Do spherical $\mathsf{\alpha}^2$-dynamos oscillate?

Abstract

Abstract. The question of whether kinematic α 2 -shell-dynamos are able to produce a cyclic activity is addressed. The α-effect is allowed to be latitudinally inhomogeneous and anisotropic but it is assumed as radially uniform in the turbulent shell. For a symmetric α-tensor we only find oscillatory solutions if i) the α-tensor component α zz vanishes or is of the opposite sign as α φφ , ii) the α-effect is strongly concentrated in the equatorial region and iii) the α-effect is concentrated in a rather thin outer shell. In the other cases almost always the nonaxisymmetric field mode S1 (which slowly drifts along the azimuthal direction) possesses the lowest critical dynamo number. The uniform but anisotropic α-effect (e.g. α zz = 0) leads to nonaxisymmetric solutions as is experimentally confirmed by the Karlsruhe dynamo installation. One of the antisymmetric parts of the α-tensor, however, plays the role of differential rotation in the induction equation. Using the results of a numerical simulation for the α-tensor of the solar convection zone for the radial profile of this effect, one finds the possibility of oscillating α 2 -dynamos even without the existence of a real nonuniform rotation law. Compared with the results of numerical simulations of the full α-tensor, the amplitude of the antisymmetric part of the tensor must be artifically increased by only a factor of three in order to find oscillating solutions.

Large-scale $\vec \alpha\mathsf{^2}$-dynamo in low-mass stars and brown dwarfs

“…While a thin spherical shell surrounding a perfectly conducting core (which the dynamo-generated field cannot penetrate) favours axisymmetric solutions, in our case we find only non-axisymmetric solutions for the α 2 dynamo. This is in agreement with Rüdiger et al (2003), who found the same for an α ∝ cos θ. The situation changes when differential rotation is added.…”

A quest for activity cycles in low‐mass stars

“…V374 Peg seems to have an axisymmetric magnetic field, and it is rotating almost as a rigid body (see Donati et al 2006;Morin et al 2008), posing an interesting question to theoreticians. The fact that we did not find any sign of an activity cycle, is consistent with the properties of an α 2 dynamo (see Rüdiger et al 2003). MHD simulations of Browning (2008) showed that fully convective stars can have strong magnetic fields as a result of convective flows acting as magnetic dynamo.…”

“…However, the fact that we detected a stellar activity cycle indicates that at least one of the components should have solar-like dynamo, thus a radiative core and a convective envelope, as according to Rüdiger et al (2003), the cyclic behavior is an "exotic exception" for the solution of α 2 dynamos, and they conclude, that cyclic stellar activity can always be the indicator of strong internal differential rotation. Küker & Rüdiger (2005) and Chabrier & Küker (2006) showed, that fully convective stars are capable to host largescale, non-axisymmetric magnetic field with α 2 dynamo, if they have weak differential rotation.…”

Orbital period modulation in close binaries due to cyclic $\alpha^2$-dynamo activity

“…The excited modes are now: λ 0 1 2 3 mode S1 S1 S0(osc) S0(osc) We find nonaxisymmetric field geometry for latitudinally spread α-effect but for α-effect concentrated in the equatorial region oscillatory and axisymmetric solutions occur. This situation remains unchanged for shallow convection zones but for deep convection zones the oscillatory modes disappear and are again replaced by drifting nonaxisymmetric modes (Rüdiger et al 2002).…”