A Synchronized Two-Dimensional $\alpha $–$\Omega $ Model of the Solar Dynamo

Abstract

We consider a conventional $\alpha $ α –$\Omega $ Ω -dynamo model with meridional circulation that exhibits typical features of the solar dynamo, including a Hale-cycle period of around 20 years and a reasonable shape of the butterfly diagram. With regard to recent ideas of a tidal synchronization of the solar cycle, we complement this model by an additional time-periodic $\alpha $ α -term that is localized in the tachocline region. It is shown that amplitudes of some decimeters per second are sufficient for this $\alpha $ α -term to become capable of entraining the underlying dynamo. We argue that such amplitudes of $\alpha $ α may indeed be realistic, since velocities in the range of m s−1 are reachable, e.g., for tidally excited magneto–Rossby waves.

Rieger, Schwabe, Suess-de Vries: The Sunny Beats of Resonance

“…At any rate, in this paper, we consider the phase stability of the Schwabe cycle as a serious working hypothesis, for which it seems worthwhile to find a reasonable physical explanation. If, someday in the future, new data show up to give unambiguous evidence to the contrary, we will be the first to declare this paper, as well as its predecessors (Stefani et al, 2016(Stefani et al, , 2018Stefani, Giesecke, and Weier, 2019;Stefani et al, 2020a;Stefani, Stepanov, and Weier, 2021;Klevs, Stefani, and Jouve, 2023), as misleading and futile.…”

“…Turning this question upside-down, in Klevs, Stefani, and Jouve (2023) we asked how much of the synchronized α-effect would actually be needed to entrain the entire solar dynamo by parametric resonance. Based on a rather conventional 2D α − -dynamo model, including meridional circulation, this value was shown to lay in the range of some dm s −1 or even less (with the resistivity jump between tachocline and convection zone being the most decisive, yet widely unknown factor).…”

“…However, the latter conclusion turns out to be a bit premature. With view on synchronized dynamo models such as in Klevs, Stefani, and Jouve (2023), we should presumably focus on the axisymmetric component of the quadratic term in Equation 3, very likely with some phase shift of one of the two factors (which would be needed when computing the helicity). For the simplest case without phase shift between the two factors, we show in Figure 8a the 3).…”

“…A this point, the discerning reader will have noticed a slight but important conceptual shift. In all previous works (Stefani et al, 2016(Stefani et al, , 2018Stefani, Giesecke, and Weier, 2019;Stefani, Stepanov, and Weier, 2021;Klevs, Stefani, and Jouve, 2023), the 11.07year periodicity was implemented as a resonance term with the generic field-dependence ∼ B 2 /(1 + B 4 ), which was interpreted in terms of an optimal reaction, on the Schwabe time scale, of the TI to the amplitude of the field. Now we reinterpret the very same resonance term as an optimal response of the magneto-Rossby waves to the magnetic field on the Rieger-type time scale.…”

Stellar Cycle and Evolution of Polar Spots in an M+WD Binary

“…We proposed that the strong tidal force from the white dwarf companion could serve as a contributing factor. The tidal force could lead to a 1:1 resonant excitation of the oscillation of the α-effect, which is capable of exciting the underlying dynamo (Stefani et al 2016(Stefani et al , 2019Klevs et al 2023), though this is still debated (De Jager & Versteegh 2005;Nataf 2022;Weisshaar et al 2023). In binary systems, the tidal interactions between binary components are much larger than tidal effects from planets and are expected to induce large-scale 3D shear and/or helical flows in stellar interiors that can significantly perturb the stellar dynamo.…”