Energetics of compressible models of fast steady-state magnetic reconnection

An understanding of the energy transfer that takes place during magnetic reconnection is crucial to the study of this fundamental process. It depends on two factors: the type of reconnection regime (which is determined by the boundary conditions) and the degree of compressibility. Here we examine the role of compressibility in the energetics of a family of reconnection models. When the inflow Mach number (or reconnection rate) M_e is small the effects of compressibility may be more important than the differences between regimes. We find that for a slow-compression regime with M_e = 0·005 compressibility decreases by 39% the efficiency of the shocks in converting magnetic energy and increases by 14% the ratio of thermal to kinetic energy in the outflow jet. This compares with a 13% decrease in the shock efficiency and a 7% decrease in the jet ratio obtained by choosing instead a flux-pile-up regime. As M_e is increased, however, the differences between regimes become larger and may be comparable to or greater than the effects of compressibility. Thus when the above Mach number is doubled we find that a change of regime now has 1-6 times the effect on the jet energy ratio as the introduction of compressibility. For those regimes, therefore, which only exist at low inflow Mach numbers, compressibility will always be important. At higher values of M_e the type of regime may be the dominant factor governing the energetics.