Abstract
Solar activity in all its varied manifestations is driven by the magnetic field. Two global quantities are particularly important for many purposes, the Sun’s total and open magnetic flux, which can be computed from sunspot number records using models. Such sunspot-driven models, however, do not take into account the presence of magnetic flux during grand minima, such as the Maunder minimum. Here we present a major update of a widely used simple model, which now takes into account the observation that the distribution of all magnetic features on the Sun follows a single power law. The exponent of the power law changes over the solar cycle. This allows for the emergence of small-scale magnetic flux even when no sunspots have been present for multiple decades and leads to non-zero total and open magnetic flux also in the deepest grand minima, such as the Maunder minimum, thus overcoming a major shortcoming of the earlier models. The results of the updated model compare well with the available observations and reconstructions of the solar total and open magnetic flux. This opens up the possibility of improved reconstructions of the sunspot number from time series of the cosmogenic isotope production rate.
Highlights
The precise history of solar activity and its underlying magnetic field is of interest for a number of reasons
The new version of the model takes into account the observation that fluxes of magnetic features follow a single power law, including internetwork fields, ephemeral regions (ERs) and active regions (ARs)
It takes into account the fact that emergence rates of magnetic bipoles with fluxes between 1016 Mx and 1023 Mx, that is from the smallest ERs to the largest ARs, follow a power law according to the analysis by Thornton & Parnell (2011)
Summary
The precise history of solar activity and its underlying magnetic field is of interest for a number of reasons. Far more sophisticated models have, in the meantime, become available to compute not just global magnetic quantities, and, for instance, the underlying spatial distribution of the magnetic flux and the detailed input from individual emerging ARs, the very simplicity of this set of models allowed them to be inverted (e.g., Lockwood 2003), so that, for example, the sunspot number could be reconstructed from measured concentrations of cosmogenic isotopes (e.g., Usoskin et al 2003, 2004, 2016; Solanki et al 2004; Wu et al 2018b). The quality of the computed open magnetic flux was tested by comparing it with two other independent data sets (without changing the free parameters of the model): (1) a compilation of spacecraft-based in situ measurements by Owens et al (2017) since 1998, and (2) a reconstruction by Wu et al (2018b) from decadal INTCAL13 14C data covering the Holocene prior to 1900 (Reimer et al 2013)
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