The strong surface gravity on a white dwarf star creates a spherical symmetry.
This underlying symmetry makes it possible to describe each pulsation mode with a
mathematical function called a spherical harmonic. Each of these functions is
described by three integer numbers, which asteroseismologists usually label
k, l, m.
The value of k determines the number of times the pulsation
wiggles back and forth from the
center of the star to the surface. This behavior is
hidden deep below the visible surface, but we can distinguish different values of
k because each has a different pulsation period - lower
values of k repeat the visible pattern more quickly.
The value of l determines the total number of borders between
hot and cool zones on the surface of the star. The value of
m can only be between -l and
+l and represents the number of borders between hot and cool
zones on the surface that pass through the pole of the star's rotation axis.
| l=1 | l=2 | l=3 | |
| m=+3 |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l3m+3B.gif",275,275,40,50)) | ||
| m=+2 |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l2m+2B.gif",275,275,40,50)) |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l3m+2B.gif",275,275,40,50)) | |
| m=+1 |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l1m+1B.gif",275,275,40,50)) |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l2m+1B.gif",275,275,40,50)) |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l3m+1B.gif",275,275,40,50)) |
| m=0 |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l1m0B.gif",275,275,40,50)) |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l2m0B.gif",275,275,40,50)) |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l3m0B.gif",275,275,40,50)) |
| m=-1 |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l1m-1B.gif",275,275,40,50)) |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l2m-1B.gif",275,275,40,50)) |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l3m-1B.gif",275,275,40,50)) |
| m=-2 |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l2m-2B.gif",275,275,40,50)) |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l3m-2B.gif",275,275,40,50)) | |
| m=-3 |
![](javascript:openPopWin("http://whitedwarf.org/education/vis/anim/l3m-3B.gif",275,275,40,50)) | ||
Click on one of the images in the table above to view an animation of the pulsation for each combination of l and m. Your browser will launch a small window for the animation, and it may not play at full speed until it is fully downloaded - if you have a slower modem connection, please be patient! Additional animations that you click on will play in the same external window.
You will view the pulsation from about 20 degrees above the equator of the star (you'll be looking slightly down from above so you can see what's going on at the pole on top). For non-zero values of m, it will seem as if the star is rotating - in one direction for positive values of m, and in the opposite direction for negative values. This is an illusion. The star is not actually rotating - the pulsation mode is!
