Coalescing neutron stars -- gravitational waves from polytropic models

The dynamics, time evolution of the mass distribution, and gravitational wave signature of coalescing neutron stars described by polytropes are compared with three simulations published previously: (a) ``Run 2'' of Zhuge et al. (1994), (b) ``Model III'' of Shibata et al. (1992), and (c) ``Model A64'' of Ruffert et al. (1996). We aim at studying the differences due to the use of different numerical methods, different implementations of the gravitational wave backreaction, and different equations of state. Comparison (a) confronts the results of our grid-based PPM scheme with those from an SPH code. We found that due to the lower numerical viscosity of the PPM code, the post-merging oscillations and pulsations could be followed for a longer time and lead to larger secondary and tertiary maxima of the gravitational wave luminosity. In case (b) two grid based codes with the same backreaction formalism but differing hydrodynamic integrators and different numerical resolution are compared. Satisfactory agreement of the amplitude of the gravitational wave luminosity is established, although due to the different initial conditions a small time delay develops in the onset of the dynamical instability. In (c) we find that using a polytropic equation of state instead of the high-density equation of state of Lattimer & Swesty (1991) does not change the overall dynamical evolution of the merger and yields agreement of the gravitational wave signature to within 20% accuracy. However, differences of the structure and evolution of the outer layers of the neutron stars are present, which has important implications for questions like mass loss and disk formation during the merging of binary neutron stars.