Introduction:
In the 1960's it was discovered by Robert Leighton, Robert Noyse, and George Simon that large cells of moving material were distributed roughly uniformly over the surface of the Sun (Leighton et al. 1962). The oscillations were detected by measuring Doppler shifts of spectral lines and revealed that they had periods of about five minutes. After further observational and theoretical work in the 1970, it was accepted that the observed oscillations are the superposition of many global resonant modes of oscillations within the Sun (Thompson 2004). These discoveries lead to the development of a new scientific field called helioseismology. As helioseismology developed through the years, it was only natural to expand the field to include oscillators other than the Sun. In recent years, with the development of sensitive instrumentation and refined observational techniques, a new field known as asteroseismology has emerged. Asteroseismology is the study of the internal structure of stars through the interpretation of their oscillation frequency spectra. It uses the same techniques as helioseismology to measure global oscillations and radial velocities, which when combined with stellar modeling will allow us to probe the interior structure of stars. This paper will briefly introduce the key processes that make asteroseismology possible and how to probe the interior structure of stars.
The Mechanism:
Stars tend to act like a resonant cavity, although there are an infinite number of small oscillations continually occurring, the stratification of the star allows the wave forms to constructively and destructive interact to form large scale standing waves which manifest themselves as global oscillation patterns. For each oscillation the surface pattern is a continuation of the internal oscillatory behavior and can be derived by measuring the surface variability. Currently, it is believed that there are three primary types of wave motions responsible for the global oscillations; they are acoustic waves, gravity waves, and surface gravity waves.
Acoustic waves, or pressure waves, are the dominant wave form measured in the Sun and are the source of p mode oscillations. P-modes are excited by the work of turbulent pressure (Reynolds stresses) and non-adiabatic gas pressure (entropy) fluctuations produced by convection in the stellar envelopes (Stein et al. 2004). Since p-modes develop from acoustic waves, their characteristics are determined by the speed of sound and density profiles in the star. Acoustic waves tend to travel in the vertical, or radial, direction outward until they are reflected at the surface by the large drop in density. The reflected waves refract as they travel deeper into the star, eventually the path will refract enough that the wave will travel back up toward the surface. The modes set up by this wave motion will allow the penetration depth to be calculated. P-mode oscillations typically will have very short horizontal wavelengths and periods between three and eight minutes. P-modes are confined to areas near the surface of the star and associated with convective layers, so they can only provide information about the regions they were created in.
Gravity waves are the source of non radial oscillations known as g-modes. The g-mode oscillations are the result of movement of material due to buoyancy and gravity. Perturbations of the material creates internal gravity waves which constructively and destructively interfere to produce g-mode oscillations. G-modes cannot exist as propagating waves within convection zones and are predicted to have their largest amplitudes deep in the interior of stars, lower frequences then p-modes, and oscillation periods around 160 minutes (Elsworth & Thompson 2004). Since g-mode oscillations are from deep within the star, their oscillations can be used to provide information about the deep interior of star. Although g-modes have not yet been detected in Sun like stars because their predicted amplitudes are too small, they have successively been detected in many other variable stars.
Surface gravity waves are produced similar to gravity waves, but they are located near the star’s surface. Surface gravity waves are the source of the non radial oscillations called f-modes or fundamental modes. The frequencies of f-mode oscillations lie between the frequency of p-mode and g-mode oscillations. The frequency is proportional to the mean density of the star and it is nearly independent of the details of the stellar structure. With f-modes there is no sensitivity to vertical motion, although estimations can be made from the horizontal motions. Using time-distance techniques, f-modes can be used as tracers of horizontal surface flows on stars, the sensitivity to horizontal motions would allow for a more accurate technique for mapping modal patterns than direct Doppler measurements (Duvall & Gizon, 2000). For the Sun, f-modes are excited with a similar frequency envelope to the acoustic p-modes, peaking at near circular frequencies of 3 mHz with an envelope peak near l = 880. In this range the f-mode kinetic energy is concentrated within 2 Mm of the solar photosphere (Duvall & Gizon, 2000).
Detections:
These three wave forms are the sources of the detectable global oscillation patterns. To date, only p-mode and f-mode oscillations have been detected in the Sun. The primary modes used in asteroseismology are p-mode and g-mode oscillations. The modes are defined in terms of spherical harmonics using three integers l, m, and n. The harmonic degree order, l, represents the number of node lines on the surface. The azimuthal order, m, represents the number of surface nodal lines crossing the equator and the phase. The radial order, n, represents the number of nodes in the radial direction. The nodes are sensitive to the physical conditions where their amplitudes are greatest. Thus, since each mode will correspond to different parts of a star’s interior, the goal would be to identify as many modes as possible and use them to model what is happening inside the star. For the application of asteroseismology it is absolutely necessary to clearly identify the l, m, and n for each mode (Kurtz 2004). From observations, it is possible to measure the period and continuum intensity of the p-mode and g-mode oscillations by the careful measurement of the Doppler shifts of spectral lines and photometry.
Techniques:
Using the same techniques as in helioseismology, astrophysicists can collect observational data form telescopes and satellites, and use it to refine current stellar models. In asteroseismology the target stars are far away and unresolved, so only a limited number of oscillation modes and intensities are detectable by photometry and spectroscopy. The degree of the detectable oscillations is restricted to 0 < l < 4 (Shibahashi & Takahara, 2004). In recent years, advances in the techniques for stabilizing the response of spectrometers have meant that we are now able to observe stellar radial velocity oscillations using ground based telescopes (Elsworth & Thompson 2004). Using a number large telescope located around the Earth, observing campaigns are conducted to collect the photometric and spectroscopic data at regular intervals for long periods of time. Photometric and spectroscopic data sets for the b Cephei star n Eridani were obtained over 148 nights using 11 different telescopes at 10 observatories on five different continents (Handler et al. 2004). Although it is difficult to get that much observing time on so many telescopes, it seems to be the typical length of an observing campaign required to obtain good temporal asteroseismological data sets.
Summary:
From the data sets, global oscillation modes are carefully identified and measurements of Doppler radial velocities and continuum intensity fluctuations are carried out. The results can then be processed using a variety of fitting or inversion techniques (Gough 1985) to deduce the interior structure of the target star. These fitting techniques will map out sound speed and density profiles which in turn can be used to locate transitions between convection and radiative zones. This information can then be used to improve current evolutionary stellar models. Although it is difficult because of the low amplitudes, the current goal of asteroseismologists is to gather p-mode data form Sun like stars. The Sun is the closest star and has been extensively studied and mapped out, so it can be used as a reference to compare the data from other Sun like stars and thus will help further refine the current data gathering techniques. In conclusion, this paper should serve as a brief introduction to what asteroseismology is, what it can tell us about stellar structures, what makes it possible, and how we go about gathering and analyzing data.
