A New Look at the Eckart‐Scuflaire‐Osaki Classification Scheme of Stellar Oscillations

For a given degree l and azimuthal order m , the eigenfunctions and their associated eigenfrequencies ω of adiabatic oscillation of a spherically symmetrical star constitute a spectrum that, under a broad range of conditions, is discrete. To each mode one can then assign an integer n , called the order of the mode, which by convention has the property of increasing as ω increases. Asymptotically, as | n | → ∞ , the order n becomes equal to the number of nodes, counted appropriately, of a suitably chosen wave function, and indeed, even when | n | is not large, that continues to be the case in the Cowling approximation. Moreover, we can associate with the wave function a spatial phase and relate n to the phase difference at the center and the surface of the star. This natural yet somewhat unconventional way of looking at the mode classification may be of use in searching for a suitable classification scheme that can be applied to the full fourth-order differential system of governing equations that takes into account the perturbation of the gravitational potential.