On the Synchronizability of Tayler–Spruit and Babcock–Leighton Type Dynamos

Stefani, Frank; Giesecke, A.; Weber, Norbert; Weier, Tom

doi:10.1007/s11207-017-1232-y

Cited by 24 publications

(33 citation statements)

References 72 publications

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“…Moreover, analyzing Dicke's ratio

\sum_{i} r_{i}^{2} / \sum_{i} {(r_{i} - r_{i - 1})}^{2}

(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.…”

Section: Introductionsupporting

confidence: 87%

Phase coherence and phase jumps in the Schwabe cycle

et al. 2020

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Guided by the working hypothesis that the Schwabe cycle of solar activity is synchronized by the 11.07‐year alignment cycle of the tidally dominant planets Venus, Earth, and Jupiter, we reconsider the phase diagrams of sediment accumulation rates in Lake Holzmaar and of methanesulfonate data in the Greenland ice core Greenland Ice Sheet Project 2 (GISP2), which are available for the period 10000–9000 cal. BP. As some half‐cycle phase jumps appearing in the output signals are, very likely, artifacts of applying a biologically substantiated transfer function, the underlying solar input signal with a dominant 11.04‐year periodicity can be considered to be mainly phase‐coherent over the 1,000‐year period in the early Holocene. For more recent times, we show that the reintroduction of a hypothesized “lost cycle” at the beginning of the Dalton minimum would lead to a real phase jump. Similarly, by analyzing various series of 14C and 10Be data and comparing them with Schove's historical cycle maxima, we support the existence of another “lost cycle” around 1565, also connected with a real phase jump. Viewed synoptically, our results lend greater plausibility to the starting hypothesis of a tidally synchronized solar cycle, which at times can undergo phase jumps, although the competing explanation in terms of a nonlinear solar dynamo with increased coherence cannot be completely ruled out.

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“…Moreover, analyzing Dicke's ratio

\sum_{i} r_{i}^{2} / \sum_{i} {(r_{i} - r_{i - 1})}^{2}

Section: Introductionsupporting

confidence: 87%

Phase coherence and phase jumps in the Schwabe cycle

et al. 2020

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“…Yet another promising synchronization mechanism was first delineated by Weber et al (2015) and later corroborated in detail by Stefani et al (2016Stefani et al ( , 2018. It starts from the numerical observation that the current-driven, kink-type Tayler instability (TI) (Tayler, 1973;Pitts and Tayler, 1985;Gellert, Rüdiger, and Hollerbach, 2011;Seilmayer et al, 2012;Rüdiger, Kitchatinov, and Hollerbach, 2013;Stefani and Kirillov, 2015) has an intrinsic tendency for oscillations of the helicity and the α-effect related to it.…”

Section: Introductionmentioning

confidence: 92%

“…As a sequel to Stefani et al (2016Stefani et al ( , 2018, the present paper investigates this spatio-temporal behaviour of a tidally synchronized dynamo of the Tayler-Spruit type. For that purpose, we replace the ODE system by a partial differential equation (PDE) system with the co-latitude as the only spatial variable.…”

Section: Introductionmentioning

confidence: 99%

A Model of a Tidally Synchronized Solar Dynamo

2019

Self Cite

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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.

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“…In particular, in Rüdiger et al (2011a, 2011b) it has been shown that for a constant current density in an infinitely long cylinder, the governing parameter is the Hartmann number, H a = B φ ( r out ) r out ( σ / ρ ν ) 1/2 , with σ , ρ , and ν being, respectively, the conductivity, density, and viscosity of the fluid, instead of Lundquist number S = H a P m 1/2 . Simulations at high Hartmann numbers (Stefani et al ; Weber et al ) have shown the production of helicity in Tayler instability that does not always decay to zero but may also saturate to a finite value, presenting in both cases new features like oscillations and limit cycles. While simulations are discovering an apparently broad family of saturation patterns, not much can be said from the analytical point of view.…”

