Helioseismology - AbsoluteAstronomy.com

Helioseismology is the study of the propagation of wave oscillations, particularly acoustic

Acoustics

Acoustics 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...

pressure waves, in the Sun

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

. Unlike seismic waves on Earth

Seismic wave

Seismic waves are waves of energy that travel through the earth, and are a result of an earthquake, explosion, or a volcano that imparts low-frequency acoustic energy. Many other natural and anthropogenic sources create low amplitude waves commonly referred to as ambient vibrations. Seismic waves...

, solar waves have practically no shear component (s-waves). Solar pressure waves are believed to be generated by the turbulence in the convection zone near the surface of the sun. Certain frequencies are amplified by constructive interference. In other words, the turbulence "rings" the sun like a bell. The acoustic waves are transmitted to the outer photosphere of the sun, which is where the light generated through absorption of radiant energy from nuclear fusion at the centre of the sun, leaves the surface. These oscillations are detectable on almost any time series of solar images, but are best observed by measuring the Doppler shift of photospheric absorption lines. Changes in the propagation of oscillation waves through the Sun reveal inner structures and allow astrophysicists to develop extremely detailed profiles of the interior conditions of the Sun.

Helioseismology was able to rule out the possibility that the solar neutrino problem

Solar neutrino problem

The solar neutrino problem was a major discrepancy between measurements of the numbers of neutrinos flowing through the Earth and theoretical models of the solar interior, lasting from the mid-1960s to about 2002...

was due to incorrect models of the interior of the Sun. Features revealed by helioseismology include that the outer convective zone and the inner radiative zone rotate at different speeds, which is thought to generate the main magnetic field of the Sun by a dynamo

Dynamo

- Engineering :* Dynamo, a magnetic device originally used as an electric generator* Dynamo theory, a theory relating to magnetic fields of celestial bodies* Solar dynamo, the physical process that generates the Sun's magnetic field- Software :...

effect, and that the convective zone has "jet stream

Jet stream

Jet streams are fast flowing, narrow air currents found in the atmospheres of some planets, including Earth. The main jet streams are located near the tropopause, the transition between the troposphere and the stratosphere . The major jet streams on Earth are westerly winds...

s" of plasma (more precisely, torsional oscillations) thousands of kilometers below the surface. These jet streams form broad fronts at the equator, breaking into smaller cyclonic storms at high latitudes. Torsional oscillations are the time variation in solar differential rotation

Differential rotation

Differential rotation is seen when different parts of a rotating object move with different angular velocities at different latitudes and/or depths of the body and/or in time. This indicates that the object is not solid. In fluid objects, such as accretion disks, this leads to shearing...

. They are alternating bands of faster and slower rotation. So far there is no generally accepted theoretical explanation for them, even though a close relation to the solar cycle

Solar cycle

The solar cycle, or the solar magnetic activity cycle, is a periodic change in the amount of irradiation from the Sun that is experienced on Earth. It has a period of about 11 years, and is one component of solar variation, the other being aperiodic fluctuations. Solar variation causes changes in...

is evident, as they have a period of eleven years, as was known since they were first observed in 1980.

Helioseismology can also be used to image the far side of the Sun from the Earth, including sunspot

Sunspot

Sunspots are temporary phenomena on the photosphere of the Sun that appear visibly as dark spots compared to surrounding regions. They are caused by intense magnetic activity, which inhibits convection by an effect comparable to the eddy current brake, forming areas of reduced surface temperature....

s. In simple terms, sunspots absorb helioseismic waves. This sunspot absorption causes a seismic deficit that can be imaged at the antipode

Antipode

Antipode, Antipodes, or Antipodeans may refer to:* Antipodal point, the diametrically opposite point on a sphere* Antipodes Water Company, a premium bottled water brand...

of the sunspot. To facilitate spaceweather forecasting, seismic images of the central portion of the solar far side have been produced nearly continuously since late 2000 by analysing data from the SOHO spacecraft, and since 2001 the entire far side has been imaged with this data.

Keep in mind that despite the name, helioseismology is the study of solar waves and not solar seismic activity - there is no such thing. The name is derived from the similar practice of studying terrestrial seismic waves to determine the composition of the Earth

Earth

Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

's interior. The science can be compared to asteroseismology

Asteroseismology

Asteroseismology also known as stellar seismology is the science that studies the internal structure of pulsating stars by the interpretation of their frequency spectra. Different oscillation modes penetrate to different depths inside the star...

, which considers the propagation of sound waves in stars.

