  A mechanism for explosive magnetic reconnection is investigated by analyzing
the nonlinear evolution of a collisionless tearing mode in a two-fluid model
that includes the effects of electron inertia and temperature. These effects
cooperatively enable a fast reconnection by forming an X-shaped current-vortex
layer centered at the reconnection point. A high-resolution simulation of this
model for an unprecedentedly small electron skin depth $d_e$ and ion-sound
gyroradius $\rho_s$, satisfying $d_e=\rho_s$, shows an explosive tendency for
nonlinear growth of the tearing mode, where it is newly found that the
explosive widening of the X-shaped layer occurs locally around the reconnection
point with the length of the X shape being shorter than the domain length and
the wavelength of the linear tearing mode. The reason for the onset of this
locally enhanced reconnection is explained theoretically by developing a novel
nonlinear and nonequilibrium inner solution that models the local X-shaped
layer, and then matching it to an outer solution that is approximated by a
linear tearing eigenmode with a shorter wavelength than the domain length. This
theoretical model proves that the local reconnection can release the magnetic
energy more efficiently than the global one and the estimated scaling of the
explosive growth rate agrees well with the simulation results.
