Helioseismology

A computer-generated image showing the pattern of a p-mode solar acoustic oscillation both in the interior and on the surface of the sun. (l=20, m=16 and n=14.) Note that the increase in the speed of sound as waves approach the center of the sun causes a corresponding increase in the acoustic wavelength.

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 (s-waves). Solar pressure waves are believed to be generated by the turbulence in the convection zone near the surface of the sun.^[1] 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 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 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 to generate the main magnetic field of the Sun, and that the convective zone has "jet streams" of plasma thousands of kilometers below the surface. These jet streams form broad fronts at the equator, breaking into smaller cyclonic storms at high latitudes.

Helioseismology can also be used to image the far side of the Sun from the Earth,^[2] including sunspots. 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 MDI.^{[citation needed]}

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's interior. The science can be compared to asteroseismology, which considers the propagation of sound waves in stars.

Types of solar oscillations

Low-resolution solar oscillation spectrum taken by the GOLF instrument between 19 February and 25 March 1996. The horizontal axis is frequency in millihertz, or thousandths of a hertz (mHz), the vertical axis is power density. The "5-minute oscillation" is the series of p-mode lines on the right between about 2 and 7 mHz.

Solar oscillations 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 or sensitive spectral line intensity imaging.

• 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: in the deep interior of the Sun, the temperature gradient 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) and g-modes cannot propagate. The g modes are evanescent through the entire convection zone, and are thought to have residual amplitudes of only millimeters at the photosphere. 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.^[3][4] At the GONG2008 / SOHO XXI conference held in Boulder, the Phoebus group 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 has just published a review over the current state of knowledge on the solar g modes.^[5]

• 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.

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). A mathematical technique known as Fourier analysis is used to recover information about individual modes from this mass of data. 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 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; however the rotation of the Sun, which leads to an equatorial bulge, lifts this degeneracy.

In general the frequencies ω_nlm of stellar oscillations depend on all three wave numbers. It is convenient, however, to separate the frequency into the multiplet frequency ω_nl, obtained as a suitable average over azimuthal order m and corresponding to the spherically symmetric structure of the star, and the frequency splitting δω_nlm = ω_nlm − ω_nl.

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 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.

This discussion is taken from the Christensen-Dalsgaard lecture notes on stellar oscillations.^[6]

Helioseismic dating

The age of the sun can be inferred with helioseismic studies.^[7] 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 applied to the Sun (Standard solar model). This method provides verification of the age of the solar system gathered from the radiometric dating of meteorites.^[8]

Internal structure

Helioseismic observations revealed the inner uniformly-rotating zone and the differentially-rotating envelope of the Sun, roughly corresponding to the radiation and convection zones, respectively. The transition layer is called the tachocline.

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.^[9]

See also

• Asteroseismology
• Magneto-gravity
• Proton-proton chain
• Solar neutrino problem
• Solar tower

References

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

Satellite instruments

• VIRGO
• SOI/MDI
• TRACE

Ground-based instruments

• BiSON
• Mark-1
• GONG
• HiDHN