New results for the Herzenberg dynamo: steady and oscillatory solutions

Abstract

The Herzenberg dynamo, consisting of two rotating electrically conducting spheres with non-parallel spin axes, immersed in a finite spherical conducting medium, is simulated numerically for a variety of parameters not accessible to the original asymptotic theory. Our model places the spheres in a spatially periodic box. The largest growth rate is obtained when the angle, ϕ, between the spin axes is somewhat larger than 125 • . In agreement with the asymptotic analysis, it is found that the critical dynamo number is approximately proportional to the cube of the ratio of the common radius of the spheres and their separation. The asymptotic prediction, strictly valid only in the limit of small spheres, remains approximately valid even when the diameter of the spheres becomes comparable to their separation. For |ϕ| < 90 • we also find oscillatory solutions, which were not predicted by Herzenberg's analysis. To understand such solutions we present a modified asymptotic analysis in which the separation of the two spheres is essentially replaced by the skin depth which, in turn, depends on the diameter of the spheres. The magnetic field consists of magnetic flux rings wrapped around the two spheres. Applications to local models of turbulent dynamos and to dynamo action in binary stars are discussed.

Swing excitation and magnetic activity in close binary systems

“…Here we restrict ourselves to binary systems with nearly aligned stellar rotation axes. If the angle ξ between the rotation axis and the orbital plane in a young binary system is sufficiently large (tan ξ∼ 1), a dynamo excitation of the Herzenberg (1958) type becomes possible (see Brandenburg, Moss & Soward 1998).…”

Current Status of Turbulent Dynamo Theory

“…Dynamo action is possible when the rotors spin faster than a certain critical value that depends on the angle between the rotors. For angles between 90 and 180 degrees the solutions are non-oscillatory, while for angles between 0 and 90 degrees there are oscillatory solutions that were discovered only more recently (Brandenburg et al 1998).…”

Simple laminar dynamos

“…Dolginov & Urpin (1979) attempted to apply the Herzenberg concept to the generation of magnetic fields in binary stars systems, concluding that in some nova and symbiotic star systems, given favourable assumptions growth times for magnetic fields could be as short as O(10 3 ) yr. Although there are some unresolved questions about this work, it might be fruitful to pursue these ideas via numerical simulations similar to those of Brandenburg et al (1998) with parameters chosen to be astrophysically relevant. Bigazzi, Brandenburg & Moss (1999) tried to use the Herzenburg dynamo concept to model magnetic fields localized near pairs of rotating vortex tubes found in some simulations of compressible magnetoconvection.…”