Numerical models of binary neutron star system mergers. I. Numerical methods and equilibrium data for Newtonian models

The numerical modeling of binary neutron star mergers has become a subject of much interest in recent years. While a full and accurate model of this phenomenon would require the evolution of the equations of relativistic hydrodynamics along with the Einstein field equations, a qualitative study of the early stages on inspiral can be accomplished by either Newtonian or post-Newtonian models, which are more tractable. However, even purely Newtonian models present numerical challenges that must be overcome in order to have accurate models of the inspiral. In particular, the simulations must maintain conservation of both energy and momenta and otherwise exhibit good numerical behavior. A spate of recent papers have detailed the results for Newtonian and post-Newtonian models of neutron star coalescence from a variety of groups who employ very different numerical schemes. These include calculations that have been carried out in both inertial and rotating frames, as well as calculations that employ both equilibrium configurations and spherical stars as initial data. However, only a few papers have given attention to the issue of the accuracy of the models and the dependence of the results on the computational frame and the initial data. In this paper we offer a comparison of results from both rotating and nonrotating (inertial) frame calculations. We find that the rotating frame calculations offer significantly improved accuracy as compared with the inertial frame models. Furthermore, we show that inertial frame models exhibit significant and erroneous angular momentum loss during the simulations that leads to an unphysical inspiral of the two neutron stars. We also examine the dependence of the models on initial conditions by considering initial configurations that consist of spherical neutron stars as well as stars that are in equilibrium and are tidally distorted. We compare our models to those given by Rasio & Shapiro in 1992 and 1994 and by New & Tohline in 1997. Finally, we investigate the use of the isolated star approximation for the construction of initial data.