A Double-Ring Algorithm for Modeling Solar Active Regions: Unifying Kinematic Dynamo Models and Surface Flux-Transport Simulations

TL;DR

This paper introduces a double-ring algorithm for modeling solar active regions that unifies kinematic dynamo models with surface flux-transport simulations, resolving previous discrepancies in the relationship between polar field strength and meridional flow speed.

Contribution

The paper presents a novel double-ring algorithm for the Babcock-Leighton mechanism within an axisymmetric dynamo model, aligning model predictions with physical insights and flux-transport simulations.

Findings

The axisymmetric formulation approximates surface flux dynamics effectively.

The double-ring eruption model produces an inverse relationship between polar field strength and meridional flow speed.

The new model reconciles differences between flux-transport simulations and dynamo models.

Abstract

The emergence of tilted bipolar active regions and the dispersal of their flux, mediated via processes such as diffusion, differential rotation and meridional circulation is believed to be responsible for the reversal of the Sun's polar field. This process (commonly known as the Babcock-Leighton mechanism) is usually modeled as a near-surface, spatially distributed $\alpha$-effect in kinematic mean-field dynamo models. However, this formulation leads to a relationship between polar field strength and meridional flow speed which is opposite to that suggested by physical insight and predicted by surface flux-transport simulations. With this in mind, we present an improved double-ring algorithm for modeling the Babcock-Leighton mechanism based on active region eruption, within the framework of an axisymmetric dynamo model. Using surface flux-transport simulations we first show that an axisymmetric formulation -- which is usually invoked in kinematic dynamo models -- can reasonably approximate the surface flux dynamics. Finally, we demonstrate that our treatment of the Babcock-Leighton mechanism through double-ring eruption leads to an inverse relationship between polar field strength and meridional flow speed as expected, reconciling the discrepancy between surface flux-transport simulations and kinematic dynamo models.