Asteroseismology
Introduction
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.
Observations
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.
Outlook
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