Introduction to helioseismology

Helioseismologist study the internal structure of the sun by observing acoustic oscillations on its surface. One of their instruments, the Michelson Doppler Imager (MDI), aboard the SOHO satellite, measures the Doppler shift of solar absorption lines formed in the lower part of the solar atmosphere Scherrer et al. (1995). This provides line-of-sight velocity measurements for points on the sun's surface that can be used to study solar oscillations. The MDI instrument records a single dopplergram every minute; every dopplergram contains $1024\times 1024$ pixels, and the field of view can be adjusted to either include the full solar disc, or zoomed to image a smaller region at higher resolution. Figure  shows a raw single full-disc dopplergram. The colormap indicates line-of-site velocity. Both the overall left-to-right trend (due to the sun's rotation), and the radial pattern (an artifact of the line-of-sight measurement), are removed or compensated for before the data is analyzed.

 

dopplergram Figure 1 Raw full-disc solar dopplergram from 9 July 1996, 09.00. Colormap shows line-of-site velocity with approximately 0.02 km/s uncertainty. Figure from the Solar Oscillations Investigation (SOI) website, http://soi.stanford.edu.

Although it is difficult to see on a single image, the stochastic nature of the solar oscillations is also apparent in Figure . Oscillations are continually excited by turbulent convective cells within the solar interior. Unlike most terrestrial seismologists who work with sources that can be localized in time and space, helioseismologists have to work with a stochastic source function, and oscillations that are continually being excited.

Helioseismologists often decompose the stochastic wavefields into spherical harmonics Gough and Toomre (1991); Harvey (1995); Kosovichev (1999). In the spherical harmonic domain, the chaotic nature of the source manifests itself in a random phase spectrum, whereas the deterministic solar structure manifests itself in the amplitude spectrum. The spherical harmonic amplitude spectrum, therefore, provides an excellent tool for studying the whole sun at one time. However, small-scale events are only described by harmonic modes of very high-order. Spherical harmonic functions are therefore inefficient for studying small, localized area's of the sun's surface.