variations on the micro-flare hypothesis use other mechanisms to stress the magnetic field or to release the energy, and are a subject of active research in 2005.


Spicules (type II)

For decades, researchers believed spicules could send heat into the corona. However, following observational research in the 1980s, it was found that spicule plasma did not reach coronal temperatures, and so the theory was discounted. As per studies performed in 2010 at the ''National Center for Atmospheric Research'' in
Colorado Colorado (, other variants) is a state in the Mountain states, Mountain West subregion of the Western United States. It encompasses most of the Southern Rocky Mountains, as well as the northeastern portion of the Colorado Plateau and the wes ...
, in collaboration with the ''Lockheed Martin's Solar and Astrophysics Laboratory'' (LMSAL) and the ''Institute of Theoretical Astrophysics'' of the
University of Oslo The University of Oslo ( no, Universitetet i Oslo; la, Universitas Osloensis) is a public research university located in Oslo, Norway. It is the highest ranked and oldest university in Norway. It is consistently ranked among the top universit ...
, a new class of spicules (TYPE II) discovered in 2007, which travel faster (up to 100 km/s) and have shorter lifespans, can account for the problem. These jets insert heated plasma into the Sun's outer atmosphere. Thus, a much greater understanding of the corona and improvement in the knowledge of the Sun's subtle influence on the Earth's upper atmosphere can be expected henceforth. The Atmospheric Imaging Assembly on NASA's recently launched Solar Dynamics Observatory and NASA's Focal Plane Package for the Solar Optical Telescope on the Japanese Hinode satellite which was used to test this hypothesis. The high spatial and temporal resolutions of the newer instruments reveal this coronal mass supply. These observations reveal a one-to-one connection between plasma that is heated to millions of degrees and the spicules that insert this plasma into the corona.


See also

*
Advanced Composition Explorer Advanced Composition Explorer (ACE or Explorer 71) is a NASA Explorer program satellite and space exploration mission to study matter comprising energetic particles from the solar wind, the interplanetary medium, and other sources. Real-tim ...
*
Geocorona The geocorona is the luminous part of the outermost region of the Earth's atmosphere, the exosphere. It is seen primarily via far-ultraviolet light ( Lyman-alpha) from the Sun that is scattered from neutral hydrogen. It extends to at minimum 1 ...
* Supra-arcade downflows * X-ray astronomy


References


External links


NASA description of the solar corona







Solar and Heliospheric Observatory, including near-real-time images of the solar corona

Coronal x-ray images from the Hinode XRT


nbsp;– a combination of thirty-three photographs of the Sun's corona that were digitally processed to highlight faint features of a total eclipse that occurred in March 2006

(University of South Wales)


Solar Interface Region – Bart de Pontieu (SETI Talks) Video
{{Authority control Light sources Plasma physics Space plasmas Sun Unsolved problems in astronomy Articles containing video clips