Anticorrelation of density and magnetic field in a fast magnetosonic mode: The case of surface waves in an inhomogeneous magnetosphere

Magnetohydrodynamic (MHD) wave theory states that fast magnetosonic waves should have correlated fluctuations in the compressional magnetic field and the plasma density / pressure. Anticorrelation, on the other hand relates either to the slow magnetosonic or mirror modes. These classic results are often used as a diagnostic in waves observed by spacecraft throughout the heliosphere. However, it is important to recognise that they are derived under the assumption of a homogeneous background plasma. Planetary magnetospheres are, in contrast, highly inhomogeneous. When allowing for a non-uniform background, the linearised MHD equations for density and pressure perturbations include terms due to the intrinsic compression associated with the wave as well as advection of plasma parcels with different background values. We argue that these two effects can compete and result in anticorrelation between the density and magnetic field, particularly when the scale of the inhomogeneity is shorter than that of the wave. We demonstrate examples of this anticorrelation applied to fast-mode magnetopause surface waves in both analytic MHD theory and a global MHD simulation. Finally, methods which identify and allow for these effects in satellite observations are discussed.