The determination of fundamental parameters for stars is among the most important problems in astrophysics, and among the most challenging. Upon these basic data rest the whole structure of modern astrophysics, most especially the distance scale to the galaxies and the ages of stellar clusters. Both the neutrino detection experiments and the application of helioseismology have demonstrated that no satisfactory solar model exists which can simultaneously match the gross physical parameters of the Sun and the superb observational data now available. The resolution of an important problem in modern astrophysics - the discrepancy between the ages of globular cluster stars and the cosmological age, may come from a deeper, more quantitative understanding of stellar interiors and evolution. Asteroseismology, the study of global oscillations in stars, is a promising new technique for measuring the fundamental parameters in stars with significantly higher precision than has previously been possible, allowing quantitative comparison of data with stellar models and the examination of the behavior of matter under conditions of pressure and temperature which cannot be achieved on Earth.

Science Goals

Stars can be characterized by five intrinsic parameters, plus distance: mass, helium fraction, the abundances of metals, age, and the mixing length ratio. In principle, measurement of the frequency separations of p-mode oscillations (i.e. sound waves) permits estimation of the age and mass of a star with useful precision (if the metallicity is known from other means). However, the uncertainty in stellar metallicity determinations increases the uncertainties in masses and ages determined from oscillation frequencies to significant levels. Additional information, such as the actual individual oscillation frequencies or other data which can help constrain the intrinsic parameters, are needed. In their study of the use of oscillation data in the determination of stellar parameters, Brown et al. (1994) concluded that the determination of ages, mixing lengths, and masses can be substantially improved when oscillation data can be included with traditional measures, especially for more distant stars for which astrometric distances cannot be obtained. The application of asteroseismology techniques to stars in clusters will ultimately allow us to obtain more accurate distances and ages for the calibration of the distance scale and for comparison to stellar evolution models. To reach that point we must begin to develop the measurement techniques on bright field stars.

Stellar oscillations can be described (for spherical stars) as radial eigenmodes multiplied by a spherical harmonic, with two quantum numbers, n and l. The radial order n is the number of nodes in the eigenfunction between a star's center and its surface. For typical solar type stars, n is of order 20. The angular quantum number l describes the number of nodes around the circumference. For observations in integrated light, l is usually small, (l=0,1,2, or perhaps, 3). Differences in frequencies of oscillation of these modes are related to the intrinsic parameters. Frequency separations of the n-modes are typically large, and are related to the time for a sound wave to cross the star (hence, density). Frequency separation of the l-modes are smaller and are related to the radial gradient of the sound speed. Measurement of the the l- and n-mode frequency splittings can yield good estimates of mass and age when combined with stellar models and other observational parameters.


To obtain meaningful asteroseismological data requires continuous observations over many stellar oscillation cycles. In recent years several observing networks have developed to allow long sequences of data to be obtained to study oscillations in particular types of stars. These include the Whole Earth Telescope (WET), the Delta Scuti Network (from the University of Vienna), MUSICOS (a collaboration devoted to the study of time variable phenomena in early type stars), and the proposed STARS satellite to detect and study acoustic waves in stars in clusters.

The Whole Earth Telescope is a useful model for examination. WET was initiated at the University of Texas to study pulsations in white dwarf stars (Arlo Landolt detected the first pulsations in white dwarfs in 1968 using the 2.1m telescope on Kitt Peak!). WET has organized numerous campaigns to monitor white dwarfs photometrically to study g-mode oscillations. Their detail observations allow precise measurements of the masses of white dwarfs, rotation periods, limits on (or detections of) magnetic fields, and evidence for chemical stratification in white dwarf envelopes.

Efforts to detect and study p-mode oscillations in solar type stars have been less successful, primarily because the amplitudes of the oscillations in integrated light are so small. Techniques include photometric monitoring, Doppler shifts, and changes in the equivalent widths of photospheric absorption lines. The best evidence for p-mode oscillations in solar type stars comes from a recent paper by Kjeldsen et al. They employed low resolution spectra (2A/pixel) from a Cassegrain spectrograph on the 2.5m Nordic Optical Telescope to look for minute variation in the equivalent widths of H-beta, gamma, delta. They observed apparently significant oscillations with a frequency of about 850 microHz (about 20 minutes) and a frequency spacing of about 40.3 microHz in the G0IV star Eta Boo. The amplitudes of these oscillations are typically 5-50 parts per million in the equivalent width. These results have yet to be confirmed.


The Kjeldsen et al. result offers a promising new technique for detecting and studying oscillations in stars. A coordinated effort to develop and apply this and related techniques to solar type stars is timely, and offers the opportunity to address seriously an outstanding problem in modern astrophysics.

With these techniques and telescopes of sufficient aperture (i.e. 2- to 4-m class) one can detect and study oscillations in solar type stars in nearby, well-studied clusters such as the Hyades, the Pleiades, Praesepe, Coma (the stellar cluster!), Ursa Major, etc. which represent a range in age of nearly a gigayear. A decade ago, these clusters seemed to be reachable only with 8- to 10-m class telescopes, but with improved detectors, instrumenation, and new techniques, many are may now be within reach of 4-m class facilities. Improvement in observing efficiencies on 4-m class may allow observations of stars near the turnoff in the solar-age cluster M67. With some stretch of the imagination, access to stars in globular clusters may be feasible with Gemini class telescopes. But even more likely (for Population II stars) is the use of subdwarfs with well determined distances from Hipparchos.

Last change: March 26, 1996