High-resolution calculations of merging neutron stars - I. Model description and hydrodynamic evolution

We present the results of 3D high-resolution calculations of the last inspiral stages and the final coalescence of neutron star binary systems. The equations of hydrodynamics are solved using the smoothed particle hydrodynamics method with up to 10⁶ particles. Using Newtonian gravity, but adding the forces emerging from the emission of gravitational waves, we focus on the impact of microphysics on the dynamical evolution of the merger; namely, we use a new equation of state based on the relativistic mean field approach of Shen et al. Neutrino emission of all flavours, the resulting cooling and the change in the electron fraction are accounted for with a detailed leakage scheme. The new equation of state is substantially stiffer than the Lattimer-Swesty equation of state that has been used in previous investigations. This leads the system to become dynamically unstable at a separation as large as 3.3 stellar radii, where the secular orbital decay undergoes a transition towards a dynamical `plunge' of the binary components towards each other. As soon as the stars come into contact a Kelvin-Helmholtz instability forms at the interface of both stars. The peak temperatures are found in the vortex rolls that form during this process. We generally find slightly lower temperatures than previously found using the Lattimer-Swesty equation of state. The central object is surrounded by a very thick disc that shows cool equatorial flows: inflows in the inner parts of the disc and outflow further out. The cool inflows become shock heated in the innermost parts of the disc and lead to an outflow of hot material in the vertical direction. The temperatures in the disc have typical values of 3-4MeV, lower than the temperatures found in previous investigations using the Lattimer-Swesty equation of state. These conditions allow for the existence of heavy nuclei even in the inner parts of the disc, we find typical mass fractions of ~0.1, which is enough for scattering off heavy nuclei to be the dominant source of neutrino opacity. The central object formed during the coalescence shows a rapid, differential rotation with periods of ~2ms. Although a final conclusion on this point is not possible from our basically Newtonian approach, we argue that the central object will remain stable without collapsing to a black hole, at least on the simulation time-scale of 20ms, but possibly for as long as ~100s, mainly stabilized by differential rotation. The massive, differentially rotating central object is expected to wind up initial magnetic fields to enormous field strengths of ~10¹⁷G and may therefore have important implications for this event as a central engine of gamma-ray bursts.