  One favored progenitor model for short duration gamma-ray bursts (SGRBs) is
the coalescence of two neutron stars (NS-NS). One possible outcome of such a
merger would be a rapidly spinning, strongly magnetized neutron star (known as
a millisecond magnetar). These magnetars may be "supra-massive", implying they
would collapse to black holes after losing centrifugal support due to magnetic
dipole spindown. By systematically analyzing the BAT-XRT light curves of all
short GRBs detected by {\em swift}, we test how well the data are consistent
with this central engine model of short GRBs. We find that the so-called
"extended emission" observed with BAT in some short GRBs are fundamentally the
same component as the "internal X-ray plateau" as observed in many short GRBs,
which is defined as a plateau in the lightcurve followed by a very rapid drop.
Based on how likely a short GRB hosts a magnetar, we characterize the entire
{\em Swift} short GRB sample into three categories: the "internal plateau"
sample, the "external plateau" sample, and the "no plateau" sample. The derived
magnetar surface magnetic field $B_{\rm p}$ and the initial spin period $P_0$
fall into the reasonable range. No GRBs in the internal plateau sample have the
total energy exceeding the maximum energy budget of a millisecond magnetar.
Assuming that the rapid fall time at the end of the internal plateau is the
collapse time of a supra-massive magnetar to a black hole, and applying the
measured mass distribution of NS-NS systems in our Galaxy, we constrain the
neutron star equation of state (EOS). The data suggest that the NS equation of
state is close to the GM1 model, which has a maximum non-rotating NS mass
$M_{\rm TOV} \sim 2.37 M_\odot$.
