Non-spherical source-surface model of the heliosphere: a scalar formulation

Abstract. The source-surface method offers an alternative to full MHD simulation of the heliosphere. It entails specification of a surface from which the solar wind flows normally outward along straight lines. Compatibility with MHD results requires this (source) surface to be non-spherical in general and prolate (aligned with the solar dipole axis) in prototypical axisymmetric cases. Mid-latitude features on the source surface thus map to significantly lower latitudes in the heliosphere. The model is usually implemented by deriving the B field (in the region surrounded by the source surface) from a scalar potential formally expanded in spherical harmonics, with coefficients chosen so as to minimize the mean-square tangential component of B over this surface. In the simplified (scalar) version the quantity minimized is instead the variance of the scalar potential over the source surface. The scalar formulation greatly reduces the time required to compute required matrix elements, while imposing essentially the same physical boundary condition as the vector formulation (viz., that the coronal magnetic field be, as nearly as possible, normal to the source surface for continuity with the heliosphere). The source surface proposed for actual application is a surface of constant F̃ ≡ r^-kB̃, where r is the heliocentric distance and B̃ is the scalar magnitude of the B field produced by currents inside the Sun. Comparison with MHD simulations suggests that k ≈ 1.4 is a good choice for the adjustable exponent. This value has been shown to map the neutral line on the source surface during Carrington Rotation 1869 (May–June 1993) to a range of latitudes that would have just grazed the position of Ulysses during that month in which sector structure disappeared from Ulysses' magnetometer observations.