Multiple-point Modeling the Parker Spiral Configuration of the Solar Wind Magnetic Field at the Solar Maximum of Solar Cycle 24

By assuming that the solar wind flow is spherically symmetric and that the flow speed becomes constant beyond some critical distance r = R ₀ (neglecting solar gravitation and acceleration by high coronal temperature), the large-scale solar wind magnetic field lines are distorted into a Parker spiral configuration, which is usually simplified to an Archimedes spiral. Using magnetic field observations near Mercury, Venus, and Earth during solar maximum of Solar Cycle 24, we statistically surveyed the Parker spiral angles and obtained the empirical equations of the Archimedes and Parker spirals by fitting the multiple-point results. We found that the solar wind magnetic field configurations are slightly different during different years. Archimedes and Parker spiral configurations are quite different from each other within 1 au. Our results provide empirical Archimedes and Parker spiral equations that depend on the solar wind velocity and the critical distance (R ₀). It is inferred that R ₀ is much larger than that previously assumed. In the near future, the statistical survey of the near-Sun solar wind velocity by Parker Solar Probe can help verify this result.