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

Abstract

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 constantF r ÿ kB , where r is the heliocentric distance andB 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. BackgroundThe magnetic field in the solar corona is traditionally modeled (Schatten et al., 1969;Altschuler and Newkirk, 1969;Hoeksema and Scherrer, 1986;Hoeksema, 1991) as being current-free (and thus derivable from a scalar potential) within a spherically annular volume of inner radius 1 r in order to achieve better agreement with dimensions of large coronal helmet structures seen in eclipse photographs.Subsequent magnetohydrodynamic (MHD) simulations by Pneuman and Kopp (1971a, b) showed (as many eclipse photographs had already indicated) that the outflow of solar wind must be significantly nonradial in the inner heliosphere. The dashed curves in .

On Solutions of the PFSS Model With GONG Synoptic Maps for 2006–2018

“…The fact that CHs in different parts of the solar disc can be captured with different locations of the source surface in the PFSS model (Figures and ) indicates that a surface where coronal magnetic field opens deviates from a spherical surface. Some efforts have been made to define a nonspherical source surface (Levine et al, ; Schulz et al, ; Schulz, ); however, no significant progress in the coronal field modeling with the nonspherical surface has been made since then.…”

A New View of the Coupling of the Sun and the Heliosphere

“…There have been a number of mathematical refinements of these models, such as adding the effect of a nonspherical source surface (Schulz, Frazier & Bougher 1978;Schulz 1997), or the effects of current sheets outside the modeling domain (Zhao & Hoeksema 1995). Note that r s is effectively a free parameter and different values are used for different purposes.…”

Solar cycle changes in coronal holes and space weather cycles

“…Shortcomings of the PFSS approach include its neglect of coronal currents and the nonpotential nature of some active regions and the use of a spherical source surface that constrains the coronal field to become radial at a specified altitude regardless of location. Although a few studies have used nonspherical source surfaces, they have been restricted to special cases because realistic multipolar field boundary conditions present computational challenges [e.g., Levine et al , 1982; Schulz , 1997]. There are also corrections that can be made to the PFSS model to better represent the effects of the heliospheric current sheet on the field geometry [e.g., Zhao and Hoeksema , 1995a; Wang and Sheeley , 1995], but we also neglect this complication in our coronal hole oriented study.…”