Helicity inversion in spherical convection as a means for equatorward dynamo wave propagation

Abstract

We discuss here a purely hydrodynamical mechanism to invert the sign of the kinetic helicity, which plays a key role in determining the direction of propagation of cyclical magnetism in most models of dynamo action by rotating convection. Such propagation provides a prominent, and puzzling constraint on dynamo models. In the Sun, active regions emerge first at mid-latitudes, then appear nearer the equator over the course of a cycle, but most previous global-scale dynamo simulations have exhibited poleward propagation (if they were cyclical at all). Here, we highlight some simulations in which the direction of propagation of dynamo waves is altered primarily by an inversion of the kinetic helicity throughout much of the interior, rather than by changes in the differential rotation. This tends to occur in cases with a low Prandtl number and internal heating, in regions where the local density gradient is relatively small. We analyse how this inversion arises, and contrast it to the case of convection that is either highly columnar (i.e., rapidly rotating) or locally very stratified; in both of those situations, the typical profile of kinetic helicity (negative throughout most of the northern hemisphere) instead prevails.

Robustness of oscillatoryα2dynamos in spherical wedges

“…Including an α-effect also concentrated at lower latitudes produces equatorward cycles with shorter cycle periods with the strongest magnetic fields appearing at lower latitudes. These results are in qualitative agreement with direct and largeeddy simulations (Käpylä et al 2012(Käpylä et al , 2013bAugustson et al 2015; Duarte et al 2016). …”

“…It is now believed that the equatorward migration in the simulations is facilitated by a region of negative shear and positive (negative) α effect in the northern (southern) hemisphere -in accordance with the ParkerYoshimura rule (Warnecke et al 2014). Recently an alternative scenario was reported by Duarte et al (2016), who found that the sign of the α effect can be inverted in certain parameter ranges allowing equatorward migration also with positive radial shear. Although it is unclear to what extent those simulations represent stellar magnetic fields, it might be helpful to understand first the mechanism operating in those simulations before trying to understand real stars.…”

Convection-driven spherical shell dynamos at varying Prandtl numbers

“…It is remarkable that this rule also seems to apply to the fully nonlinear convective dynamo simulations (Warnecke et al , 2016b. The current simulations can produce equatorward migration only in cases where a region with a negative radial gradient of Ω occurs at mid-latitudes (e.g., Käpylä et al 2012Käpylä et al , 2013Augustson et al 2015) or if the sign of the kinetic helicity, which is a proxy of the α effect, is inverted in the bulk of the convection zone (Duarte et al 2016).…”

Magnetism, dynamo action and the solar-stellar connection

“…In such models, the product of α and ∂Ω/∂r must therefore be negative in the northern hemisphere in order to obtain an equatorward butterfly diagram. As noted above, the sign of α is related to that of the kinetic helicity, H k = v · (∇ × v), and H k in turn is typically negative in the northern hemisphere owing to the properties of the rotating convection (but see discussion in, e.g., Duarte et al 2015, who point out circumstances where the opposite sign may prevail). One problem arose when helioseismology revealed that the differential rotation profile was nearly conical at mid-latitudes (e.g., Thompson et al 1996), i.e.…”