Differential rotation of the Sun and magnetic diffusivity after the Maunder minimum as well as numerical models of the solar dynamo

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Sunspots are the key indicator for solar activity, since we have information about them for about 400 years. The positions of sunspots have been utilized only since 1874. During the Maunder minimum period in the 17th century, very few spots were observed, in order to fill the gap between the measurements starting in 1874 and the scattered observations known from the Maunder minimum, we plan the precise analysis of about 1000 observations made by in 1749-1796. The differential rotation of the Sun in the 18th century as well as the magnetic diffusivity at that time will be determined, and a search for active longitudes will be performed. North-south asymmetries and the coherence of the cycle in the northern and southern hemispheres will be studied. The solar images will be made accessible to the Virtual Solar Observatory.The work will include theoretical modelling of dynamo processes that can lead to the observed behaviour, based on the measured differential rotation and diffusivity shortly after the Maunder minimum. We are particularly addressing the issues of helicity fluxes necessary to allow for dynamos growing fast enough and to high enough saturation amplitudes. While most of these studies were performed in Cartesian boxes, we plan to run simulations in spherical shells, based on both driven helical turbulence and more realistic convection.