A Model of a Tidally Synchronized Solar Dynamo

Abstract

We discuss a solar dynamo model of Tayler-Spruit type whose Ωeffect is conventionally produced by a solar-like differential rotation but whose α-effect is assumed to be periodically modulated by planetary tidal forcing. This resonance-like effect has its rationale in the tendency of the current-driven Tayler instability to undergo intrinsic helicity oscillations which, in turn, can be synchronized by periodic tidal perturbations. Specifically, we focus on the 11.07 years alignment periodicity of the tidally dominant planets Venus, Earth, and Jupiter, whose persistent synchronization with the solar dynamo is briefly touched upon. The typically emerging dynamo modes are dipolar fields, oscillating with a 22.14 years period or pulsating with an 11.07 years period, but also quadrupolar fields with corresponding periodicities. In the absence of any constant part of α, we prove the subcritical nature of this Tayler-Spruit type dynamo. The resulting amplitude of the α oscillation that is required for dynamo action turns out to lie in the order of 1 m/s, which seems not implausible for the sun. When starting with a more classical, non-periodic part of α, even less of the oscillatory α part is needed to synchronize the entire dynamo. Typically, the dipole solutions show butterfly diagrams, although their shapes are not convincing yet. Phase coherent transitions between dipoles and quadrupoles, which are reminiscent of the observed behaviour during the Maunder minimum, can be easily triggered by long-term variations of dynamo parameters, but may also occur spontaneously even for fixed parameters. Further interesting features of the model are the typical second intensity peak and the intermittent appearance of reversed helicities in both hemispheres.

Phase coherence and phase jumps in the Schwabe cycle

“…While such a long phase coherence, observed in two rather unrelated proxy datasets for the Schwabe cycle, is most remarkably in itself, one might be even more puzzled by the almost complete equivalence of the cycle period of 11.04 years with the corresponding 11.07‐year period as derived for the last centuries (Stefani et al 2019, 2020). Ironically, the latter value for the more recent times is more disputable than the value for the early Holocene given that the systematic observation of sunspots goes back only to the times of Scheiner and Galileo (Arlt & Vaquero 2020), with grave uncertainties for the time of the Maunder minimum (1645–1715).…”

“…Moreover, analyzing Dicke's ratio (Dicke 1978) between the mean square of the residuals r i (defined as the distances between the actual minima and the hypothetical minima of a perfect 11.07‐year cycle) to the mean square of the differences r i − r i − 1 between two consecutive residuals, the solar cycle was shown to have much closer resemblance to a clocked process than to a random walk process (Stefani et al 2019). This gave further support for our conjecture (Stefani et al 2016, 2017, 2018, 2019) that the Schwabe cycle results from synchronizing a rather conventional α − Ω dynamo by means of an additional 11.07‐year oscillation of the α effect, which in turn is related to the helicity oscillation of either a kink‐type ( m = 1) Tayler instability in the tachocline region (Weber et al 2015) or a ( m = 1) magneto‐Rossby wave (Dikpati et al 2017; Zaqarashvili 2018). Building on and corroborating earlier ideas of Hung (2007), Scafetta (2012), Wilson (2013), and Okhlopkov (2014, 2016), the source of this synchronized helicity was hypothesized to be the 11.07‐year periodic tidal ( m = 2) forcing of Venus, Earth, and Jupiter, which are the tidally dominant planets in the solar system.…”

“…A second objection is related to the questionable quality of Schove's minima and maxima data. While they show a remarkable phase coherence over one or even two millennia (Stefani et al 2019, 2020), this coherence would be destroyed in case that Schove had forgotten (or “smuggled in”) one cycle or another. Sections 3 and 4 will deal with such “lost cycles” and the real phase jumps connected with them.…”

Oscillations of solar photosphere: 45 years of observations

“…However, this is hardly understandable: in what manner does the planet, revolving around the Sun with a sidereal period ≈12 years, induce the beating period (or respective frequency shift) of the photosphere, equal to the planetary revolution time relative to the Earth? It seems reasonable then to suggest that the current model of the Sun—see, for example, Roxburgh (1985), Christensen‐Dalsgaard et al (1996), and Vinyoles et al (2017)–would be improved (particularly in view of the recently developed theory of the tidal synchronization of the solar dynamo; see, for example, Stefani et al 2019; Scafetta 2020).…”

Крымские Наблюдения Магнитного Солнца: 1967–2018 Гг.

“…А в связи с глобальными пульсациями Солнца (с периодом 9600 с неизвестной природы; см. Kotov, Haneychuk, 2020), указанными выше резонансами системы Солнце -Земля и имея ввиду, в частности, теорию приливной синхронизации солнечного динамо (Stefani et al, 2019;Scafetta, 2020), разумно полагать, что модель Солнца должна быть улучшена.…”