Asymmetric magnetic reconnection with a flow shear and applications to the magnetopause

We perform a systematic theoretical and numerical study of antiparallel two-dimensional magnetic reconnection with asymmetries in the plasma density and reconnecting magnetic field strength in addition to a bulk flow shear across the reconnection site in the plane of the reconnecting fields, which commonly occurs at planetary magnetospheres. We analytically predict the speed at which an isolated X line is convected by the flow, the reconnection rate, and the critical flow speed at which reconnection no longer takes place for arbitrary reconnecting magnetic field strengths, densities, and upstream flow speeds, and we confirm the results with two-fluid numerical simulations. The predictions and simulation results counter the prevailing model of reconnection at Earth's dayside magnetopause which says reconnection occurs with a stationary X line for sub-Alfvenic magnetosheath flow, reconnection occurs but the X line convects for magnetosheath flows between the Alfven speed and double the Alfven speed, and reconnection does not occur for magnetosheath flows greater than double the Alfven speed. In particular, we find that X line motion is governed by momentum conservation from the upstream flows, which are weighted differently in asymmetric systems, so the X line convects for generic conditions including sub-Alfvenic upstream speeds. For the reconnection rate, as with symmetric reconnection, it drops with increasing flow shear and there is a cutoff speed above which reconnection is not predominant. However, while the cutoff condition for symmetric reconnection is that the difference in flows on the two sides of the reconnection site is twice the Alfven speed, we find asymmetries cause the cutoff speed for asymmetric reconnection to be higher than twice the asymmetric form of the Alfven speed. The stronger the asymmetries, the more the cutoff exceeds double the asymmetric Alfven speed. This is due to the fact that in asymmetric reconnection, the plasma with the smaller mass flux into the dissipation region contributes a smaller mass to the dissipation region, so the effect of its flow on opposing the release of energy by the reconnected magnetic fields is diminished and the reconnection is not suppressed to the extent previously thought. The results compare favorably with an observation of reconnection at Earth's polar cusps during a period of northward interplanetary magnetic field, where reconnection occurs despite the magnetosheath flow speed being more than twice the magnetosheath Alfven speed, the previously proposed suppression condition. These results are expected to be of broad importance for magnetospheric physics of Earth and other planets; particular applications are discussed.