Eigenmode approach to coronal magnetic structure with differential solar rotation

Diffusion of field line foot points in the photosphere couples with latitud e-dependent solar rotation to define an eigenvalue problem, such that coron al magnetic structures derived from certain specific linear combinations of spherical harmonic functions are found to rotate rigidly about the Sun. Su ch eigenmodes and their corresponding complex eigenfrequencies are readily identified by diagonalizing progressively larger matrix representations of the eigenvalue problem. For azimuthal harmonic number m = 1, the eigenvalue with the least negative imaginary part (approximate to - 0.6 year(-1) for footpoint diffusion coefficient D-perpendicular to = 600 km(2)s(-1) and oth erwise roughly proportional to D-perpendicular to(1/2)) corresponds to an e igenmode whose main component is the dipole (n = 1) moment perpendicular to the Sun's rotation axis. Associated values of Re omega (1)(1) correspond t o heliomagnetic rotation at 99.4% of the Sun's equatorial rate for D-perpen dicular to = 600 km(2)s(-1) and otherwise to a retrograde deviation roughly proportional to D-perpendicular to(1/2) from the Sun's equatorial rotation rate. This eigenmode corresponds to the almost rigidly rotating coronal st ructure found by Wang et al. [1988] in their numerical simulations of the c oronal magnetic field. The associated heliospheric current sheet rotates al most rigidly about the Sun despite the anchorage of adjacent field lines in a differentially rotating photosphere. This particular eigenmode also corr esponds most nearly to the nonaxial part of the tilted dipole in the helios pheric model of Fisk [1996], whereby differential solar rotation leads to a latitudinal circulation of field lines through the heliosphere and thus to large-scale heliospheric convection.