The spectrum of adiabatic stellar oscillations.

Details The spectrum of adiabatic stellar oscillations. The spectrum of adiabatic stellar oscillations.

Sep 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995jmp....36.4792b&link_type=abstract

Journal of Mathematical Physics, Vol. 36, No. 9, p. 4792 - 4814

Mathematics

Mathematical Physics

8

Stellar Oscillations: Polytropes

Scientific paper

The stability analysis for spherically symmetric stellar equilibrium models with respect to "small" adiabatic Lagrangian perturbations leads to the consideration of a class of densely defined, linear symmetric operators in Hilbert space, which are induced by certain singular vector-integro-partial differential operator. The extension properties of these operators as well as the spectral properties of the linear self-adjoint extensions which are chosen by physical boundary conditions are investigated. For this, the equilibrium models are assumed to be polytropic, with a constant adiabatic index only near the center and near the boundary of the star. Among others it is shown that the operators of the class having a polytropic index near the boundary which is ≥1 are in particular essentially self-adjoint and have a closure with a pure point spectrum.

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