Astrophysique stellaire
   Stellar Astrophysics





     Photosphere
     Theoretical model
     Earth oscillations
     Convective zones
     HR diagram
     HR diagram with variable stars
     Overshooting in a Scuti star

     Acknowledgements

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Photosphere

      In order to understand our Universe, one has to start from its main constituent which are the stars. Since the beginning of the XXth century, scientists have been able to analyse the light coming from the stars. They have derived with more and more accuracy the chemical composition of the stellar matter as well as informations about the physical conditions of the stellar surface layers.

      However, the opacity of a star is so large that we can only see through a very tiny layer surrounding the star, which is called the photosphere. One of the main dreams of astrophysicists has always been to enter the star down to its center and to know what really happens there.

Theoretical model

      In the meantime, the theory of stellar structure and stellar evolution was making giant steps and models of stars were being built which could be confronted with the observations. The goal was to compare a whole theoretical structure where complex physical processes are taking place to the only observations we had consisting of some properties of its surface. Can you possibly know what there is inside an orange by just looking at its surface ? The one and only way to probe the internal layers of a star is through asteroseismology.

      The best way of understanding what asteroseismology means comes from musical instruments. Take a violin. The music, in all its tones and harmonics, that comes out of this instrument is caracteristic of the instrument itself. Even the best gifted violonist cannot make a violin sounds like a flute or even a cello. Each instrument has what is called a system of eigenfrequencies which is like the genetic code of the instrument. Knowing this code is like peeking through the whole instrument.

Earth oscillations

      In the early sixties, following the violent earthquake of Chile, oscillations of this type were detected for the Earth. At that time, the internal structure could be theoretically described with some rather crude estimations. From these models, the eigenfrequencies were then computed and they showed that many transition limits were badly located. This was the first victory of seismology.

      In the seventies, it became clear that the Sun was also oscillating in a variety of modes with periods around five minutes. This was the starting point of helioseismology. Huge efforts have been made since then to identify these modes with ultrahigh accuracy either from ground-based observations or from space-borne experiments.

Convective zones

      Achievements have been spectacular. Theoretical solar models were not correct. First, the adopted Helium abundance was wrong which meant that a physical process called diffusion, ignored in the theoretical computations, was acting in the Sun. Second, the convective envelope had not the right extension. And third, and probably the most important result, a description of the way all the internal layers were rotating could be found. And all this, just by knowing what the frequencies of oscillation were.

HR Diagram

      Stars can be very different from the Sun. Taking into account only their surface properties we can put them in a diagram which is called the Hertzsprung-Russell diagram or HR diagram.


On the ordinate axis, the absolute brightness of the star is indicated while the other axis shows the colour or the surface temperature. The Sun is inside a diagonal region which represents the so-called main sequence where 80 % of the stars can be found. Theoretical evolutionary tracks computed for different values of the mass are represented on this diagram. As for the Sun, many unknowns undermine our knowledge of the internal structure of these stars. Fortunately, a large number of these stars are variable. They show slight variations in brightness in the course of time.

HR diagram with variable stars

      This is another HR diagram with the location of variable stars. In fact, most stars do belong to a class of variable stars.


Large amplitude oscillations can be detected from the ground while small ones require space observations. This is where asteroseismology enter the game. Finding the eigenfrequencies of stars different from the Sun will be like seeing through all of them and finding what neither theory nor classical observations have never been able to show.

Overshooting in a Scuti star

      Just to illustrate this point, here is an example with a Scuti star similar to what will be observed with the COROT experiment.


This is an HR diagram again with the observational box of GX Pegasi. Here are three theoretical evolutionary tracks for a star of 2 M computed with different assumptions for the extent of the convective core, indicated here by the value of a convection parameter . Of course, the distribution of hydrogen is different in each of these cases as you can see here, the steep gradient being located at the limit of the convective core.


Now what is the best model ? From the HR diagram it is really impossible to say. Each track passes through the box and is as good as the others.

      Now if we turn towards asteroseismology and compute the oscillation modes, here is what we get. The frequencies are indicated there as a function of the surface temperature.


Changes in the distribution of modes occur at different values of the surface temperature according to the assumption adopted for the extent of the convective core. For the black track, changes start to occur here while for the blue one they occur at a much lower surface temperature. If COROT gives us the disribution of modes, it will clearly be possible to discriminate between these models, which means that we will be able to see where the limit of the convective core is really located.

Acknowledgements

      We would like to acknowledge support from an SSTC/PRODEX contract.



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Web Pages:  Sandrine Sohy
Last modification: 20 janvier 2009.