The distribution law of stellarp-modes

Abstract

We show that the overall density g(o) of asymptotic acoustic frequencies of a star obeys a Weyl law g(o) oc a?- 1 where D is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed, D is equal to the actual dimensionality of the star, D = 3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameter D = 4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range o > o i ~ 2 x fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval o) i o:.