COALESCING NEUTRON-STARS - GRAVITATIONAL-WAVES FROM POLYTROPIC MODELS

The dynamics, time evolution of the mass distribution, and gravitation al wave signature of coalescing neutron stars described by polytropes are compared with three simulations published previously: (a) ''Run 3' ' 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. We integrate the three-dimensional Newtonian equat ions of hydrodynamics by the Riemann-solver based ''Piecewise Paraboli c Method'' on an equidistant Cartesian grid. Comparison (a) confronts the results of our grid-based PPM scheme with those from an SPH code. We find that due to the lower numerical viscosity of the PPM code, the post-merging oscillations and pulsations can be followed for a longer time and lead to larger secondary and tertiary maxima of the gravitat ional wave luminosity and to a stronger peak of the gravitational wave spectrum at a frequency of about f approximate to 1.8 KHz when compar ed to the results of Zhuge et al. (1994). In case (b) two grid based c odes with the same backreaction formalism but differing hy drodynamic integrators and slightly different initial conditions are compared. In stead of rotationally deformed initial neutron stars we use sphericall y shaped stars. Satisfactory agreement of the amplitude of the gravita tional wave luminosity is established, although due to the different i nitial conditions a small time delay develops in the onset of the dyna mical instability setting in when the two stars come very close. In (c ) we find that using a polytropic equation of state instead of the hig h-density equation of state of Lattimer & Swesty (1991) employed by Ru ffert et al. (1996) does not change the overall dynamical evolution of the merger and yields agreement of the gravitational wave signature t o within 20% accuracy. Whereas the polytropic law describes the dynami cal behaviour of the bulk of the matter at and above nuclear density s ufficiently well, we, however, find clear differences of the structure and evolution of the outer layers of the neutron stars where the stif fness of the equation of state is largely overestimated. This has impo rtant implications for questions like mass loss and disk formation dur ing the merging of binary neutron stars.