  Binary neutron stars (NSNS) are expected to be among the leading sources of
gravitational waves observable by ground-based laser interferometers and may be
the progenitors of short-hard gamma ray bursts. We present a series of general
relativistic NSNS coalescence simulations both for unmagnetized and magnetized
stars. We adopt quasiequilibrium initial data for circular, irrotational
binaries constructed in the conformal thin-sandwich (CTS) framework. We adopt
the BSSN formulation for evolving the metric and a high-resolution
shock-capturing scheme to handle the magnetohydrodynamics. Our simulations of
unmagnetized binaries confirm the results of Shibata, Taniguchi and Uryu
(2003). In cases in which the mergers result in a prompt collapse to a black
hole, we are able to use puncture gauge conditions to extend the evolution and
determine the mass of the material that forms a disk. We find that the disk
mass is less than 2% of the total mass in all cases studied. We then add a
small poloidal magnetic field to the initial configurations and study the
subsequent evolution. For cases in which the remnant is a hypermassive neutron
star, we see measurable differences in both the amplitude and phase of the
gravitational waveforms following the merger. For cases in which the remnant is
a black hole surrounded by a disk, the disk mass and the gravitational
waveforms are about the same as the unmagnetized cases. Magnetic fields
substantially affect the long-term, secular evolution of a hypermassive neutron
star (driving `delayed collapse') and an accretion disk around a nascent black
hole.
