The Study of Stellar Oscillations
Understanding stars is central to much of modern astrophysics. Stars are
the fundamental entities providing light and energy in the universe and they
have produced most of the elements (except hydrogen and helium) from which
the Earth is made. In this respect, they are the very source of life on
Earth. Stars also provide vital information about the history and the
structure of the universe, being the only objects for which we can determine
But we are still very far from a detailed physical understanding of stars,
as much of our knowledge is based on limited measurements of the light
emitted from the stellar surfaces from which we rely on theoretical models
to derive their internal properties.
Although the light from the stars
(including the Sun), is created deep within the stellar interior,
where the nuclear reactions takes place, its way out of the dense central
regions is very long, as it is constantly scattered on the particles in the
stellar plasma. It only reaches the surface and escapes the star,
after a trip of a few million years. It then carries information about the
outer regions from which is emitted, and not about the inner regions, where
it was created.
Still, the information contained in the starlight can be
compared with the theoretical stellar models, but this indirect process
is somewhat similar to trying to understand the human body by looking at
the skin only.
But pulsating stars offer more possibilities.
Pulsating stars are stars which size, brightness and temperature vary
periodically with time, due to some internal physical processes.
As it was already mentioned in "DASC and Kepler", these stars can be categorized
according to the manner in which they oscillate, and the stars within the
same class of pulsating stars are also physically similar. With the previous
discussion on the stellar structure and evolution in mind, we can now show
this in more detail.
Pulsations are found in groups of stars all across the Hertzsprung-Russell diagram (or HR diagram).
The figure below shows the positions of different groups of pulsating stars in
the HR diagram. Most of these groups are named after the first star of each
class where pulsations were detected. For instance, the β Cepheid
stars are named after the second brightest (hence Greek
β, the second letter in the Greek alphabet) in the constellation Cepheus,
in which variability has been known to astronomers for more than 100 years.
Move the mouse over the different regions of pulsating stars to see an
example of the typical pulsations observed in the stars belonging to the group.
For each type of stars, two figures are shown; the upper diagram shows how
the stellar brightness changes with time during one day, the lower
one shows the results of a mathematical analysis called Fourier analysis,
which is used to separate the individual oscillation frequencies - or
tones - which are present in the complicated light curve.
This technique for analyzing stellar oscillations in order to extract the
frequencies will be described further in the next section
"Measuring Stellar Oscillations".
The Hertzsprung-Russell diagram ...|
... (also referred to as the HR diagram or HRD)
shows the relationship between the luminosity and the surface temperature
of stars. The diagram, which was first created nearly 100 years ago by Ejnar
Hertzsprung and Henry Norris Russell, improved significantly the
understanding of stellar evolution, or the 'lives of stars'.
In the diagram,
hot, luminous stars are found to the upper left, while cool, dim stars are
found in the lower right part of the diagram.
As illustrated in the Section "Sun-like Stars" a star moves in this diagram as it evolves and hence
changes its surface temperature and luminosity. Thus, plotting values of
temperature and luminosity for many stars as we measure them at present
allows us to determine, for instance, whether a given star is in the main
sequence phase of its life, or if it has evolved away from the main sequence
to become a red giant.
What this diagram actually shows is that the onset of pulsations in a star
is connected to its physical properties - to its luminosity or mass, and
to its evolutionary stage or age. These, together, determine the
position of the star in the HR diagram.
As the star evolves along its evolutionary track (see the section on stellar evolution), it may pass
through one of the marked areas in the figure, and become unstable towards pulsations. This is
due to some internal excitation mechanism that can operate in stars in this
exact region of the HR diagram, and which can cause the star to pulsate.
It then becomes member of the corresponding class of variable stars.
Each group typically contains from a few tens to a few hundred stars in which the type of
pulsations has been detected. These numbers are expected to be significantly
increased by the Kepler mission, as many new variable stars will be detected from the extensive
data sets on hundred thousands of stars.
As the star continues to evolve with time, it will eventually leave the
unstable region again and stop pulsating. What happens here is that due to
changes within the star - such as, for example, a change in density
because the entire star expands - the excitation mechanism is no longer
efficient and can no longer make the star pulsate.
This already tells us a lot about the structure of stars across the HR diagram,
as our theoretical models must be able to reproduce the specific type of
pulsations found in each one of these specific regions in the HR diagram.
We can now, however, do more than this.
Thanks to a fast technological development in instrumentation we can now do ultra-precise and
extensive measurements of these "star quakes" in the individual stars, opening
up a door to the stellar interior, enabling us to apply the technique of
asteroseismology, and actually use the stellar oscillations to look beyond
the stellar surface.
