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ID: 3215.0, MPI für Gravitationsphysik / Astrophysical Relativity
A framework for perturbations and stability of differentially rotating stars
Authors:Beyer, Horst R.
Date of Publication (YYYY-MM-DD):2000
Title of Journal:Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences
Issue / Number:2018
Start Page:359
End Page:380
Review Status:Peer-review
Abstract / Description:The paper provides a new framework for the description of linearized adiabatic lagrangian perturbations and stability of differentially rotating newtonian stars. In doing so it overcomes problems in a previous framework by Dyson and Schutz and provides the basis of a rigorous analysis of the stability of such stars. For this the governing equation of the oscillations is written as a first order system in time. From that system the generator of time evolution is read off and a Hilbert space is given where it generates a strongly continuous group. As a consequence the governing equation has a well-posed initial value problem. The spectrum of the generator relevant for stability considerations is shown to be equal to the spectrum of an operator polynomial whose coefficients can be read off from the governing equation. Finally, we give for the first time sufficient criteria for stability in the form of inequalities for the coefficients of the polynomial. These show that a negative canonical energy of the star does not necessarily indicate instability. It is still unclear whether these criteria are strong enough to prove stability for realistic stars.
External Publication Status:published
Document Type:Article
Communicated by:Bernhard F. Schutz
Affiliations:MPI für Gravitationsphysik/Astrophysical Relativity
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