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-beta and high-Alfven-speed regime of the Earth's magnetotail to investigate the scaling of electron bulk heating produced by reconnection. The ranges of inflow Alfven speed and inflow electron beta(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, Delta T-e, is correlated with the inflow Alfven speed, V-Ax,V-in, based on the reconnecting magnetic field and the inflow plasma density. Furthermore, Delta T-e is linearly proportional to the inflowing magnetic energy per particle, m(i)V(Ax,in)(2), and the best fit to the data produces the empirical relation Delta T-e = 0.020 m(i)V(Ax,in)(2), 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 beta, 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 similar to 10-4000 km s(-1) and beta(e) similar to 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 Alfven speed of the ambient plasma.