Types of solar oscillations

Individual oscillations in the Sun are damped

Damping

In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...

so that they die out within a few periods. However, interference between these localised waves produces global standing waves, also known as normal modes. Analysis of these overlapping modes constitutes the discipline of global helioseismology.

Solar oscillation modes are essentially divided up into three categories, based on the restoring force that drives them: acoustic, gravity, and surface-gravity wave modes.

p-mode or acoustic waves have pressure as their restoring force, hence the name "p-mode". Their dynamics are determined by the variation of the speed of sound inside the sun. P-mode oscillations have frequencies > 1 mHz and are very strong in the 2-4 mHz range, where they are often referred to as "5-minute oscillations". (Note: 5 minutes per cycle is 1/300 cycles per second = 3.33 mHz.) P-modes at the solar surface have amplitudes of hundreds of kilometers and are readily detectable with Doppler imaging
Dopplergraph
The word dopplergraph is a combination of the words doppler and photograph . Just as a photograph is a two-dimensional record of variations in light intensity, a dopplergraph is a two dimensional record of variations in the doppler shift in light intensity...

or sensitive spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

intensity imaging. Thousands of p-modes of high and intermediate degree l (see below for the wavenumber degree l) have been detected by the Michelson Doppler Imager (MDI) instrument aboard the SOHO spacecraft, with those of degree l below 200 clearly separated and higher degree modes ridged together. About 10 p-modes below 1.5mHz have been detected by the GOLF instrument aboard the SOHO spacecraft.

g-mode or gravity waves are density waves which have gravity (negative buoyancy of displaced material) as their restoring force, hence the name "g-mode". The g-mode oscillations are low frequency waves (0-0.4 mHz). They are confined to the interior of the sun below the convection zone (which extends from 0.7-1.0 solar radius), and are practically inobservable at the surface. The restoring force is caused by adiabatic expansion
Adiabatic process
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...

: in the deep interior of the Sun, the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

is weak, and a small packet of gas that moves (for example) upward will be cooler and denser than the surrounding gas, and will therefore be pulled back to its original position; this restoring force drives g-modes. In the solar convection zone, the temperature gradient is slightly greater than the adiabatic lapse rate, so that there is an anti-restoring force (that drives convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....

) and g-modes cannot propagate. The g modes are evanescent
Evanescent wave
An evanescent wave is a nearfield standing wave with an intensity that exhibits exponential decay with distance from the boundary at which the wave was formed. Evanescent waves are a general property of wave-equations, and can in principle occur in any context to which a wave-equation applies...

through the entire convection zone, and are thought to have residual amplitudes of only millimeters at the photosphere, though more prominent as temperature perturbations. Since the '80s, there have been several claims of g-mode detection, none of which have been confirmed. In 2007, another g-mode detection was claimed using the GOLF data. At the GONG2008 / SOHO XXI conference held in Boulder, the Phoebus group
Phoebus group
The Phoebus group is an international team of European, Japanese and American scientists aiming at detecting the solar g modes. As of October 5, 2009, the group has finally produced a review summarising the work performed over the past 12 years....

reported that it could not confirm these findings, putting an upper limit on the g-mode amplitude to 3 mm/s, right at the detection limit of the GOLF instrument. Finally, the Phoebus group
Phoebus group
The Phoebus group is an international team of European, Japanese and American scientists aiming at detecting the solar g modes. As of October 5, 2009, the group has finally produced a review summarising the work performed over the past 12 years....

has just published a review over the current state of knowledge on the solar g modes.

f-mode or surface gravity waves are also gravity waves, but occur at or near the photosphere, where the temperature gradient again drops below the adiabatic lapse rate. Some f-modes of moderate and high degree, between l = 117 and l = 300, (see below for the wavenumber degree l) have been observed by MDI.

Analysis of oscillation data

The data from time-series of solar spectra shows all the oscillations overlapping. Thousands of modes have been detected (with the true number perhaps being in the millions). The mathematical technique of Fourier analysis is used to recover information about individual modes from this mass of data. The idea is that any periodic function f can be written as a sum of multiples of the simplest periodic functions, which are sine

Sine

In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....

s and cosines (of different frequencies). To find out how much (the 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...

) of each simple function goes into f, one applies the Fourier transform

Fourier transform

In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

: at each point the value of this transform is obtained by computing a particular integral involving a modified version of f.

