Editing Stellar corona (section)

==Physics of the corona==
[[File:171879main LimbFlareJan12 lg.jpg|thumb|left|This image, taken by [[Hinode (satellite)|Hinode]] on 12 January 2007, reveals the filamentary nature of the corona.]]
The matter in the external part of the solar atmosphere is in the state of [[plasma (physics)|plasma]], at very high temperature (a few million kelvin) and at very low density (of the order of 10<sup>15</sup> particles/m<sup>3</sup>).
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 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]]), electrons have a mass roughly {{gaps|1|800}} 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,<ref name="Jeffrey">{{cite book
|last = Jeffrey
|first = Alan
|year =1969
|title = Magneto-hydrodynamics
|publisher = UNIVERSITY MATHEMATICAL TEXTS
}}</ref> even though it is still not clear how they can be transmitted or generated in the corona.

===Radiation===
{{see also|Coronal radiative losses}}
Coronal plasma is optically thin and therefore transparent to the [[electromagnetic radiation]] that it emits and to that coming from lower layers. The plasma is very rarefied and the [[photon]] [[mean free path]] overcomes by far all the other length-scales, including the typical sizes of common coronal features.{{citation needed|date=January 2022}}

Electromagnetic radiation from the corona has been identified coming from three main sources, located in the same volume of space: 
* The K-corona (K&nbsp;for {{lang|de|kontinuierlich}}, "continuous" in German) is created by sunlight [[Thomson scattering]] off free [[electron]]s; [[doppler broadening]] of the reflected photospheric [[absorption line]]s spreads them so greatly as to completely obscure them, giving the spectral appearance of a continuum with no absorption lines. 
* The F-corona (F&nbsp;for [[Joseph von Fraunhofer|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 (astronomy)|elongation]] angles from the Sun, where it is called the [[zodiacal light]]. 
* 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 line|forbidden]] or hot [[spectral line|spectral emission lines]] and is the main source of information about the corona's composition.<ref name="Corfield">{{cite book
|last=Corfield
|first=Richard
|year=2007
|title=Lives of the Planets
|publisher=Basic Books
|isbn=978-0-465-01403-3
|url-access=registration
|url=https://archive.org/details/livesofplanetsna00corf
}}
</ref>

===Thermal conduction===
[[File:STEREO-A first images.jpg|thumb|A mosaic of the extreme ultraviolet images taken from [[STEREO]] on December 4, 2006. These false color images show the Sun's atmospheres at a range of different temperatures. Clockwise from top left: 1 million degrees C (171 Å—blue), 1.5 million °C ({{gaps|195|Å—green}}), {{gaps|60|000}}–{{gaps|80|000|°C}} (304 Å—red), and 2.5 million °C (286 Å—yellow).]]
[[File:STEREO-A first images slow anim.gif|thumb|[[STEREO]]&nbsp;– First images as a slow animation]]
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]] of the plasma becomes higher in the direction which is parallel to the field lines rather than in the perpendicular direction.<ref name="Spitzer">{{cite book
|last=Spitzer
|first= L.
|year=1962
|title= Physics of fully ionized gas
|publisher= Interscience tracts of physics and astronomy
}}</ref>
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]] 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<ref name="Spitzer" />
<math display="block">
k = 20 \left(\frac{2}{\pi}\right)^{3/2}\frac{\left(k_\text{B} T \right)^{5/2}k_\text{B}}{m_e^{1/2} e^4 \ln \Lambda} \approx \frac{T^{5/2}}{\ln \Lambda} \times 1.8 \times 10^{-10}~ \mathrm{W m^{-1}K^{-1}}
</math>
where <math>k_\text{B}</math> is the [[Boltzmann constant]], <math>T</math> is the temperature in kelvin, <math>m_e</math> is the electron mass, <math>e</math> is the electric charge of the electron,
<math display="block"> \ln \Lambda = \ln \left(12\pi n \lambda_D^3 \right) </math>
is the Coulomb logarithm, and
<math display="block">\lambda_D = \sqrt{ \frac{k_\text{B} T }{4 \pi n e^2 }}</math>
is the [[Debye length]] of the plasma with particle density  <math>n</math>. The Coulomb logarithm <math> \ln \Lambda </math> is roughly 20 in the corona, with a mean temperature of 1 MK and a density of 10<sup>15</sup> particles/m<sup>3</sup>, and about 10 in the chromosphere, where the temperature is approximately 10kK and the particle density is of the order of 10<sup>18</sup> particles/m<sup>3</sup>, and in practice it can be assumed constant.

Thence, if we indicate with <math>q</math> the heat for a volume unit, expressed in J m<sup>−3</sup>, the Fourier equation of heat transfer, to be computed only along the direction <math>x</math> of the field line, becomes
<math display="block"> \frac{\partial q}{\partial t} = 0.9 \times 10^{-11}~ \frac{\partial^2  T^{7/2}}{\partial x ^2 }.</math>

Numerical calculations have shown that the thermal conductivity of the corona is comparable to that of copper.

===Coronal seismology===
{{main|Coronal seismology}}
Coronal seismology is a method of studying the plasma of the solar corona with the use of [[magnetohydrodynamic]] (MHD) waves. MHD studies the [[dynamics (mechanics)|dynamics]] of [[electrical conduction|electrically conducting]] [[fluid]]s – in this case, the fluid is the coronal plasma. Philosophically, coronal seismology is similar to the Earth's [[seismology]], the Sun's [[helioseismology]], 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]], [[fine structure]] and heating has been demonstrated by different research groups.