The branch of asteroseismology which deals with the pulsations of the Sun. An observational study of the solar five-minute variability was first published by Robert Leighton, Robert Noyes, and George Simon in 1962, though the nature of this variability was not understood at the time. The five-minute variability is now understood to be thousands of superimposed acoustic waves passing through the solar interior -- the Sun is ringing like a giant bell. The field of helioseismology has flourished from the 1970s onward, and is still a topic of ongoing research and debate.

Helioseismology has been successful for several reasons. For one, the Sun is so close and so bright that we are able to obtain data with very high signal to noise ratio, and can thus determine the spectrum of oscillations with high accuracy. Furthermore, the Sun is a resolved object, which means that we can observe oscillation modes of high angular degree, l, unlike unresolved stars where we can only observe modes of up to l = 2 or 3. Both of these facts combined means that we can observe thousands of independent pulsation modes. These modes allow us to precisely constrain the structure of the solar interior.

There are many things that helioseismology can reveal about the Sun. For example, it allows us to determine the radius of the base of the convection zone. It allows us to determine the chemical composition of the solar envelope, and study the effects of diffusion, rotation, and turbulence on the Sun's interior structure. Precise knowledge of the Sun's structure also provides a calibration point for studying other stars, particularly in the development of computer simulations for studying stellar evolution. It also allows us to determine equation of state and opacity data for stellar plasmas, again useful for studying other stars. The primary failing of helioseismology is that we have yet to observe oscillation modes that sensitively probe the core of the Sun. For that, we rely on neutrino observations and extrapolation of current data on nuclear reactions and the equation of state at high temperatures and densities.

Several observational studies of the Sun are ongoing. The Solar and Heliospheric Observatory or SOHO satellite has been observing the Sun from the Earth-Sun L1 Lagrange point in space since early 1996, and the GOLF (Global Oscillations at Low Frequencies) and MDI/SOI (Michelson Doppler Imager/Solar Oscillations Investigation) instruments on board are dedicated to helioseismology. On the ground, the Global Oscillation Network Group (GONG), LOWL (for "Low-l"), and Birmingham Solar Oscillations Network (BiSON) have been observing the Sun for many years as well.

Sources: the SOHO website at http://sohowww.nascom.nasa.gov, a good helioseismology summary at http://soi.stanford.edu/results/heliowhat.html, and piles of papers on my desk.