Coronal seismology
Encyclopedia
Coronal seismology is a technique of studying the plasma
of the Sun's corona
with the use of magnetohydrodynamic
(MHD) wave
s and oscillation
s. Magnetohydrodynamics studies the dynamics
of electrically conducting fluid
s - in this case the fluid is the coronal plasma. Observed properties of the waves (e.g. period
, wavelength
, amplitude
, temporal and spatial signatures, characteristic scenarios of the wave evolution), combined with a theoretical modelling of the wave phenomena (dispersion relation
s, evolutionary equations, etc.), reveal physical parameters of the corona which are not open to direct observations, such as the coronal magnetic field
strength and Alfvén velocity and coronal dissipative coefficients. Originally, the method of MHD coronal seismology was suggested by Y. Uchida in 1970
for global seismology (standing waves) and B. Roberts et al. in 1984
for local seismology (propagating waves), but was not practically applied until the late 90s due to a lack of necessary observational resolution.
Philosophically, coronal seismology is similar to the Earth's seismology
, helioseismology
, and MHD spectroscopy of laboratory plasma devices. In all these approaches, waves of various kind are used to probe a medium.
The theoretical foundation of coronal seismology is the dispersion relation
of MHD modes of a plasma cylinder: a plasma structure which is nonuniform in the transverse direction and extended along the magnetic field. This model works well for the description of a number of plasma structures observed in the solar corona: e.g. coronal loops, prominence fibrils, plumes, various filaments. Such a structure acts as a waveguide
of MHD waves.
This discussion is adapted from Valery M. Nakariakov and Erwin Verwichte,
"Coronal Waves and Oscillations",
Living Rev. Solar Phys. 2, (2005), (cited on November 26, 2009).
, polarisation, and propagation
properties:
For kink modes the parameter
is equal to 1.
For sausage modes the parameter
is equal to 0.
Where we define
as the sound speed and 
as the Alfvèn speed.
(SOHO), the Transition Region and Coronal Explorer (TRACE), the Nobeyama Radioheliograph (NoRH, see the Nobeyama radio observatory
). Phenomenologically, researchers distinguish between compressible waves in polar plumes and in legs of large coronal loops, flare-generated transverse oscillations of loops, acoustic oscillations of loops, propagating kink waves in loops and in structures above arcades (an arcade being a close collection of loops in a cylindrical structure, see image to right), sausage oscillations of flaring loops, and oscillations of prominences and fibrils (see solar prominence
), and this list is continuously updated.
Coronal seismology is one of the aims of the Atmospheric Imaging Assembly (AIA) instrument on the Solar Dynamics Observatory
(SDO) mission.
A mission to send a spacecraft as close as 9 solar radii from the sun, NASA Solar probe
, is planned for launch in 2015 and aims to provide in-situ measurements of the solar magnetic field, solar wind and corona. It should include a magnetometer and plasma wave sensor, allowing unprecedented observations for coronal seismology.
, density scale height
, "fine structure" (by which is meant the variation in structure of an inhomogeneous structure such as an inhomogeneous coronal loop) and heating has been demonstrated by different research groups. Work relating to the coronal magnetic field was mentioned earlier.
It has been shown that sufficiently broadband slow magnetoacoustic waves, consistent with currently available observations in the low frequency part of the spectrum, could provide the rate of heat deposition sufficient to heat a coronal loop
. Regarding the density scale height, transverse oscillations of coronal loops that have both variable circular cross-sectional area and plasma density in the longitudinal direction have been studied theoretically. A second order ordinary differential equation has been derived describing the displacement of the loop axis. Together with boundary conditions, solving this equation determines the eigenfrequencies and eigenmodes. The coronal density scale height could then be estimated by using the observed ratio of the fundamental frequency and first overtone of loop kink oscillations. Little is known of coronal fine structure. Doppler shift oscillations in hot active region loops obtained with the Solar Ultraviolet Measurements of Emitted Radiation instrument (SUMER) aboard SOHO have been studied. The spectra were recorded along a 300 arcsec slit placed at a fixed position in the corona above the active regions. Some oscillations showed phase propagation along the slit in one or both directions with apparent speeds in the range of 8–102 km per second, together with distinctly different intensity and line width distributions along the slit. These features can be explained by the excitation of the oscillation at a footpoint of an inhomogeneous coronal loop, e.g. a loop with fine structure.