The simplest modes to analyse are the radial ones; however most solar modes are non-radial. A nonradial mode is characterized by three wavenumbers: the spherical-harmonic degree l and azimuthal order m which determine the behaviour of the mode over the surface of the star and the radial order n which reflects the properties in the radial direction (see the diagram on the top right for an example). Note that if the Sun were spherically symmetric, the azimuthal order would exhibit degeneracy

Degeneracy

Degeneracy may refer to:* DegenerationIn science and mathematics:* Degeneracy , a property of quantum states sharing the same energy levels...

; however the rotation of the Sun (along with other perturbations), which leads to an equatorial bulge, lifts this degeneracy. By convention, n corresponds to the number of nodes of the radial eigenfunction

Eigenfunction

In mathematics, an eigenfunction of a linear operator, A, defined on some function space is any non-zero function f in that space that returns from the operator exactly as is, except for a multiplicative scaling factor. More precisely, one has...

, l indicates the total number of nodal lines on spheres, and m tells how many of these nodal lines cross the equator.

In general the frequencies

of stellar oscillations depend on all three wave numbers. It is convenient, however, to separate the frequency

Frequency separation

Frequency separation is a term used in Helio and Asteroseismology for the spacing in frequency between adjacent modes of oscillation having the same angular degree but different radial order ....

into the multiplet frequency

, obtained as a suitable average over azimuthal order m and corresponding to the spherically symmetric structure of the star, and the frequency splitting

.

Analyses of oscillation data must attempt to separate these different frequency components. In the case of the Sun the oscillations can be observed directly as functions of position on the solar disk as well as time. Thus here it is possible to analyze their spatial
properties. This is done by means of a generalized 2-dimensional Fourier transform

Fourier transform

in
position on the solar surface, to isolate particular values of l and m. This is followed by
a Fourier transform in time which isolates the frequencies of the modes of that type. In
fact, the average over the stellar surface implicit in observations of stellar oscillations can
be thought of as one example of such a spatial Fourier transform.

Note that the oscillation data, rather than a continuous function, amounts to values constrained by experimental error evaluated at a grid of positions and times. When computing transforms, values of this "function" outside this grid have to be interpolated and the integrals approximated by finite sums, a process inevitably introducing further errors. Details of the numerical methods used are included with the transformed data for purposes of comparison and constraining errors.

This discussion is adapted from the Jørgen Christensen-Dalsgaard lecture notes on stellar oscillations.

Inversion

Information about helioseismic waves (such as mode frequencies and frequency-splitting) collected by transforming the oscillation data can be used to infer numerical details of internal features of the Sun. For example, the internal sound speed, the internal differential rotation

Differential rotation

within the Sun. Equations and analytic relations such as integrals can be manipulated to relate the desired internal properties to the transformed data. The numerical methods used are adapted to the particular internal features examined so as to extract the maximum amount of information, with the least error, from the oscillations about the internal features. This process is termed helioseismic inversion.

As an example in slightly more detail, the oscillation frequency splitting can be related, via an integral, to the angular velocity within the sun.

Internal structure

Helioseismic observations reveal the inner uniformly-rotating zone and the differentially-rotating

Differential rotation

envelope of the Sun, roughly corresponding to the radiation

Radiation zone

The radiation zone is the middle zone in the Sun's interior. Energy travels out of the core into the radiation zone. Energy that travels through the radiation zone is in the form of electromagnetic radiation. The radiation zone is so dense that the waves bounce around...

and convection

Convection zone

The convection zone of a star is the range of radii in which energy is transported primarily by convection. In the radiation zone, energy is transported by radiation...

zones, respectively. See the diagram on the right. The transition layer is called the tachocline

Tachocline

The tachocline is the transition region of the Sun between the radiative interior and the differentially rotating outer convective zone. It is in the outer third of the sun . This causes the region to have a very large shear as the rotation rate changes very rapidly...

Helioseismic dating

The age of the sun can be inferred with helioseismic studies. This is because the propagation of acoustic waves deep within the sun depends on the composition of the sun, in particular the relative abundance of helium and hydrogen in the core. Since the sun has been fusing hydrogen into helium throughout its lifetime, the present day abundance of helium in the core can be used to infer the age of the sun, using numerical models of stellar evolution

Stellar structure

Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star....

applied to the Sun (Standard solar model

Standard Solar Model

The Standard Solar Model refers to a mathematical treatment of the Sun as a spherical ball of gas...

).
This method provides verification of the age of the solar system gathered from the radiometric dating of meteorites.

