Coronal Seismology

Coronal seismology is a method for studying plasma in the solar corona using data on magnetohydrodynamic waves (MHD waves) and oscillations. Magnetic hydrodynamics studies the dynamics of liquids conducting electricity - in this case, the plasma of the corona acts as a liquid. Observed wave properties (e.g., oscillation period , wavelength , amplitude , temporal and spatial features (what is the shape of the wave perturbation?), Characteristic wave evolution scenarios (is the wave attenuated?) In conjunction with theoretical wave modeling ( dispersion relations , wave evolution equations, and etc.) can provide information on the physical parameters of the corona that cannot be directly measured, such as the strength of the magnetic field of the corona, Alfven speed , ^[1] dissipation coefficients in the corona. ^[2] Initially, the MHD method -seismology of the corona was proposed by J. Uchida ( English Y. Uchida ) in 1970 ^[3] for propagating waves and B. Roberts ( English B. Roberts ) and others in 1984 ^[4] for standing waves , but practical The method was applied only in the late 1990s due to a lack of the required quality of observations.From a philosophical point of view, coronal seismology is similar to Earth seismology , helioseismology and MHD spectroscopy in laboratory plasma research devices. In all these areas of science, waves of various types are used to study the environment.

The theoretical basis of coronal seismology is the dispersion law for MHD modes in a plasma cylinder: a region in a plasma that is not uniform in the transverse direction and elongated along the magnetic field. Such a model works well when describing a number of plasma structures observed in the solar corona: coronal loops , prominence fibers, jets, and fibers. Similar structures are waveguides for MHD waves. ^[five]

Content

Types of magnetohydrodynamic waves

There are several types of MHD modes with different dispersion, polarization properties and propagation parameters:

Bending (transverse) modes ( English kink, transverse modes ), inclined fast magnetoacoustic waves directed by the plasma structure; there is a shift in the axis of the plasma structure. Such modes are weakly subject to compression; they can be observed in the form of periodic standing or propagating displacements of coronal structures, for example, coronal loops. The frequency of the transverse modes is determined by the equation

\omega _{K}={\sqrt {\frac {2k_{z}B^{2}}{\mu (\rho _{i}+\rho _{e})}}}.

{\ displaystyle \ omega _ {K} = {\ sqrt {\ frac {2k_ {z} B ^ {2}} {\ mu (\ rho _ {i} + \ rho _ {e})}}}.}

For transverse modes, the azimuthal wave number in the cylindrical loop model $m$ ${\ displaystyle m}$ equal to 1, this means that the cylinder oscillates, but the edges remain motionless.

"Sausage" modes ( English sausage modes ), also inclined fast magnetoacoustic waves, guided by the plasma structure; in this mode, expansion and contraction of the plasma structure occur, but the axis does not move. Such modes are subject to compression and can lead to substantial changes in the absolute value of the magnetic field in the vibrating structure. The frequency of these modes is given by

\omega _{S}={\sqrt {\frac {k_{z}^{2}B^{2}}{\mu \rho _{e}}}}.

{\ displaystyle \ omega _ {S} = {\ sqrt {\ frac {k_ {z} ^ {2} B ^ {2}} {\ mu \ rho _ {e}}}}.}

For sausage modes, the parameter $m$ ${\ displaystyle m}$ equal to 0; this means that the structure is “breathing”, but the edge points also remain motionless.

Slow, acoustic (longitude) modes are the slow magnetoacoustic waves propagating mainly along the lines of the magnetic field along the plasma structure; such modes are most subject to compression. The perturbation of the magnetic field is negligible. The frequency of slow modes is given by

\omega _{L}={\sqrt {k_{z}^{2}\left({\frac {C_{s}^{2}C_{A}^{2}}{C_{s}^{2}+C_{A}^{2}}}\right)}}.

{\ displaystyle \ omega _ {L} = {\ sqrt {k_ {z} ^ {2} \ left ({\ frac {C_ {s} ^ {2} C_ {A} ^ {2}} {C_ {s } ^ {2} + C_ {A} ^ {2}}} \ right)}}.}

Here $C_{s}$ ${\ displaystyle C_ {s}}$ is the speed of sound $C_{A}$ ${\ displaystyle C_ {A}}$ - Alfven speed.