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
of the Sun's corona
Corona
A corona is a type of plasma "atmosphere" of the Sun or other celestial body, extending millions of kilometers into space, most easily seen during a total solar eclipse, but also observable in a coronagraph...
with the use of magnetohydrodynamic
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
(MHD) wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
s and oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
s. Magnetohydrodynamics studies the dynamics
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...
of electrically conducting fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
s - in this case the fluid is the coronal plasma. Observed properties of the waves (e.g. period
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
, wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
, amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
, temporal and spatial signatures, characteristic scenarios of the wave evolution), combined with a theoretical modelling of the wave phenomena (dispersion relation
Dispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....
s, evolutionary equations, etc.), reveal physical parameters of the corona which are not open to direct observations, such as the coronal magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
strength and Alfvén velocity and coronal dissipative coefficients. Originally, the method of MHD coronal seismology was suggested by Y. Uchida in 1970
for global seismology (standing waves) and B. Roberts et al. in 1984
for local seismology (propagating waves), but was not practically applied until the late 90s due to a lack of necessary observational resolution.
Philosophically, coronal seismology is similar to the Earth's seismology
Seismology
Seismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other planet-like bodies. The field also includes studies of earthquake effects, such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, oceanic,...
, helioseismology
Helioseismology
Helioseismology is the study of the propagation of wave oscillations, particularly acoustic pressure waves, in the Sun. Unlike seismic waves on Earth, solar waves have practically no shear component . Solar pressure waves are believed to be generated by the turbulence in the convection zone near...
, and MHD spectroscopy of laboratory plasma devices. In all these approaches, waves of various kind are used to probe a medium.
Dispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....
of MHD modes of a plasma cylinder: a plasma structure which is nonuniform in the transverse direction and extended along the magnetic field. This model works well for the description of a number of plasma structures observed in the solar corona: e.g. coronal loops, prominence fibrils, plumes, various filaments. Such a structure acts as a waveguide
Waveguide
A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguides for each type of wave...
of MHD waves.
This discussion is adapted from Valery M. Nakariakov and Erwin Verwichte,
"Coronal Waves and Oscillations",
Living Rev. Solar Phys. 2, (2005), (cited on November 26, 2009).
Types of magnetohydrodynamic waves
There are several distinct kinds of MHD modes which have quite different dispersiveDispersive mass transfer
Dispersive mass transfer, in fluid dynamics, is the spreading of mass from highly concentrated areas to less concentrated areas. It is one form of mass transfer....
, polarisation, and propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
properties:
- Kink (or transverseTransverse waveA transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer...
) modes, which are obliqueOblique shockAn oblique shock wave, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream streamlines are uniformly deflected after the shock wave...
fast magnetoacoustic (also known as magnetosonic waveMagnetosonic waveA magnetosonic wave is a longitudinal wave of ions in a magnetized plasma propagating perpendicular to the stationary magnetic field...
s) guided by the plasma structure; the mode causes the displacement of the axis of the plasma structure. These modes are weakly compressible, but could nevertheless be observed with imaging instruments as periodic standing or propagating displacements of coronal structures, e.g. coronal loopCoronal loopCoronal loops form the basic structure of the lower corona and transition region of the Sun. These highly structured and elegant loops are a direct consequence of the twisted solar magnetic flux within the solar body. The population of coronal loops can be directly linked with the solar cycle; it...
s. The frequency of transverse or "kink" modes is given by the following expression:
For kink modes the parameter
is equal to 1.- Sausage modes, which are also oblique fast magnetoacoustic waves guided by the plasma structure; the mode causes expansions and contractions of the plasma structure, but does not displace its axis. These modes are compressible and cause significant variation of the absolute value of the magnetic field in the oscillating structure. The frequency of sausage modes is given by the following expression:
For sausage modes the parameter
is equal to 0.- Longitudinal (or slow, or acousticAcousticsAcoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
) modes, which are slow magnetoacoustic waves propagating mainly along the magnetic field in the plasma structure; these mode are essentially compressible. The magnetic field perturbationPerturbation theoryPerturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
in these modes is negligible. The frequency of slow modes is given by the following expression:
Where we define
as the sound speed and as the Alfvèn speed.- Torsional (AlfvénAlfvén waveAn Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave.-Definition:An Alfvén wave in a plasma is a low-frequency travelling oscillation of the ions and the magnetic field...
or twist) modes are incompressible transverse perturbations of the magnetic field along certain individual magnetic surfaces. In contrast with kink modes, torsional modes cannot be observed with imaging instruments, as they do not cause the displacement of either the structure axis or its boundary.
