Electron heating during magnetic reconnection: A simulation scaling study

Electron bulk heating during magnetic reconnection with symmetric inflow conditions is examined using kinetic particle-in-cell simulations. Inflowing plasma parameters are varied over a wide range of conditions, and the increase in electron temperature is measured in the exhaust well downstream of the x-line. The degree of electron heating is well correlated with the inflowing Alfvén speed c_Ar based on the reconnecting magnetic field through the relation $ΔTe=0.033 mi cAr2$⁠, where ΔT_e is the increase in electron temperature. For the range of simulations performed, the heating shows almost no correlation with inflow total temperature $Ttot=Ti+Te$ or plasma β. An out-of-plane (guide) magnetic field of similar magnitude to the reconnecting field does not affect the total heating, but it does quench perpendicular heating, with almost all heating being in the parallel direction. These results are qualitatively consistent with a recent statistical survey of electron heating in the dayside magnetopause (Phan et al., Geophys. Res. Lett. 40, 4475, 2013), which also found that ΔT_e was proportional to the inflowing Alfvén speed. The net electron heating varies very little with distance downstream of the x-line. The simulations show at most a very weak dependence of electron heating on the ion to electron mass ratio. In the antiparallel reconnection case, the largely parallel heating is eventually isotropized downstream due a scattering mechanism, such as stochastic particle motion or instabilities. The simulation size is large enough to be directly relevant to reconnection in the Earth's magnetosphere, and the present findings may prove to be universal in nature with applications to the solar wind, the solar corona, and other astrophysical plasmas. The study highlights key properties that must be satisfied by an electron heating mechanism: (1) preferential heating in the parallel direction; (2) heating proportional to $mi cAr2$⁠; (3) at most a weak dependence on electron mass; and (4) an exhaust electron temperature that varies little with distance from the x-line.