Scaling of Magnetic Reconnection Electron Bulk Heating in the High-Alfven-Speed and Low-Beta Regime of Earth's Magnetotail

We have surveyed 21 reconnection exhaust events observed by Magnetospheric MultiScale in the low-plasma-β and high-Alfvén-speed regime of the Earth's magnetotail to investigate the scaling of electron bulk heating produced by reconnection. The ranges of inflow Alfvén speed and inflow electron β_e covered by this study are 800–4000 km s⁻¹ and 0.001–0.1, respectively, and the observed heating ranges from a few hundred electronvolts to several kiloelectronvolts. We find that the temperature change in the reconnection exhaust relative to the inflow, ΔT_e, is correlated with the inflow Alfvén speed, V_Ax,in, based on the reconnecting magnetic field and the inflow plasma density. Furthermore, ΔT_e is linearly proportional to the inflowing magnetic energy per particle, m_iV_Ax,in², and the best fit to the data produces the empirical relation ΔT_e = 0.020 m_iV_Ax,in², i.e., the electron temperature increase is on average ∼2% of the inflowing magnetic energy per particle. This magnetotail study extends a previous magnetopause reconnection study by two orders of magnitude in both magnetic energy and electron β, to a regime that is comparable to the solar corona. The validity of the empirical relation over such a large combined magnetopause–magnetotail plasma parameter range of V_A ∼ 10–4000 km s⁻¹ and β_e ∼ 0.001–10 suggests that one can predict the magnitude of the bulk electron heating by reconnection in a variety of contexts from the simple knowledge of a single parameter: the Alfvén speed of the ambient plasma.