Coronal magnetic-field model with non-spherical source surface

Abstract

Previous global models of coronal magnetic fields have used a geometrical construction based on a spherical source surface because of requirements for computational speed. As a result they have had difficulty accounting for (a) the tendency of full magnetohydrodynamic (MHD) models to predict non-radial plasma flow out to r ∼ 10r _⊙ and (b) the appreciable magnitude, ∼ 3γ, of B _r , (the radial component of B) consistently observed at r ∼ 1 AU. We present a new modelling technique based on a non-spherical source surface, which is taken to be an isogauss of the underlying potential field generated by currents in or below the photosphere. This modification of the source surface significantly improves the agreement between the geometrical construction and the MHD solution while retaining most of the computational ease provided by a spherical source surface. A detailed comparison between the present source-surface model and the MHD solution is made for the internal dipole case. The resulting B field agrees well in magnitude and direction with the coronal B field derived from the full MHD equations. It shows evidence of the slightly equatorward meridional plasma flow that is characteristic of the MHD solution. Moreover, the B field obtained by using our non-spherical source surface agrees well with that observed by spacecraft in the vicinity of the Earth's orbit. Applied to a solar dipole field with a moment of 1 G-r ³_⊙ , the present model predicts that B _r at r ∼ 1 AU lies in the range of ∼ 1–2γ and is remarkably insensitive to heliomagnetic latitude. Our method should be applicable also to more general (i.e., more realistic) configurations of the solar magnetic field. Isogauss surfaces for two representative solar rotations, as calculated from expansions of observed photospheric magnetic-field data, are found to show large and significant deviations from sphericity.