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günter houdek
vienna university
University of Vienna
Department of Astrophysics
Helioseismology
Last Updated: Monday, 29 August 2022, 12:04 GMT

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
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.

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.
Günter Houdek, Department of Astrophysics, Türkenschanzstr. 17, 1180 Vienna, Austria Tel: +43 (1) 4277 51801 Email:guenter.houdek@univie.ac.at