  Many short gamma-ray bursts (sGRBs) exhibit a prolonged plateau in the X-ray
light curve following the main burst. It is shown that an X-ray plateau at the
observed luminosity emerges naturally from a plerion-like model of the sGRB
remnant, in which the magnetized, relativistic wind of a millisecond magnetar
injects shock-accelerated electrons into a cavity confined by the sGRB blast
wave. A geometry-dependent fraction of the plerionic radiation is also
intercepted and reprocessed by the optically thick merger ejecta. The relative
contributions of the plerion and ejecta to the composite X-ray light curve are
estimated approximately with the aid of established ejecta models. The
plerionic component of the electron energy spectrum is evolved under the action
of time-dependent, power-law injection and adiabatic and synchrotron cooling in
order to calculate the X-ray light curve analytically. The model yields an
anti-correlation between the luminosity and duration of the plateau as well as
a sudden cut-off in the X-ray flux, if the decelerating magnetar collapses to
form a black hole. Both features are broadly consistent with the data and can
be related to the surface magnetic field of the magnetar and its angular
velocity at birth. The analogy with core-collapse supernova remnants is
discussed briefly.