Section: Basic Formalismmentioning

confidence: 99%

“…The effect of a finite Prandtl number has been investigated in cylindrical geometry (Rüdiger et al ), while the role played by a finite electrical resistivity in liquid conductor has been discussed in Weber et al (). A recent work in this direction (Weber et al ) discussed the numerical evidence that the saturation state of the Tayler instability at low magnetic Prantdl number and high Hartmann number is characterized by helicity oscillations: a result of important consequences if confirmed (Stefani et al ).…”

Section: Introductionmentioning

confidence: 99%

On the possibility of helicity oscillations in the saturation of the Tayler instability

Bonanno

Guarnieri

2017

Astron Nachr

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Recent numerical results of current-driven instabilities at low magnetic Prandtl number and high Hartmann number support the possibility of a saturation state characterized by helicity oscillations. We investigate the underlying mechanism by analyzing this possibility using a higher order Landau-Ginzburg effective Lagrangian for the weakly nonlinear amplitude dynamics, where the magnetic and velocity perturbations are linearly dependent. We find that, if the mirror symmetry between left-and right-handed modes is spontaneously broken, it is impossible to achieve an oscillating helical state. We argue that the result is likely to hold also for adding higher order terms and in the presence of an explicit symmetry breaking. We conclude that an oscillating saturating state for the Tayler instability is unlikely to depend on the interaction of chiral modes. KEYWORDS instabilities, magnetic fields, magnetohydrodynamics (MHD) INTRODUCTIONThe Tayler instability is the instability of a toroidal field in a stably stratified medium due to the presence of an electric current along the axis of symmetry (Tayler 1973). In its simplest realization, in cylindrical geometry with axial symmetry, it can be shown that a purely toroidal field B (r), where r is the cylindrical radius, is stable against axisymmetric perturbations if it satisfies the condition d(B ∕r)∕dr < 0, and to non-axisymmetric perturbations if d(r B 2 )∕dr ≤ 0. In recent times, this problem has attracted a considerable amount of analytical and numerical investigations (Bodo et al. 2013;Bonanno & Urpin 2011;Ibáñez-Mejía & Braithwaite 2015;Jouve et al. 2015) as well as experimental verification (Seilmayer et al. 2012), mainly for its relevance for our understanding of magnetism in stellar radiative regions (Braithwaite & Spruit 2015;Kitchatinov & Rüdiger 2008) but also for its implications in the tachocline stability problem and the solar dynamo (Bonanno 2013;Kitchatinov & Rüdiger 2007).In particular, it was noted in Bonanno & Urpin (2008) that the unstable modes are helical and, in the presence of a vertical component B z , also invariant under the symmetry transformation P LR z ∶ (m, ) → (−m, − ), with = B z ∕B and m the azimuthal wavenumber. This has led to the speculation that this instability can produce a magnetic -effect which, in turn, could produce a dynamo action (Rüdiger et al. 2012b; Spruit 2002). The effect of a finite Prandtl number has been investigated in cylindrical geometry (Rüdiger et al. 2012a), while the role played by a finite electrical resistivity in liquid conductor has been discussed in Weber et al. (2013). A recent work in this direction discussed the numerical evidence that the saturation state of the Tayler instability at low magnetic Prantdl number and high Hartmann number is characterized by helicity oscillations: a result of important consequences if confirmed .The aim of this paper is to extend the approach to the nonlinear saturation phase of the Tayler instability discussed in Bonanno et al. (2012) in order to account for additiona...

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On the Synchronizability of Tayler–Spruit and Babcock–Leighton Type Dynamos

Cited by 24 publications

References 72 publications

Phase coherence and phase jumps in the Schwabe cycle

Phase coherence and phase jumps in the Schwabe cycle

A Model of a Tidally Synchronized Solar Dynamo

On the possibility of helicity oscillations in the saturation of the Tayler instability

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