Fig. 1: Pulsation pattern for an oscillation with l = 3. The yellow coloured surfaces move outward, while the blue coloured ones move inward. Also the movement of the node lines is illustrated. Please click on a certain model to see an animation (from Zima (1999, Master Thesis)). |
A pulsation is radial, when the star oscillates around the equilibrium state by changing it's radius under maintenance of it's spherical shape. The radial pulsation is just a special case of nonradial pulsation. Nonradial pulsation means that some parts of the stellar surface move inwards, while others move outwards at the same time.
Such an oscillation can be described with three parameters (quantum numbers): the radial order n, degree l, and the azimuthal number m. The degree l is equivalent to the number of node lines on the stellar surface (on a node line no radial motion takes place). Of those l node lines a total of m lines lie in meridional direction (there are 2l +1 possible m-values for one l-value). Modes with m <> 0 represent waves travelling around the star. They can be prograd (m > 0) or retrograd (m < 0), dependent on the direction of their movement around the star.
In a nonradially pulsating nonrotating star without a magnetic field for one l value the frequencies of all m-modes have the same value. This is called degeneration in 2l+1 folds. This degeneration can be lifted by stellar rotation or a magnetic field. The so called rotational frequency splitting enables us to calculate the stellar rotation period. The frequency sm of a rotationally split mode is written as: sm = s0+(CL-1)mW+(DLm²W²)/s0 ,where W is the rotational frequency and CL and DL are dependent on the coriolis force and the centrifugal force. Both factors depend on the internal structure of the star and hence contain asteroseismological information.
Pulsation modes are further distinguished by n, the number of nodes in the radial component of displacement from the center to the surface of a star. For n-values of 0 the star oscillates in the fundamental mode. n=1 is the first overtone, n=2 the second overtone, etc. A radial pulsation with n=2 is shown in Figure 2.
Fig. 2: Schematic illustration of the node lines in the stellar interior for a radial pulsation with n=2 (from Zima (1999, Master Thesis)). |