Modeling the Sun's open magnetic flux

Abstract

Context. The heliospheric magnetic field can be extrapolated from the photospheric field distribution using models based upon various approximations. Such models are required for the reconstruction of the open solar magnetic flux prior to the time of direct measurements on the basis of surface flux transport simulations. Aims. We evaluate the consistency of extrapolation models with direct measurements of the heliospheric magnetic field. Furthermore, we study whether extrapolations on the basis of a surface flux transport model for the photospheric magnetic field reproduce the temporal evolution of the measured near-Earth magnetic field. Methods. We use the potential field source surface (PFSS) model and the current sheet source surface (CSSS) model to extrapolate the heliospheric field on the basis of the Wilcox Solar Observatory (WSO) synoptic maps of the solar surface field from 1976-2005. The results are compared with the near-Earth measurements of the radial heliospheric field and its independence of latitude found with Ulysses. Furthermore, we determine extrapolations on the basis of photospheric flux distributions computed with a surface flux transport code, using as input sunspot group areas from the SOON database. Results. The CSSS model based upon WSO data, with a source surface located at >10 R ⊙ and cusp surface at 1.7 R ⊙ . yields the best agreement with the measurements. The flux transport simulations reproduce the observed surface flux together with the open flux if the tilt angle of emerging bipolar magnetic regions is smaller than commonly assumed, but consistent with sunspot observations. Conclusions. The CSSS model with a source surface in the vicinity of the Alfvenic point of the solar wind leads to a good extrapolation of the heliospheric field from solar surface data. A surface flux transport model based upon sunspot data with consistently calibrated tilt angles reproduces the observed evolution of the solar total open flux.