The solar magnetic field since 1700: II. Physical reconstruction of total, polar and open flux

We have used semi-synthetic records of emerging sunspot groups based on sunspot number data as input for a surface flux transport model to reconstruct the evolution of the large-scale solar magnetic field and the open heliospheric flux from the year 1700 onward. The statistical properties of the semi-synthetic sunspot group records reflect those of the observed the Royal Greenwich Observatory photoheliographic results. These include correlations between the sunspot numbers and sunspot group latitudes, longitudes, areas and tilt angles. The reconstruction results for the total surface flux, the polar field, and the heliospheric open flux (determined by a current sheet source surface extrapolation) agree well with the available observational or empirically derived data and reconstructions. We confirm a significant positive correlation between the polar field during activity minimum periods and the strength of the subsequent sunspot cycle, which has implications for flux transport dynamo models for the solar cycle. Just prior to the Dalton minimum, at the end of the 18th century, a long cycle was followed by a weak cycle. We find that introducing a possibly `lost' cycle between 1793 and 1800 leads to a shift of the minimum of the open flux by 15 years which is inconsistent with the cosmogenic isotope record.