Local Helioseismology

The goal of local helioseismology, a term first used in 1993, is to interpret the full wave field observed at the surface, not just the mode (more precisely, eigenmode) frequencies. Another way to look at it, is that global helioseismology studies standing waves of the entire Sun and local helioseismology studies propagating waves in parts of the Sun. A variety of solar phenomena are being studied, including sunspots, plage

Plage (astronomy)

A plage is a bright region in the chromosphere of the Sun, typically found in regions of the chromosphere near sunspots.The term itself is poetically taken from the French word for "beach." The plage regions map closely to the faculae in the photosphere below, but the latter have much smaller...

, supergranulation

Supergranulation

Supergranulation is a particular pattern on the Sun's surface. It was discovered in the 1950s by A.B.Hart using Doppler velocity measurements showing horizontal flows on the photosphere ....

, giant cell convection, magnetically-active region evolution, meridional circulation, and solar rotation

Solar rotation

Solar rotation is able to vary with latitude because the Sun is composed of a gaseous plasma. The rate of rotation is observed to be fastest at the equator , and to decrease as latitude increases...

. Local helioseismology provides a three-dimensional view of the solar interior, which is important to understand large-scale flows, magnetic structures, and their interactions in the solar interior.

There are many techniques used in this new and expanding field, which include:

Fourier–Hankel spectral method, first introduced by Braun and Duvall, was originally used to search for wave absorption by sunspots.

Ring-diagram analysis, first introduced by F. Hill, is used to infer the speed and direction of horizontal flows below the solar surface by observing the Doppler shifts of ambient acoustic waves from power spectra of solar oscillations computed over patches of the solar surface (typically 15° × 15°). Thus ring analysis is a generalization of global helioseismology applied to local areas on the Sun (as opposed to half of the Sun). For example, sound speed, and adiabatic index can be compared within magnetically active and inactive (quiet Sun) regions.

Time-distance helioseismology, introduced by Duvall et al., aims to measure and interpret the travel times of solar waves between any two locations on the solar surface. A travel time anomaly contains the seismic signature of buried inhomogeneities within the proximity of the ray path that connects two surface locations. An inverse problem must then be solved to infer the local structure and dynamics of the solar interior.

Helioseismic holography, introduced in detail by Lindsey and Braun for the purpose of far-side (magnetic) imaging, a special case of phase-sensitive holography. The idea is to use the wavefield on the visible disk to learn about active regions on the far side of the Sun. The basic idea in helioseismic holography is that the wavefield, e.g., the line-of-sight Doppler velocity observed at the solar surface, can be used to make an estimate of the wavefield at any location in the solar interior at any instant in time. In this sense, holography is much like seismic migration, a technique in geophysics that has been in use since the 1940s. As another example, this technique has been used to give a seismic image of a solar flare. Acoustic holography, applied to MDI data, is ideal for the detection of sources and sinks of acoustic waves on the Sun. Braun and Fan discovered a region of lower acoustic emission in the 3 – 4 mHz frequency band which extends far beyond the sunspots (the ‘acoustic moat’). Acoustic moats extend beyond magnetic regions into the quiet Sun. In addition, Braun and Lindsey discovered high-frequency emission (‘acoustic glories’) surrounding active regions.

Direct modelling, after Woodard. Here the idea is to estimate subsurface flows from direct inversion of the frequency-wavenumber correlations seen in the wavefield in the Fourier domain. Woodard gave a practical demonstration of the ability of the technique to recover near-surface flows from the f-mode part of the spectrum.

This section is adapted from Laurent Gizon and Aaron C. Birch, "Local Helioseismology", Living Rev. Solar Phys. 2, (2005), 6. online article (cited on November 22, 2009).

Jet stream movement may affect solar cycle

An internal jet stream moving behind schedule may explain the delayed start to the solar cycle in 2009.

External links

Non-technical description of helio- and asteroseismology retrieved November 2009
Laurent Gizon and Aaron C. Birch, "Local Helioseismology", Living Rev. Solar Phys. 2 (2005) 6 online article
Scientists Issue Unprecedented Forecast of Next Sunspot Cycle National Science Foundation press release, March 6, 2006
Large-Scale Dynamics of the Convection Zone and Tachocline by Mark S. Miesch
European Helio- and Asteroseismology Network (HELAS)
Farside and Earthside images of the Sun
Living Reviews in Solar Physics

Satellite instruments

Ground-based instruments

BiSON
Mark-1
GONG
HiDHN

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

Types of solar oscillations

Analysis of oscillation data

Inversion

Internal structure

Helioseismic dating

Local Helioseismology

Jet stream movement may affect solar cycle

See also

External links

Satellite instruments

Ground-based instruments