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. We integrate the three-dimensional Newtonian equations of hydrodynamics by the Riemann-solver based “Piecewise Parabolic 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 gravitational wave luminosity and to a stronger peak of the gravitational wave spectrum at a frequency of about f 1:8 KHz when compared to the results of Zhuge et al. (1994). In case (b) two grid based codes with the same backreaction formalism but differing hydrodynamic integrators and slightly different initial conditions are compared. Instead of rotationally deformed initial neutron stars we use spherically shaped stars. 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 setting in when the two stars come very close. In (c) we find that using a polytropic equation of state instead of the high-density equation of state of Lattimer & Swesty (1991) employed by Ruffert et al. (1996) does not change the overall dynamical evolution of the merger and yields agreement of the gravitational wave signature to within 20% accuracy. Whereas the polytropic law describes the dynamical behaviour of the bulk of the matter at and above nuclear density sufficiently well, we, however, find clear differences of the structure and evoluSend offprint requests to: M. Ruffert ? e-mail: [email protected] ?? e-mail: [email protected] ??? e-mail: [email protected] tion of the outer layers of the neutron stars where the stiffness of the equation of state is largely overestimated. This has important implications for questions like mass loss and disk formation during the merging of binary neutron stars.