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- W4255133034 abstract "To determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the Vlasov theory for galaxy dynamics. In this article, we study the stability of isotropic spherical symmetric galaxy models f 0(E), for which the distribution function f 0 depends on the particle energy E only. In the first part of the article, we derive the first sufficient criterion for linear instability of f 0(E) : f 0(E) is linearly unstable if the second-order operator $$A_{0} equiv-Delta+4piint f_{0}^{prime}(E){I-{mathcal{P}}}dv$$ has a negative direction, where $${mathcal{P}}$$ is the projection onto the function space {g(E, L)}, L being the angular momentum [see the explicit formulae (29) and (28)]. In the second part of the article, we prove that for the important King model, the corresponding A 0 is positive definite. Such a positivity leads to the nonlinear stability of the King model under all spherically symmetric perturbations." @default.
- W4255133034 created "2022-05-12" @default.
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- W4255133034 date "2008-02-29" @default.
- W4255133034 modified "2023-10-14" @default.
- W4255133034 title "Unstable and Stable Galaxy Models" @default.
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- W4255133034 doi "https://doi.org/10.1007/s00220-008-0439-z" @default.
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