Almost all chemical elements are produced by nucleosynthesis in stars.
Our nearest star, the Sun, will not only produce all the chemical elements
found in living organisms during its lifetime of several billion years,
but it is also the source of energy without which no life can exist on Earth.
Studying our Sun and sunlike stars is therefore a very exciting branch of
astrophysics. In 1962 the epoch-making discovery of the so-called five-minute
oscillations in the Sun was reported. Patches of the solar surface are moving
up and down (oscillating) with a typical period of approximately five minutes.
These oscillations are manifestations of acoustic waves travelling through the
whole Sun. From these sound waves we can learn about the interior of the Sun in
a way similar to the way by which geophysicists use earthquakes to learn about
the interior of the Earth. The science of studying solar waves is called
helioseismology.
In the Sun and in sunlike stars these sound waves are generated in the outer turbulent
layers. In these layers bubbles of hot gas rise towards the surface where they cool
and sink back again (such as the bubbles in a pot of boiling water). The sound propagates
inside the star and is refracted away from the centre as a result of the increase of
temperature (and therefore sound speed) with depth. Sound waves of particular (resonant)
frequencies interfere constructively to form standing waves, just as in a musical
instrument (such as a bell or cymbal). And, as in the case of a musical instrument, from
the frequencies of the sound we can learn about the nature of the oscillating object, namely
the star. The standing waves are called oscillation modes. The shapes of the modes on
the star's surface are spherical harmonics.
The modes can be measured either from Doppler shifts of spectral lines or from intensity fluctuations.
Roughly speaking, the Doppler shift of light from a moving source, causing a change in colour, is
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Spherical harmonics of a standing wave in the Sun.
The cut-out on the right-hand side reveals the pattern
of the standing wave inside the Sun.
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like the Doppler shift
of sound, causing a change in tone: the sound of a car moving towards someone standing on
the roadside is higher in pitch than it becomes after the car has passed and is moving away.
One particular mode of the Sun is shown in the Figure, in which blue patches of the surface are moving towards
the observer and red patches are moving away. The cut-out on the right-hand side of the picture reveals the pattern
of the mode inside the Sun. The frequencies of the oscillations are obtained by projecting the measured surface Doppler
or intensity signal at each time onto spherical harmonics and taking a Fourier power spectrum of the time series of
the resultant amplitude. The outcome is illustrated by the overlaid diagram, which shows the oscillation power spectrum
for the sunlike star ß Hydri, the brightest star in the southern constellation Hydrus. The blue spectrum is the Doppler
measurement and the magenta spectrum is a theoretical expectation, obtained by scaling the Sun to ß Hydri. From measuring
such oscillations we are able to study the physics of the interiors of stars with a precision that was quite out of reach before.
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