Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

A framework for perturbations and stability of differentially rotating stars


Beyer,  Horst R.
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

(Preprint), 239KB

Supplementary Material (public)
There is no public supplementary material available

Beyer, H. R. (2000). A framework for perturbations and stability of differentially rotating stars. Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 458(2018), 359-380.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5767-E
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.