A Low-Order Solar Dynamo Model: Inferred Meridional Circulation Variations Since 1750

In this work we present the possible variations that the meridional circulation of the Sun might have undergone during the last 250 years. In order to do this, we reduce an α-Ω dynamo to a low-order system that focuses on the time evolution of one of the solar magnetic field components. Afterward we used a method based on the analysis of phase space of the superficial toroidal magnetic field to infer changes in the superficial meridional circulation. We used sunspot numbers to build a time series that approximately represents the magnetic field behavior. After reconstructing the time series' phase space we assume equilibrium solutions for each solar cycle and we fit them to our model. The resulting fit parameters are shown to depend on background quantities of the theoretical model, such as magnetic diffusivity, differential rotation, meridional circulation, etc. The methodology presented here allows one to extract information about the meridional circulation average behavior, and possibly other parameters, from more that 250 years of sunspot number observations