The Homepage of Liron McLey

Snow on the way to Lake Louise, AB, Canada

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Background     The Equations     Data feed     Numerical method     Compiling and running     Validation of the code


Background

Asteroseismology is the study of the inner structure of stars by observing and analyzing the luminosity oscillations on their surface. Different oscillation modes penetrate to different depths inside the star and their propagation is highly dependent on the stellar conditions (temperature, density, etc.) which means much information can be extracted from analyzing their frequency spectrum. So, bottom line, these oscillation modes are really interesting!

In general, modes are characterized by two parameters, n the mode order and l the angular degree. Both must have integer values and l must also be non-negative, for the values to have a physical meaning. Below is a figure that presents numerical results for the cyclic frequencies (\nu = \omega / 2 \pi) of oscillation modes in the Sun as a function of the angular degree. each line represents a single mode order:

From Figure 5.6 in Lecture Notes on Stellar Oscillations by J. Christensen-Dalsgaard
Notice the following:
  1. l is not an integer (the line is continuous). The reason for this is that it is easier for the numerical calculations this way, however, only integer values have an actual physical meaning.
  2. The mode order: n > 0 are called p-modes, n = 0 is called f-mode and n < 0 are called g-modes.
  3. Because g-modes can't be purely radial, n < 0 modes cannot have an angular degree of l = 0.
The following figure is an example of an eigenfunction for n = 17, l = 20:

From Figure 5.8 in Lecture Notes on Stellar Oscillations by J. Christensen-Dalsgaard
Both figures were taken from Jørgen Christensen-Dalsgaard's Lecture Notes on Stellar Oscillations.


References

The physics in this project and also most of the numerical rationalization were based on Jørgen Christensen-Dalsgaard's Lecture Notes on Stellar Oscillations and Notes on Adiabatic Oscillation Program.

It is worth noting that the display of the beautiful equations throughout this site was made possible thanks to CodeCogs and their equation editor. This is a link to their site, where you can find a straight forward explanation how to do that.


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Last Updated: 10th of June 2014