A steady state of the disc dynamo

Abstract

We discuss the steady states of the αω-dynamo in a thin disc which arise due to α-quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD ₀, and the other for |D| ? 1. Asymptotic solutions for |D—D ₀| ? |D ₀| have a rather universal character provided only that the bifurcation is supercritical. For |D| ? 1 the asymptotic solution crucially depends on whether or not the mean helicity α, as a function ofB, has a positive root (hereB is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(l), while near the disc surface thin boundary layers appear where the field rapidly decreases to zero (if the disc is surrounded by vacuum). Otherwise, when α = O(|B|^?s) for |B| → ∞, we demonstrate that |B| = O(|D|^1/s ) and the solution is free of boundary layers. The results obtained here admit direct comparison with observations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified.     

Torus dynamo in the outer rings of galaxies

ABSTRACT

The magnetic fields in the inner parts of some spiral galaxies are understood quite well. Their generation is connected with the dynamo mechanism that is based on the joint action of turbulent diffusion and the α-effect. Usually the galactic dynamo is described with the so-called no-z approximation which takes into account that the galaxy disc is quite thin, with the implication that some spatial derivatives may be replaced by algebraic expressions. Some galaxies have outer rings that are situated at some distance from the galactic centre. The magnetic field can be described there also using the no-z model. As the thickness of such objects is comparable with their width, it is necessary to take into account the z-dependence of the field. We have studied the magnetic field evolution using the no-z approximation and torus dynamo model for the torus with rectangular cross-section in the axisymmetric case.     

Magnetic instability in a rapidly rotating cylindrical annulus with a finitely conducting inner core

Abstract

We consider the stability of a toroidal magnetic field B = B(s*) (where (s*,φ,z*) are cylindrical polar coordinates) in a cylindrical annulus of conducting fluid with inner and outer radii s_i and s _o rotating rapidly about its axis. The outer boundary is taken to be either insulating or perfectly conducting, and the effect of a finite magnetic diffusivity in the inner core is investigated. The ratio of magnetic diffusivity in the inner core to that of the outer core is denoted by ηη→0 corresponding to a perfectly conducting inner core and η→∞ to an insulating one. Comparisons with the results of Fearn (1983b, 1988) were made and a good match found in the limits η→0 and η→∞ with his perfectly conducting and insulating results, respectively. In addition a new mode of instability was found in the eta;→0 regime. Features of this new mode are low frequency (both the frequency and growth rate →0 as η→0) and penetration deep into the inner core. Typically it is unstable at lower magnetic field strengths than the previously known instabilities.     

A comparison of the asymptotic and no-z approximations for galactic dynamos

Abstract

The asymptotic and the no-z approximation methods of solving the axisymmetric mean field αΩ dynamo equation in a galactic disc are compared. The behaviour of the solutions is explored in both the linear and nonlinear regimes for a variety of dynamo parameters and two different rotation curves. The solutions obtained from the two different approaches are found to be in good agreement.