The Sun swings
For a long time there were no possibilities in solar physics research to determine directly information about the solar structure. All knowledge was based on theoretical considerations and model calculations. Not until the 1970s helioseismology developed to the branch of solar physics that allowed to revise the theoretical results on the observations of low-frequency sound waves that show up on the solar surface.
Roger K. Ulrich and – independent from him – John W. Leibacher with Robert F. Stein elaborated the necessary theoretical foundations. They calculated that the Sun is possibly subject to oscillations and swings like a musical instrument. These oscillations hum through the whole solar body. In the same way as the tones characterize a musical instrument and its design the sound waves that travel through the Sun are characteristic for the internal properties of the Sun. In turn it should be possible to determine these internal solar properties by investigating the sound waves probing the Sun. This is in deed where helioseismology is very successful.
The first evidence of solar oscillations goes back to Robert Leighton in 1962. Together with Robert W. Noyes and George W. Simon he investigated flow velocities at the solar surface by the Doppler effect and found indications of a wave motion with a period of 5 minutes. At that time these waves were considered to be an atmospheric phenomenon. The theoretical ideas, that these sound waves penetrate through the whole Sun were proofen by Franz-Ludwig Deubner in 1975.
Since then solar oscillations, and based on them the solar interior, were studied with great precision. The details that were derived about the solar interior exceed by far the usual accuracy of any other investigation of an astronomic object.
The Sun as a Resonance Cavity
Three types of oscillations are descriminated on the Sun. The main source of information are acoustic waves. The pressure gradient is their driving force. These waves are called p modes (p: pressure).
Waves where boyancy drives the oscillation are called g modes (g: gravity). Theoretically they might exist in the Sun, but until now they were not detected.
A special type of waves are surface waves. They correspond to waves, that are known from the surfaces of deep water. They are called f modes (f: fundamental).
The discrete spectrum of waves as it is observed on the Sun is only possible if the waves penetrate through large areas in the solar interior and finally interfere constructively. This comes abouth as following: sound waves are refelected inwards at the solar surface because of the rapidly decreasing gas pressure. Towards the solar center the temperature increases continously. Connected with this temperature increase the sound speed increases as well. The lower part of a wave front that is reflected at the surface with a non-vanishing inclination angle moves faster than the upper part. The wave turns away from its originally almost vertical orientation towards the center and migrates back towards the surface. Waves migrating inwards and waves migrating outwards interfer and for certain frequencies this interference leads to formation of standing waves with characteristic patterns. A single standing wave – or a oscillation mode – has a surface amplitude in the order of cm/sec. The simultaneous occurrence of approximately 10 millions of standing waves in the Sun results at the surface in the well-known phenomenon of the “Five-Minute Oscillations” with velocity amplitudes of some kilometers per second.
Following a sound wave on its way from the surface, the wave is directed first almost vertically towards the solar center. As the sound speed increases the wave path is more and more bended and the waves misses the center of the Sun. Therefore, the path of a wave through the solar interior depends particularly on the course of the sound speed in the solar interior. The point of the closes encounter with the solar center is called turning point of the modus. Having passed the turning point the wave migrates back outwards until it reaches the surface again. There the wave is reflected as by a mirror turning is orientation back towards the center.
These kind of sound waves are the origin for standing waves that are generated if inwards and outwards migrating waves are superimposed. In the Sun we have to speak of standing waves in a three-dimensional sense.
The oscillation pattern at the surface exhibits node lines, where the motion is at rest. The total number of node lines at the surface is called harmonic degree l. Some modes show node lines that connect the poles. These number m of node lines is alway lower than or equal to the harmonic degree l. In the solar interior the oscillation modes do also exhibit the nature of standing waves by having a certain number n of nodes along the radius. This number of radial nodes is called radial order. Any mode can be definetively identified by the three numbers n, l, and m.