Observations
Wave and oscillatory phenomena are observed in the hot plasma of the corona mainly in EUV, optical and microwave bands with a number of spaceborne and ground-based instruments, e.g. the Solar and Heliospheric ObservatorySolar and Heliospheric Observatory
The Solar and Heliospheric Observatory is a spacecraft built by a European industrial consortium led by Matra Marconi Space that was launched on a Lockheed Martin Atlas IIAS launch vehicle on December 2, 1995 to study the Sun, and has discovered over 2100 comets. It began normal operations in May...
(SOHO), the Transition Region and Coronal Explorer (TRACE), the Nobeyama Radioheliograph (NoRH, see the Nobeyama radio observatory
Nobeyama radio observatory
The Nobeyama Radio Observatory is a division of the National Astronomical Observatory of Japan and consists of three radio instruments located in Nobeyama, a village in the Japan Alps at an elevation of 1350m....
). Phenomenologically, researchers distinguish between compressible waves in polar plumes and in legs of large coronal loops, flare-generated transverse oscillations of loops, acoustic oscillations of loops, propagating kink waves in loops and in structures above arcades (an arcade being a close collection of loops in a cylindrical structure, see image to right), sausage oscillations of flaring loops, and oscillations of prominences and fibrils (see solar prominence
Solar prominence
A prominence is a large, bright feature extending outward from the Sun's surface, often in a loop shape. Prominences are anchored to the Sun's surface in the photosphere, and extend outwards into the Sun's corona...
), and this list is continuously updated.
Coronal seismology is one of the aims of the Atmospheric Imaging Assembly (AIA) instrument on the Solar Dynamics Observatory
Solar Dynamics Observatory
The Solar Dynamics Observatory is a NASA mission which will observe the Sun for over five years. Launched on February 11, 2010, the observatory is part of the Living With a Star program...
(SDO) mission.
A mission to send a spacecraft as close as 9 solar radii from the sun, NASA Solar probe
NASA Solar probe
Solar Probe Plus, previously NASA Solar Probe, is a planned robotic spacecraft to probe the outer corona of the Sun. It will approach to within 8.5 solar radii to the 'surface' of the Sun. The project was announced as a new mission start in the fiscal 2009 budget year...
, is planned for launch in 2015 and aims to provide in-situ measurements of the solar magnetic field, solar wind and corona. It should include a magnetometer and plasma wave sensor, allowing unprecedented observations for coronal seismology.
Conclusions
The potential of coronal seismology in the estimation of the coronal magnetic fieldMagnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
, density scale height
Scale height
In various scientific contexts, a scale height is a distance over which a quantity decreases by a factor of e...
, "fine structure" (by which is meant the variation in structure of an inhomogeneous structure such as an inhomogeneous coronal loop) and heating has been demonstrated by different research groups. Work relating to the coronal magnetic field was mentioned earlier.
It has been shown that sufficiently broadband slow magnetoacoustic waves, consistent with currently available observations in the low frequency part of the spectrum, could provide the rate of heat deposition sufficient to heat a coronal loop
Coronal loop
Coronal loops form the basic structure of the lower corona and transition region of the Sun. These highly structured and elegant loops are a direct consequence of the twisted solar magnetic flux within the solar body. The population of coronal loops can be directly linked with the solar cycle; it...
. Regarding the density scale height, transverse oscillations of coronal loops that have both variable circular cross-sectional area and plasma density in the longitudinal direction have been studied theoretically. A second order ordinary differential equation has been derived describing the displacement of the loop axis. Together with boundary conditions, solving this equation determines the eigenfrequencies and eigenmodes. The coronal density scale height could then be estimated by using the observed ratio of the fundamental frequency and first overtone of loop kink oscillations. Little is known of coronal fine structure. Doppler shift oscillations in hot active region loops obtained with the Solar Ultraviolet Measurements of Emitted Radiation instrument (SUMER) aboard SOHO have been studied. The spectra were recorded along a 300 arcsec slit placed at a fixed position in the corona above the active regions. Some oscillations showed phase propagation along the slit in one or both directions with apparent speeds in the range of 8–102 km per second, together with distinctly different intensity and line width distributions along the slit. These features can be explained by the excitation of the oscillation at a footpoint of an inhomogeneous coronal loop, e.g. a loop with fine structure.
External links
- Verwichte, E., Plasma diagnostics using MHD waves