A 3D kinematic Babcock Leighton solar dynamo model sustained by dynamic magnetic buoyancy and flux transport processes

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.

Dynamo models of the solar cycle

“…Some recent Babcock-Leighton solar cycle models abandon the axisymmetric approximation, either by solving the problem in three spatial dimensions (Yeates and Muñoz-Jaramillo 2013a;Miesch and Dikpati 2014;Miesch and Teweldebirhan 2016;Karak and Miesch 2017;Kumar et al 2019;Whitbread et al 2019), or solving a (non-axisymmetric) surface magnetic flux evolution model concurrently with a axisymmetric mean-field-like interior dynamo model (Lemerle and Charbonneau 2017;Nagy et al 2017). All of these dynamo models are still kinematic (prescribed, time independent differential rotation and meridional flow), and use a mean-field-like turbulent diffusivity.…”

“…Alternately, it is also possible to force magnetic flux emergence from the interior to the surface by introducing short-lived and spatially localised vortical upflows whenever and wherever the deep toroidal magnetic field exceeds a set threshold. This is the approach introduced by Yeates and Muñoz-Jaramillo (2013b, see also Kumar et al 2019;Whitbread et al 2019). The helicity of their prescribed upflows is set to vary as the sine of latitude, and they adjust the amplitude of its horizontal component so as to reproduce Joy's Law (see their Fig.…”

Does the mean-fieldαeffect have any impact on the memory of the solar cycle?

“…In recent years, dynamo models based on the Babcock-Leighton mechanism have been successful in explaining different observational aspects regarding solar activity (Dikpati & Charbonneau 1999;Nandy & Choudhuri 2002;Choudhuri et al 2004;Nandy et al 2011;Choudhuri & Karak 2012;Bhowmik & Nandy 2018;Hazra & Nandy 2019;Bhowmik 2019). Recently, data-driven 2.5D kinematic dynamo models and 3D kinematic solar dynamo models have also been developed to study different observational aspects regarding solar activity (Brun 2007;Jouve et al 2011;Yeates & Muñoz-Jaramillo 2013;Hung et al 2017;Hazra et al 2017;Karak & Miesch 2017;Hazra & Miesch 2018;Kumar et al 2019). For reviews of the solar and stellar dynamo model, see Charbonneau (2005), Brun et al (2015), and Brun & Browning (2017).…”

Impact of nonlinear surface inflows into activity belts on the solar dynamo

“…The corresponding zonally-averaged radial surface field is then fed to the FTD via its outer boundary condition at r = R , closing the dynamo loop. This so-called "2 × 2D" model, so dubbed because it runs concurrently two distinct but coupled two-dimensional simulations, has the advantage of being much faster than full three-dimensional Babcock-Leighton models (see, e.g., Yeates and Muñoz-Jaramillo, 2013; Karak and Miesch, 2017;Kumar et al, 2019), while still incorporating a detailed longitude-latitude representation of the model photosphere. Bhowmik and Nandy (2018) present a conceptually similar dynamo model implementation.…”