How the electron frozen-in-law is broken during anti-parallel magnetic reconnection*

The mechanism that breaks the electron frozen-in-law has represented a long-standing open issue in collisionless magnetic reconnection. Aided by fully kinetic simulations, a resolution to this problem for anti-parallel reconnection is presented here. We find that magnetic field aligned electron pressure anisotropy develops upstream of the electron diffusion region (EDR), imposing strong off-diagonal electron stresses within the EDR. Along the direction of the reconnection X-line, however, these stresses cancel, and the electron frozen-in law is instead broken by thermal forces related to heating of the electrons directly by the reconnection electric field itself. The reconnection rate then freely adjusts to the value imposed externally by the ion dynamics.