Theoretical models of polar-cap convection under the influence of a northward interplanetary magnetic field

The unexpected patterns of high-latitude auroral luminosity and ionospheric convection that are observed when the interplanetary magnetic field (IMF) has a northward orientation have inspired a variety of theoretical interpretations. The existing models, all referring to steady-state conditions, can be classified according to the topology of the polar magnetic field lines and of the polar-cap convection streamlines. The classes of model include: (1) a closed magnetosphere model, (2) a conventional open model with a distorted, but topologically unchanged, polar-cap boundary, (3) a conventional open model with distorted, but topologically unchanged, polar-cap convection cells, (4) a modified open model with 'lobe convection cells' contained wholly on open magnetic-field lines, and (5) a modified open model with a bifurcated polar cap. The third and fourth types require significant regions of sunward flow on open polar-cap field lines, a concept that presents serious theoretical difficulties. The other three types appear equally viable from a theoretical point of view, and the comparison against observations is an ongoing enterprise. Outstanding theoretical questions include (a) how do observed structures in the polar ionosphere map along magnetic field lines into the magnetosphere?, (b) what is the mechanism that drives the observed sunward convection at highest latitudes on the day side?, and (c) what role does time dependence play in the observed phenomena?