Abstract
Context. Magnetohydrodynamic interactions between plasma flows and magnetic fields is fundamental to the origin and sustenance of the 11-year sunspot cycle. These processes are intrinsically three-dimensional (3D) in nature. Aims. Our goal is to construct a 3D solar dynamo model that on the one hand captures the buoyant emergence of tilted bipolar sunspot pairs, and on the other hand produces cyclic large-scale field reversals mediated via surface flux-transport processes – that is, the Babcock-Leighton mechanism. Furthermore, we seek to explore the relative roles of flux transport by buoyancy, advection by meridional circulation, and turbulent diffusion in this 3D dynamo model. Methods. We perform kinematic dynamo simulations where the prescribed velocity field is a combination of solar-like differential rotation and meridional circulation, along with a parametrized turbulent diffusivity. We use a novel methodology for modeling magnetic buoyancy through field-strength-dependent 3D helical up-flows that results in the formation of tilted bipolar sunspots. Results. The bipolar spots produced in our simulations participate in the process of poloidal-field generation through the Babcock-Leighton mechanism, resulting in self-sustained and periodic large-scale magnetic field reversal. Our parameter space study varying the amplitude of the meridional flow, the convection zone diffusivity, and parameters governing the efficiency of the magnetic buoyancy mechanism reveal their relative roles in determining properties of the sunspot cycle such as amplitude, period, and dynamical memory relevant to solar cycle prediction. We also derive a new dynamo number for the Babcock-Leighton solar dynamo mechanism which reasonably captures our model dynamics. Conclusions. This study elucidates the relative roles of different flux-transport processes in the Sun’s convection zone in determining the properties and physics of the sunspot cycle and could potentially lead to realistic, data-driven 3D dynamo models for solar-activity predictions and exploration of stellar magnetism and starspot formation in other stars.
Highlights
The solar magnetic cycle and the magnetized sunspots that it generates eventually determine many aspects of solar activity such as flares and coronal mass ejections, solar irradiance, solar wind, and heliospheric open flux variations (Ossendrijver 2003)
The newly generated poloidal field is subducted by a variety of flux transport processes and subject to shearing by differential rotation which produces the toroidal field of the subsequent sunspot cycle
We present a global 3D kinematic solar dynamo model to explore flux transport processes that sustain the Babcock-Leighton dynamo
Summary
The solar magnetic cycle and the magnetized sunspots that it generates eventually determine many aspects of solar activity such as flares and coronal mass ejections, solar irradiance, solar wind, and heliospheric open flux variations (Ossendrijver 2003). Various levels of treatment have evolved in sophistication, starting from the direct addition of a net effective azimuthally averaged poloidal field close to the near-surface layer to placing double-rings in terms of the axisymmetric vector potential for the poloidal field at near-surface layers to mimic the eruption of bipolar sunspot pairs (Durney 1995, 1997; Nandy & Choudhuri 2001; Muñoz-Jaramillo et al 2010) These models reproduce large-scale solar-cycle features reasonably well, they do not adequately capture the actual production of non-axisymmetric tilted bipolar magnetic regions (BMRs) or how they result in this effective poloidal flux – processes that are intrinsically 3D. On the other hand, Yeates & Muñoz-Jaramillo (2013) adopted a different approach where they employed an additional radial velocity in the convection zone that transports the toroidal flux from the base of the convection zone to the surface to produce bipolar spots They focussed only on one magnetic cycle, and did not demonstrate the ability of their model to achieve sustained long-term cyclic dynamo action.
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