The Oscillation Modes

A three-dimensional body, like a star, needs three numbers to characterize its oscillation modes. These are: 'n' (the order of the mode), 'l' (the degree of the mode) and 'm' (the azimuthal order of the mode). The number of nodes - places where the oscillation amplitude is zero - that exist between the stellar center and the surface is indicated by 'n'. 'l' and 'm' give us more detailed information about the mode, with 'l' indicating the number of lines that divide the stellar surface in oscillations of opposing phase. When the symmetry is broken, for example in the case of a rotating body, the number modes increases up to 2l+1 = m. The modes with m=0 are called zonal, and the nodes are latitudinal lines. The modes with m=l are called sectorial, and the nodes are longitudinal lines. The others are generically called teseral ones.

The l=0 modes, called radial are those that are displayed by the classical pulsating stars (mainly Cepheides and RR Lyrae stars). These are modes in which the restoring force is driven by pressure, which are called p modes. In general, their number increases with increasing frequency.

The l<>0 modes are non-radial ones. They may be p or g modes, the latter ones named after gravity which is their main restoring force. The number of gravity modes increases towards lower frequencies, in the opposite way as the p modes. A star is being characterized through its oscillations through a propagation diagram.

Here are animations of stars with several oscillation modes.