Constraining the outer boundary condition for the Babcock-Leighton dynamo models

Context. The evolution of the Sun’s large-scale surface magnetic field is well captured by surface flux transport models, which can therefore provide a natural constraint on the outer boundary condition (BC) of Babcock–Leighton (BL) dynamo models. Aims. For the first time, we propose a zero radial diffusion BC for BL dynamo models, enabling their surface field evolution to align consistently with surface flux transport simulations. Methods. We derived a zero radial diffusion BC from the magnetohydrodynamic induction equation and evaluated its effects in comparison with two alternatives: (i) a radial outer BC and (ii) a radial outer BC combined with strong near-surface radial pumping. The comparison was made both for the evolution of a single bipolar magnetic region and within a full BL dynamo model. Results. The zero radial diffusion outer BC effectively suppresses radial diffusion across the surface, ensuring consistency between the evolution of the bipolar magnetic region in the BL dynamo and the surface flux transport model. With this outer BC, the full BL dynamo model successfully reproduces the fundamental properties of the solar cycle. In addition, the model naturally produces a surface magnetic field that is not purely radial, in closer agreement with solar observations. Conclusions. The physically motivated zero radial diffusion BC paves the way for deeper insight into the solar and stellar cycles.