  We present results from the first large parameter study of neutron star
mergers using fully general relativistic simulations with finite-temperature
microphysical equations of state and neutrino cooling. We consider equal and
unequal-mass binaries drawn from the galactic population and simulate each
binary with three different equations of state. Our focus is on the emission of
energy and angular momentum in gravitational waves in the postmerger phase. We
find that the emitted gravitational-wave energy in the first
$\sim$$10\,\mathrm{ms}$ of the life of the resulting hypermassive neutron star
(HMNS) is about twice the energy emitted over the entire inspiral history of
the binary. The total radiated energy per binary mass is comparable to or
larger than that of nonspinning black hole inspiral-mergers. About $0.8-2.5\%$
of the binary mass-energy is emitted at kHz frequencies in the early HMNS
evolution. We find a clear dependence of the postmerger GW emission on binary
configuration and equation of state and show that it can be encoded as a broad
function of the binary tidal coupling constant $\kappa^T_2$. Our results also
demonstrate that the dimensionless spin of black holes resulting from
subsequent HMNS collapse are limited to $\lesssim0.7-0.8$. This may
significantly impact the neutrino pair annihilation mechanism for powering
short gamma-ray bursts (sGRB).