Torsional ( Alfven ) modes ( English torsional, twist mode ) are incompressible transverse perturbations of the magnetic field along individual surfaces. In contrast to transverse modes, torsion modes cannot be observed on instruments receiving the image of the region, since they do not lead to a displacement of the axis of the structure or its boundary. The frequency is given by

\omega _{A}={\sqrt {\frac {k_{z}^{2}B^{2}}{\mu \rho _{i}}}}

{\ displaystyle \ omega _ {A} = {\ sqrt {\ frac {k_ {z} ^ {2} B ^ {2}} {\ mu \ rho _ {i}}}}}

Observations

The image of the arch in the crown after the flash, obtained on the TRACE instrument

Waves and vibrational processes are observed in the hot plasma of the corona mainly in the extreme ultraviolet, optical, and microwave ranges on a whole series of space and ground instruments, for example, the Solar and Heliospheric Observatory (SOHO), Transition Region and Coronal Explorer (TRACE), and the Nobeyama radio heliograph (NoRH , see the Nobeyama Radio Observatory ). Researchers distinguish between compressible waves in polar flares and at the base of coronal loops , transverse vibrations created by flashes in loops, acoustic vibrations in loops, propagating transverse vibrations in loops and structures above arches (an arch is a set of closely spaced loops forming a cylindrical structure, see image on the right ), "sausage" oscillations of flashing loops, oscillations in prominences and fibers; This list is periodically updated.

Coronal seismology is one of the objectives of the study of the instrument (AIA) of the Solar Dynamics Observatory (SDO) mission.

Parker Solar Probe is expected to be able to measure solar magnetic field, solar wind, and corona parameters. The device is equipped with a magnetometer and a sensor for detecting plasma waves, which will allow measurements to be made with unprecedented accuracy.

Conclusions

The potential of such a branch of astronomy as coronal seismology in the field of estimating the parameters of the corona magnetic field, vertical density scale, and “fine structure” (this term refers to the variation in the structure of inhomogeneous formations such as inhomogeneous coronal loops) and heating has been shown by various research groups. The works related to the coronal magnetic field were mentioned above. ^[1] It has been shown that sufficiently wide slow magnetoacoustic waves, consistent with observations in the low-frequency region of the spectrum, can create a heat transfer rate sufficient to heat the coronal loop. ^[6] The transverse vibrations of coronal loops with variable circular cross section and plasma density in the longitudinal direction were theoretically investigated. A second-order differential equation was derived to describe the displacement of the loop axis. The solution of the equation together with the boundary conditions determines the eigenfrequencies and eigenmodes. The scale of heights of density in the corona can be estimated using the observed ratio of the fundamental frequency and the first overtone of the transverse oscillations of the loop. ^[7] Little is known about the fine structure of the corona. The data on the Doppler shift oscillations in hot active regions obtained with the SUMER instrument of the SOHO space observatory are analyzed. Spectra were taken along a slit with an angular size of 300 seconds, located in the direction of the corona above the active regions. Some oscillations were characterized by phase propagation along the gap in one or both directions at a visible speed in the range of 8–102 km / s, and significantly different intensities and line widths along the gap were observed. These features can be explained by the excitation of vibrations at the base of an inhomogeneous coronal loop, for example, a loop with a fine structure . ^[eight]

