Positive residual energy of magnetohydrodynamic fast-mode shocks

The difference in energy between velocity and magnetic field fluctuations in a plasma is quantified by the residual energy.  In the solar wind, residual energy is typically negative at magnetohydrodynamic (MHD) inertial scales, indicating an excess of magnetic fluctuation energy that arises from the presence of magnetically dominated structures and a turbulent cascade.  Recent observations have shown that fast-mode shock waves, in contrast, have a conspicuous positive signature – i.e. an excess of velocity fluctuation energy – in spectrograms of residual energy.  We show how the positive residual energy of super-Alfvénic (i.e. fast-mode) MHD shocks is a natural consequence of the Rankine-Hugoniot jump conditions.  The jump conditions have been used to derive an equation for the residual energy in terms of the shock angle, density compression ratio and upstream Alfvén Mach number.  Values obtained from this equation agree well with the observed residual energies of 141 interplanetary shocks.  The potential use of positive residual energy as a fast-mode shock identification signature in spacecraft data is considered, and the significance of these findings for understanding compressive fluctuations more generally in the solar wind is briefly discussed.