Stability of contrasting solutions of nonlinear hydromagnetic dynamo equations and magnetic fields reversals in galaxiesстатья
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Аннотация:It is known that steady solutions of the hydromagnetic dynamo problem describe sufficiently well the Global Magnetic Patterns (GMP) in spiral galaxies. This paper is devoted to nonlinear quasi-steady state GMP in a thin disc and the stability of these patterns. It is shown that for a majority of spiral galaxies (with a flat rotation curve and with the disc thickness being a linear function of the radius) any stable or long-living axisymmetric GMP with reversals of magnetic field do not exist. For Milky Way it is shown that the analytical results are in a qualitative agreement with the observational information revealing several stable or quasi-steady reversals.
The main mathematical instrument is the method of boundary functions of the theory of singular perturbations. The ratio of thickness of the galactic disc to its radius is used as an asymptotic (small) parameter.