Notes

↑ ¹ ² Nakariakov, VM; Ofman, L. Determination of the coronal magnetic field by coronal loop oscillations (Eng.) // Astronomy and Astrophysics : journal. - 2001. - Vol. 372 , no. 3 . - P. L53 — L56 . - DOI : 10.1051 / 0004-6361: 20010607 . - .
↑ Nakariakov, VM; Ofman, L .; Deluca, EE; Roberts, B .; Davila, JM TRACE observation of damped coronal loop oscillations: Implications for coronal heating (Eng.) // Science : journal. - 1999. - Vol. 285 , no. 5429 . - P. 862-864 . - DOI : 10.1126 / science.285.5429.862 . - . - PMID 10436148 .
↑ Uchida, Y. Diagnosis of coronal magnetic structure by flare-associated hydromagnetic disturbances (English) // Publications of the Astronomical Society of Japan : journal. - 1970. - Vol. 22 . - P. 341-364 . - .
↑ Roberts, B .; Edwin, PM; Benz, AO On coronal oscillations (Eng.) // The Astrophysical Journal : journal. - IOP Publishing , 1984. - Vol. 279 . - P. 857-865 . - DOI : 10.1086 / 161956 . - .
↑ Nakariakov, VM; Verwichte, E. Coronal Waves and Oscillations (Eng.) // Living Reviews in Solar Physics : journal. - 2005. - Vol. 2 , no. 1 . - P. 3 . - DOI : 10.12942 / lrsp-2005-3 . - .
↑ Tsiklauri, D .; Nakariakov, VM Wide-spectrum slow magnetoacoustic waves in coronal loops (Eng.) // Astronomy and Astrophysics : journal. - 2001. - Vol. 379 , no. 3 . - P. 1106-1112 . - DOI : 10.1051 / 0004-6361: 20011378 . - . - arXiv : astro-ph / 0107579 .
↑ Ruderman, MS; Verth, G .; Erdelyi, R. Transverse Oscillations of Longitudinally Stratified Coronal Loops with Variable Cross Section // The Astrophysical Journal : journal. - IOP Publishing 2008. - Vol. 686 , no. 1 . - P. 694-700 . - DOI : 10.1086 / 591444 . - .
↑ Wang, TJ et al. Hot coronal loop oscillations observed with SUMER: Examples and statistics // Astronomy and Astrophysics : journal. - 2003. - Vol. 406 , no. 3 . - P. 1105-1121 . - DOI : 10.1051 / 0004-6361: 20030858 . - .

Literature

Nakariakov, VM; Verwichte, E. Coronal Waves and Oscillations (Eng.) // Living Reviews in Solar Physics : journal. - 2005. - Vol. 2 , no. 1 . - P. 3 . - DOI : 10.12942 / lrsp-2005-3 . - .
Roberts, B., Nakariakov, VM, "Coronal seismology - a new science", Frontiers 15, 2003
Verwichte, E., Plasma diagnostics using MHD waves
Stepanov, AV, Zaitsev, VV and Nakariakov, VM, "Coronal Seismology" Wiley-VCH 2012 ISBN 978-3527409945

[Nakariakov2001-1] ¹ ² Nakariakov, VM; Ofman, L. Determination of the coronal magnetic field by coronal loop oscillations (Eng.) // Astronomy and Astrophysics : journal. - 2001. - Vol. 372 , no. 3 . - P. L53 — L56 . - DOI : 10.1051 / 0004-6361: 20010607 . - .

[2] Nakariakov, VM; Ofman, L .; Deluca, EE; Roberts, B .; Davila, JM TRACE observation of damped coronal loop oscillations: Implications for coronal heating (Eng.) // Science : journal. - 1999. - Vol. 285 , no. 5429 . - P. 862-864 . - DOI : 10.1126 / science.285.5429.862 . - . - PMID 10436148 .

[3] Uchida, Y. Diagnosis of coronal magnetic structure by flare-associated hydromagnetic disturbances (English) // Publications of the Astronomical Society of Japan : journal. - 1970. - Vol. 22 . - P. 341-364 . - .

[4] Roberts, B .; Edwin, PM; Benz, AO On coronal oscillations (Eng.) // The Astrophysical Journal : journal. - IOP Publishing , 1984. - Vol. 279 . - P. 857-865 . - DOI : 10.1086 / 161956 . - .

[5] Nakariakov, VM; Verwichte, E. Coronal Waves and Oscillations (Eng.) // Living Reviews in Solar Physics : journal. - 2005. - Vol. 2 , no. 1 . - P. 3 . - DOI : 10.12942 / lrsp-2005-3 . - .

[6] Tsiklauri, D .; Nakariakov, VM Wide-spectrum slow magnetoacoustic waves in coronal loops (Eng.) // Astronomy and Astrophysics : journal. - 2001. - Vol. 379 , no. 3 . - P. 1106-1112 . - DOI : 10.1051 / 0004-6361: 20011378 . - . - arXiv : astro-ph / 0107579 .

[7] Ruderman, MS; Verth, G .; Erdelyi, R. Transverse Oscillations of Longitudinally Stratified Coronal Loops with Variable Cross Section // The Astrophysical Journal : journal. - IOP Publishing 2008. - Vol. 686 , no. 1 . - P. 694-700 . - DOI : 10.1086 / 591444 . - .

[8] Wang, TJ et al. Hot coronal loop oscillations observed with SUMER: Examples and statistics // Astronomy and Astrophysics : journal. - 2003. - Vol. 406 , no. 3 . - P. 1105-1121 . - DOI : 10.1051 / 0004-6361: 20030858 . - .