Recent advances in the 3D kinematic Babcock-Leighton solar dynamo modeling

In this review, we explain recent progress made in the Babcock-Leighton dynamo models for the Sun, which have been most successful to explain various properties of the solar cycle. In general, these models are two-dimensional (2D) axisymmetric and the mean-field dynamo equations are solved in the meridional plane of the Sun. Various physical processes (e.g., magnetic buoyancy and Babcock-Leighton mechanism) involved in these models are inherently three-dimensional (3D) processes and could not be modeled properly in a 2D framework. After pointing out limitations of 2D models (e.g., mean-field Babcock-Leighton dynamo models and surface flux transport models), we describe recently developed next-generation 3D dynamo models that implement a more sophisticated flux emergence algorithm of buoyant flux tube rise through the convection zone and capture the Babcock-Leighton process more realistically than previous 2D models. The detailed results from these 3D dynamo models including surface flux transport counterparts are presented. We explain the cycle irregularities that are reproduced in 3D dynamo models by introducing scattering around the tilt angle only. Some results by assimilating observed photospheric convective velocity fields into the 3D models are also discussed, pointing out the wide opportunity that these 3D models hold to deliver.