Evolution of the solar magnetic flux on time scales of years to millenia

Aims. We improve the description of the evolution of the Sun's open and total magnetic flux on time scales of years to millenia. Methods. In the model employed here the evolution of the solar total and open magnetic flux is computed from the flux emerging at the solar surface in the form of bipolar magnetic features, which is related to the sunspot number cycle parameters and can be estimated from historical records. Compared to earlier versions of the model in addition to the long-lived open flux, now also a more rapidly decaying component of the open flux is considered. The model parameters are constrained by comparing its output with observations of the total surface magnetic flux and with a reconstruction of the open magnetic flux based on the geomagnetic indexes. A method to compute the Sun's total magnetic flux and the sunspot number during the Holocene, starting from the open flux obtained from cosmogenic isotopes records, is also presented. Results. By considering separately a rapidly evolving and a slowly evolving component of the open flux the model reproduces the Sun's open flux, as reconstructed based on the aa-index, much better and a reasonable description of the radial component of interplanetary magnetic field data is obtained. The greatest improvement is in the reproduction of the cyclic variation of the open flux, including the amplitudes of individual cycles. Furthermore, we found that approximately 25% of the modeled open flux values since the end of the Maunder minimum are lower than the averaged value over 2008, i.e. during the current low minimum. The same proportion is observed in reconstructions of the open flux during the Holocene based on cosmogenic isotopes, which suggests that the present solar minimum conditions are below average, but not exceptional in terms of the heliospheric magnetic flux.