The principles in asteroseismology are the same as those geophysicists use to
infer the internal structure of the Earth: by using vibrations of the Earth's
crust, either brought about naturally by earthquakes or with explosives,
in combination with mathematical and physical models, very detailed
investigations of the structure of the Earth's interior can be carried out.
Two diagrams showing asteroseismic measurements of the nearby star Alpha
Centauri A (4.3 light years away), obtained by the SONG group, compared with data for the Sun.|
As the sizes and internal properties of these two stars are different from each other, their oscillations also show different patterns on the two diagrams below.
The study of the stellar structure and evolution through asteroseismology
is likewise an interplay between complicated theoretical calculations and
ultra-precise observations of stellar oscillations, carried out with
the best telescopes and instruments available, at the best astronomical
sites in the world.
The background for asteroseismology is, however, found in
The Sun is the best-studied star in the sky. This is because we receive
far more light from it than we do from the distant stars, which makes
it much easier to collect precise data. Furthermore, it is close enough
that we can resolve its surface, which is not the case for the other stars.
There are several telescope networks, set up all around the globe, with the
sole purpose of observing the Sun. In each network, 6-8 telescopes are
strategically positioned at different longitudes, allowing for precise,
continuous observations of the solar surface. At the same time, several satellites
observe the Sun, all of which has been taking place for the last
From these measurements, it has been found that the Sun is pulsating
simultaneously in millions of different tones. The typical oscillation periods
for the individual tones are about 5 minutes, which is far too long for
our ears to hear - if we could stand on the surface of the Sun and
listen to its ringing. All these tones mean that the overall brightness of the
Sun varies in a very complicated manner.
But because of very extensive datasets, collected with the telescope networks and the satellites, the
individual tones have been determined to high precision. These many tones, or
frequencies, can accordingly be used to determine the internal properties of the
Sun and be compared with very complicated mathematical and physical computer
models of the structure of the Sun, which in turn can be improved and
developed, in order better to match the observations.
In this way, a very detailed knowledge of the interior structure of the
Sun has emerged, and we have obtained a deep understanding of how a star
like the Sun works.
However, the problem with helioseismology is that we are only investigating
one single star; the Sun.
But are younger or older, or more or less massive
stars, similar in structure to the Sun?
To answer this question, we must observe other stars as well. And the answer to the question is, perhaps not
surprisingly, that although the basic principles are the same, there are
quite significant differences in structure between stars, in particular
between stars of different mass. Stars of about the same mass and
age, on the other hand, are quite alike. This means that by doing seismic
studies of a number of stars with different properties (mass, age), a more detailed picture of
the inner structure of stars can be obtained, and we can investigate how
We can, for instance, study stars that are similar in mass to
the Sun, but older or younger, and obtain knowledge of both the
past and the future of the Sun.
Click on the image to listen to some star sounds
However, although very exciting results are being obtained at present,
asteroseismology is still well behind helioseismology.
This is because we need to study many stars, which takes time. And again because we receive
much less light from the stars.
Furthermore, we cannot resolve their surfaces,
as we can with the Sun. And since the stellar oscillations manifest
themselves in variations in the overall stellar brightness, as well as in
complicated local variations across the stellar surface, we simply have less
information to work with, as compared to the Sun.
This makes it very demanding to obtain sufficient data for determining the
tones precisely, which is necessary for doing asteroseismology and
to compare observationally determined frequencies with theoretical stellar
In the next section, we describe how observations of stellar oscillations
are being done, and why a space telescope such as Kepler, offers fantastic
possibilities for asteroseismology.
Click here, if you want to read more about asteroseismology.
A short history of helio- and asteroseismology|
First evidence for periodic variation in the surface velocity of selected areas of the Sun.|
Solar full-disk observations reveal global oscillations.|
The BiSON network starts limited operations. This network is still operating. |
The IRIS 7-station network starts operation. Operation ends 2001.|
The first evidence for solar-like oscillations in another star (Procyon) is published. Controversial at the time, but later confirmed.|
The GONG network for solar oscillation observations starts full operations. Operations are still ongoing.|
The first detection of individual oscillation modes is published for the star Eta Bootis. Controversial at the time, but later (2003) confirmed. |
First clear detection of excess power in another star (Beta Hyi).|
First definite solar-like oscillation measurements in Alpha Cen A |
First detection of l=3 modes and measurement of mode lifetime in another star (Alpha Cen A).|
Most precise measurements of stellar radial velocities are made with the ESO VLT and the UVES spectrograph (Alpha Cen B).|