A mean-field magnetic polytrope model shows radiation pressure can unbind an n=3 polytrope when the central overpressure exceeds roughly 0.15 times a mass-dependent factor under small radial perturbations.
Non-linear stability of gaseous stars
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We construct steady states of the Euler-Poisson system with a barotropic equation of state as minimizers of a suitably defined energy functional. Their minimizing property implies the non-linear stability of such states against general, i.e., not necessarily spherically symmetric perturbations. The mathematical approach is based on previous stability results for the Vlasov-Poisson system by Y. Guo and the author, exploiting the energy-Casimir technique. The analysis is conditional in the sense that it assumes the existence of solutions to the initial value problem for the Euler-Poisson system which preserve mass and energy. The relation between the Euler-Poisson and the Vlasov-Poisson system in this context is also explored.
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Non-linear Dynamical Stability of Magnetic Polytropes
A mean-field magnetic polytrope model shows radiation pressure can unbind an n=3 polytrope when the central overpressure exceeds roughly 0.15 times a mass-dependent factor under small radial perturbations.