Models
The reason why we want to do so much detailed work on observing oscillations
on the Sun and on other stars is that we want to improve our models and
our understanding of the physics of stellar interiors.
For this reason we have been constructing models of stars for a very
long time, in the last few decades using extensive computer programmes --
the physical effects that are included in the models are
now so extensive and varied that we can no longer do the calculations
using just paper and pencil. The more details we get from the observations,
the better the models that we can construct, and the greater is our
understanding of the stars. Making stellar models involves a number of
physical principles :
- Thermodynamics : The Sun and stars shine, emitting energy
into the rest of the Universe and they therefore lose energy from their
interior. From the colour of the light coming from the Sun (or a distant
star) we know the temperature on the surface. That temperature is so
high that we immediately know that stars cannot be anything other than
plasma : highly ionized gas. The physics that applies to stars is therefore
the physics of hot gas and radiation.
- Hydrostatic equilibrium : At every point inside the Sun
and in stable stars (and most stars are) the force of gravity must be
balanced precisely by the gas pressure. Just as the pressure on your body
increases as you dive deeper and deeper into the sea, so does the pressure
increase as you go deeper and deeper into the Sun.
- Nuclear physics : The Sun has been shining steadily for at
least as long as the earth has existed. The output of energy (light) is
enormous, and so we know of only one source of energy that can sustain
that output for so long : nuclear fusion of light elements. In the Sun
the energy is generated by four hydrogen nuclei fusing into one helium
nucleus.
- Atomic physics : The energy that is produced
in the central parts of the Sun is transported outward by radiation
throughout most of the solar interior. To describe this transport of
energy we need to be able to calculate how radiation is absorbed and
emitted by the matter inside the Sun, which requires a detailed
knowledge of atomic physics.
- Hydrodynamics : In the outer parts of the Sun
the transport of energy occurs through the rising of elements of hot gas
and the sinking down of cold gas : this process is called
convection. The details of the gas
motions are very complicated and not at all well understood, but we can
make extensive computer models of the processes using hydrodynamical
simulations.
To construct a model of the Sun as it is today, we must follow its evolution.
The reason for this is that the structure of the Sun changes due to the fact
that hydrogen is converted into helium. The Sun is now about 4.5 billion years
old and has, according to our models, used up about half of the available
hydrogen in its central parts. We can therefore count on the Sun to live
another 4 billion years before the hydrogen is completely used up.
One of the predictions of the computer models is the way the gas density
and temperature behave inside the Sun as a function of radius.
Some results of the model calculations are shown
here. Especially the temperature is important for us because there
is a direct relation between the temperature and the
sound speed in gas -- a quantity we can measure using seismological
methods. This means that we can compare directly our computer models
with the Sun throughout its interior, and so gain in our understanding of
the physical conditions. How well we do is shown on the
Results page.
By comparing the models with reality we can see whether we did the
calculations correctly. However it also shows whether the physical assumptions
we used in the calculations are correct. In other words we can use the
observations to learn something about fundamental physics. With sufficiently
accurate observations we can in fact use the Sun as a kind of big laboratory,
in which we can study the properties of matter under conditions that we cannot
possibly reproduce in laboratories on Earth.