Delayed Babcock-Leighton dynamos in the diffusion-dominated regime

Abstract

Context. Solar dynamo models of Babcock-Leighton type typically assume the rise of magnetic flux tubes to be instantaneous. Solutions with high-magnetic-diffusivity have too short periods and a wrong migration of their active belts. Only the low-diffusivity regime with advective meridional flows is usually considered. Aims. In the present paper we discuss these assumptions and applied a time delay in the source term of the azimuthally averaged induction equation. This delay is set to be the rise time of magnetic flux tubes which supposedly form at the tachocline. We study the effect of the delay, which adds to the spacial non-locality a non-linear temporal one, in the advective but particularly in the diffusive regime. Methods. Fournier et al. (2017) obtained the rise time according to stellar parameters such as rotation, and the magnetic field strength at the bottom of the convection zone. These results allowed us to constrain the delay in the mean-field model used in a parameter study. Results. We identify an unknown family of solutions. These solutions self-quench, and exhibit longer periods than their non-delayed counterparts. Additionally, we demonstrate that the non-linear delay is responsible for the recover of the equatorward migration of the active belts at high turbulent diffusivities. Conclusions. By introducing a non-linear temporal non-locality (the delay) in a Babcock-Leighton dynamo model, we could obtain solutions quantitatively comparable to the solar butterfly diagram in the diffusion-dominated regime.

arXiv comment11 pages, 10 Figures

References in corpus (22)

• Flux-transport dynamos with Lorentz force feedback on differential rotation and meridional flow: Saturation mechanism and torsional oscillations
• Full--Sphere Simulations of a Circulation--Dominated Solar Dynamo: Exploring the Parity Issue
• The crucial role of surface magnetic fields for the solar dynamo
• The Rise of Active Region Flux Tubes in the Turbulent Solar Convective Envelope
• Towards A Mean-Field Formulation Of The Babcock-Leighton Type Solar Dynamo. I. Alpha Coefficient Versus Durney's Double Ring Approach
• Importance of Meridional Circulation in Flux Transport Dynamo: The Possibility of a Maunder-like Grand Minimum
• Exploring the $P_{cyc}$ vs $P_{rot}$ relation with flux transport dynamo models of solar-like stars
• Grand Minima and North-South Asymmetry of Solar Activity
• A Stochastically Forced Time Delay Solar Dynamo Model: Self-Consistent Recovery from a Maunder-like Grand Minimum Necessitates a Mean-Field Alpha Effect
• Differential rotation and meridional flow on the lower zero age main sequence: Reynolds stress versus baroclinic flow
• Global Dynamics of Subsurface Solar Active Regions
• Modeling spatio-temporal nonlocality in mean-field dynamos
• Buoyancy-induced time delays in Babcock-Leighton flux-transport dynamo models
• Nonlinear regimes in mean-field full-sphere dynamo
• The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures
• Nature of grand minima and maxima from fully non-linear Flux-Transport Dynamos
• How can large-scale twisted magnetic structures naturally emerge from buoyancy instabilities?
• Alleviation of catastrophic quenching in solar dynamo model with nonlocal alpha-effect
• Magnetic field intensification by three-dimensional explosion process
• 3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension
• Flux-dominated solar dynamo model with a thin shear layer
• Origin and Recovery from Grand Solar Minima in a Time Delay Dynamo Model with Magnetic Noise as an Additional Poloidal Source

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