Is Quadrupole Structure of Out-of-Plane Magnetic Field Evidence for Hall Reconnection?

The experimental observation of a quadrupole pattern in the "out-of-plane" field B-y is usually interpreted as a tell-tale sign of Hall MHD mediated magnetic reconnection in the vicinity of a reconnecting X-point. In contrast to these conventional expectations, it is shown by means of analytical equations describing the generation of B-y that quadrupole structure can be formed even in the absence of Hall effects. In general, B-y can be generated due to inhomogeneous ion flow, inhomogeneous current (Hall effect), or terms proportional to a pre-existing B-y. This prediction is validated in a 3D global MHD simulation where it is shown that vortex flows at the dayside magnetopause lead to formation of a finite B-y even in the absence of a pre-existing IMF B-y. The generated field is shown to have a quadrupolar pattern in B-y with peak amplitude similar to 0.5 of the total field. Similar vortex flows are also observed in 3D global hybrid simulations but the resulting B-y structure in this case is a combination of the Hall effects and the inhomogeneous ion flows. Thus special care must be taken in using observations of quadrupole B-y in satellite and experiments to infer information about its particular generation mechanism or attributing it to the Hall MHD reconnection regime.