Astronomy and Astrophysics – Astrophysics
Scientific paper
2007-02-14
Mon.Not.Roy.Astron.Soc.377:630-644,2007
Astronomy and Astrophysics
Astrophysics
16 pages, accepted for publication in MNRAS
Scientific paper
10.1111/j.1365-2966.2007.11625.x
Motivated by the possibility of radiation driven instabilities in rotating magnetic stars, we study the stability properties of general linear perturbations of a stationary and axisymmetric, infinitely conducting perfect fluid configuration threaded by a magnetic field and surrounded by vacuum. We develop a Lagrangian perturbation framework which enables us to formulate a strict stability criterion based on the notion of a canonical energy (a functional of the fluid displacement $\xi $ and its first time derivative). For any given choice of $\{\xi,\partial_t \xi \} $, the sign of the canonical energy determines whether the configuration is stable or not at the linear level. Our analysis provides the first complete description of the stability problem for a magnetic star, allowing for both rotation and the presence of a magnetic field in the exterior vacuum region. A key feature of the Lagrangian formulation is the existence of so-called `trivial' fluid displacements, which do not represent true physical perturbations. In order for the stability criterion to make rigorous sense one has to isolate these trivials and consider only the physical `canonical' displacements. We discuss this problem and formulate a condition which must be satisfied by all canonical displacements. Having obtained a well-defined stability criterion we provide examples which indicate that the magnetic field has a stabilising effect on radiation driven instabilities.
Andersson Nils.
Glampedakis Kostas
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