Optimization of surface flux transport models for the solar polar magnetic field

The choice of free parameters in surface flux transport (SFT) models describing the evolution of the large-scale poloidal magnetic field of the Sun is critical for the correct reproduction of the polar magnetic flux built up during a solar cycle, which in turn is known to be a good predictor of the amplitude of the upcoming cycle. For an informed choice of parameters it is important to understand the effect and interplay of the various parameters and to optimize the models for the polar magnetic field. Here we present the results of a large-scale systematic study of the parameter space in an SFT model where the source term representing the net effect of tilted flux emergence was chosen to represent a typical, average solar cycle as described by observations. Comparing the results with observational constraints on the spatiotemporal variation of the polar magnetic field, as seen in magnetograms for the last four solar cycles, we mark allowed and excluded regions in the 3D parameter space defined by the flow amplitude u0, the magnetic diffusivity eta and the decay time scale tau, for three different assumed meridional flow profiles. Without a significant decay term in the SFT equation (i.e., for tau >10 yr) the global dipole moment reverses too late in the cycle for all flow profiles and parameters, providing independent supporting evidence for the need of a decay term, even in the case of identical cycles. An allowed domain is found to exist for tau values in the 5-10 yr range for all flow profiles considered. Generally higher values of eta (500-800 km^2/s) are preferred though some solutions with lower eta are still allowed.