  We present 3D Newtonian simulations of the coalescence of two neutron stars,
using a Smoothed Particle Hydrodynamics (SPH) code. We begin the simulations
with the two stars in a hard, circular binary, and have them spiral together as
angular momentum is lost through gravitational radiation at the rate predicted
by modeling the system as two point masses. We model the neutron stars as hard
polytropes ($\gamma=2.4$) of equal mass, and investigate the effect of the
initial spin of the two stars on the coalescence. The process of coalescence,
from initial contact to the formation of an axially symmetric object, takes
only a few orbital periods. Some of the material from the two neutron stars is
shed, forming a thick disk around the central, coalesced object. The mass of
this disk is dependent on the initial neutron star spins; higher spin rates
resulting in greater mass loss, and thus more massive disks. For spin rates
that are most likely to be applicable to real systems, the central coalesced
object has a mass of $2.4M_\odot$, which is tantalizingly close to the maximum
mass allowed by any neutron star equation of state for an object that is
supported in part by rotation. Using a realistic nuclear equation of state, we
estimate the temperature of the material after the coalescence. We find that
the central object is at a temperature of $\sim 10$MeV, whilst the disk is
heated by shocks to a temperature of 2-4MeV.
