Numerical Models of Newtonian and Post-Newtonian Binary Neutron Star   Mergers
  This article describes a comparison of two calculations of the merger of a binary neutron star (NS) system which is initially within the tidal instability as described by Rasio and Shapiro. The same initial data is used with one simulation involving a purely Newtonian evolution of the Euler equations for compressible fluids and another similarly evolved except there is an inclusion of a gravitational radiation reaction (GRR) term at the 2.5 Post-Newtonian (PN) order as prescribed by Blanchet, Damour, and Schafer. The inclusion of GRR is to allow an approximation of the full relativistic effect which forces the inspiral of binary systems. The initial data is identical at the start of each evolution and only the inclusion of the 2.5PN term differs in the evolutions. We chose two co-rotating, gamma=2 polytropic stars with masses 1.4M_Solar, radii R=9.56km and central densities of 2.5E15 g/cm3. The initial binary separation is 2.9R, inside the region where the dynamical tidal instability has been shown to cause the merger of the two stars. Comparisons between measured quantities will indicate a substantial difference between the two evolutions. It will be shown that the effect of GRR on the dynamics of the merger is significant. 
Edward Y. M. Wang, F. Douglas Swesty, and Alan C. Calder