Conformally flat smoothed particle hydrodynamics application to neutron star mergers

We present a new 3D smoothed particle hydrodynamics code that solves the general relativistic $\mathrm{field}+\mathrm{hydrodynamic}$ equations in the conformally flat approximation. Several test cases are considered to test different aspects of the code. We then apply the code to the coalescence of a neutron star binary system. The neutron stars are modeled by a polytropic equation of state with adiabatic indices $\Gamma =2.0,\hspace{0.5em}\Gamma =2.6,$ and $\Gamma =\mathrm{3.0.}\mathrm{}$ We calculate the gravitational wave signals, luminosities, and frequency spectra by employing the quadrupole approximation for emission and back reaction in the slow motion limit. In addition, we consider the amount of ejected mass.