Source‐surface modeling of planetary magnetospheres

Abstract

In the source‐surface approach to field modeling, the magnetosphere is divided conceptually into inner and outer regions (called S and T) by prescribing a cross‐magnetospheric surface that marks the tail entrance. The source surface thus consists of the prescribed magnetopause and the prescribed tail‐entrance surface. In the inner region (S) enclosed by the source surface, the magnetic field B is expanded formally in a series of analytical functions (e.g., gradients of spherical harmonics) with coefficients determined by a least‐squares fit to the desired boundary conditions (namely that the field be tangential to the magnetopause and normal to the tail‐entrance surface). Field lines in the tail region (T) are constructed geometrically so as to intersect the tail‐entrance surface normally but not to intersect each other or the magnetopause. Expansion coefficients for region S are determined by minimizing a user‐specified linear combination of the mean‐square normal component of B on the magnetopause and the meansquare tangential component of B on the tail‐entrance surface. This model leads to a neutral line (contour of vanishing normal component of B) on the prescribed cross‐tail surface. The neutral line constitutes the inner edge of the neutral sheet and marks the boundary (separatrix) between closed and open magnetic field lines. A mapping of the separatrix along magnetic field lines to the planetary surface defines (in the absence of a penetrating interplanetary magnetic field, which can be added later) the poleward boundary of the auroral oval. This mapping accounts well for quiet‐time auroral ovals seen in DMSP images. The source‐surface model also yields the position and shape of the neutral sheet in the tail region (T), where the strength of B can be calculated (from the normal component of B at the tail‐entrance surface) by invoking flux conservation. The current density J in region T can be computed from ▿ × B there.