Coalescing neutron stars -A step towards physical models

III. Improved numerics and different neutron star masses and spins

¹ Department of Mathematics & Statistics, University of Edinburgh, Edinburgh, EH9 3JZ, Scotland, UK
² Max-Planck-Institut für Astrophysik, Postfach 1317, 85741 Garching, Germany e-mail: thj@mpa-garching.mpg.de

Corresponding author: M. Ruffert, m.ruffert@ed.ac.uk

Received: 13 June 2001
Accepted: 12 October 2001

Abstract

In this paper we present a compilation of results from our most advanced neutron star merger simulations. Special aspects of these models were refered to in earlier publications (Ruffert & Janka [CITE]; Janka et al. [CITE]), but a description of the employed numerical procedures and a more complete overview over a large number of computed models are given here. The three-dimensional hydrodynamic simulations were done with a code based on the Piecewise Parabolic Method (PPM), which solves the discretized conservation laws for mass, momentum, energy and, in addition, for the electron lepton number in an Eulerian frame of reference. Up to five levels of nested cartesian grids ensure higher numerical resolution (about 0.6km) around the center of mass while the evolution is followed in a large computational volume (side length between 300 and 400km). The simulations are basically Newtonian, but gravitational-wave emission and the corresponding back-reaction on the hydrodynamic flow are taken into account. The use of a physical nuclear equation of state allows us to follow the thermodynamic history of the stellar medium and to compute the energy and lepton number loss due to the emission of neutrinos. The computed models differ concerning the neutron star masses and mass ratios, the neutron star spins, the numerical resolution expressed by the cell size of the finest grid and the number of grid levels, and the calculation of the temperature from the solution of the entropy equation instead of the energy equation. The models were evaluated for the corresponding gravitational-wave and neutrino emission and the mass loss which occurs during the dynamical phase of the merging. The results can serve for comparison with smoothed particle hydrodynamics (SPH) simulations. In addition, they define a reference point for future models with a better treatment of general relativity and with improvements of the complex input physics. Our simulations show that the details of the gravitational-wave emission are still sensitive to the numerical resolution, even in our highest-quality calculations. The amount of mass which can be ejected from neutron star mergers depends strongly on the angular momentum of the system. Our results do not support the initial conditions of temperature and proton-to-nucleon ratio needed according to recent work for producing a solar r-process pattern for nuclei around and above the peak. The improved models confirm our previous conclusion that gamma-ray bursts are not powered by neutrino emission during the dynamical phase of the merging of two neutron stars.