The mean solar butterfly diagram and poloidal field generation rate at the surface of the Sun

The difference between individual solar cycles in the magnetic butterfly diagram can mostly be ascribed to the stochasticity of the emergence process. We aim to obtain the expectation value of the butterfly diagram from observations of four cycles. This allows us to further determine the generation rate of the surface radial magnetic field. We used data from Wilcox Solar Observatory to generate time-latitude diagrams of the surface radial and toroidal magnetic fields spanning cycles 21 to 24. We symmetrized them across the equator and cycle-averaged them. From the mean butterfly diagram and surface toroidal field, we then inferred the mean poloidal field generation rate at the surface of the Sun. The averaging procedure removes realization noise from individual cycles. The amount of emerging flux required to account for the evolution of the surface radial field is found to match that provided by the observed surface toroidal field and Joy's law. Cycle-averaging butterfly diagrams removes realization noise and artefacts due to imperfect scale separation and corresponds to an ensemble average that can be interpreted in the mean-field framework. The result can then be directly compared to $ dynamo models. The Babcock-Leighton alpha -effect is consistent with observations, a result that can be appreciated only if the observational data are averaged in some way.