Coronal Field Geometry and Solar Wind Speed

The Wang–Sheeley–Arge (WSA) solar wind (SW) model is based on the idea that weakly expanding coronal magnetic field tubes are associated with sources of fast SWs and vice versa. A parameter called the “flux tube expansion” (FTE) is used to determine the degree of expansion of magnetic tubes. The FTE is calculated based on the coronal magnetic field model, usually in the potential approximation. The second input parameter for the WSA model is the great circle distance from the base of the open magnetic field line in the photosphere to the boundary of the corresponding coronal hole (DCHB). These two coronal magnetic field parameters are related by an empirical relationship with the solar wind velocity near the Sun. The WSA model has shortcomings and does not fully explain the solar wind formation mechanisms. In the present work, we model various coronal magnetic field parameters in the potential-field source-surface (PFSS) approximation from a long series of magnetographic observations: the Solar Telescope-magnetograph for Operative Prognoses (STOP) (Kislovodsk Mountain Astronomical Station), the Helioseismic and magnetic imager (SDO/HMI), and data from the Wilcox Solar Observatory (WSO). Our main goal is to identify correlations between the coronal magnetic field parameters and the observed SW velocity in order to use them for modeling SW. We found that the SW velocity correlates relatively well with some geometric properties of the magnetic tubes, including the force line length, the latitude of the force line footpoints, and the DCHB. We propose a formula for calculating the SW velocity based on these parameters. The presented relationship does not use FTE and showed a better correlation with observations compared to the WSA model.