1 Introduction

With an estimated rate of about 10^-5 events per year per galaxy (e.g., see the recent numbers in Bulik et al. 1999; Fryer et al. 1999; Kalogera & Lorimer 2000, and references therein) neutron star mergers are among the most frequent and most promising candidates for gravitational-wave emission which is strong enough to be measurable by the upcoming interferometric experiments in the US (LIGO), Europe (GEO600, VIRGO), and Japan (TAMA) (Thorne 1995). Theoretical models and wave templates, however, are needed to help filter out the weak signals from disturbing background noise. Gravitational waves from neutron star mergers could be one of the most fruitful ways to learn about the internal properties of neutron stars.

Merging neutron stars are also considered as possible sources of at least the subclass of short and hard cosmic gamma-ray bursts, especially if the merger remnant collapses to a black hole on a dynamical timescale (for recent discussions and model calculations, see, e.g., Popham et al. 1999; Ruffert & Janka 1999). Coincident detections of gravitational waves and gamma rays would be a convincing observational confirmation of this hypothesis and might in fact be the only possibility to identify the central engine of a gamma-ray burst unequivocally. The X-ray satellite HETE-2, which was launched in Fall 2000, is hoped to bring a similar breakthrough in the observation of short bursts as the BeppoSAX satellite did in case of the long ones.

The energy of the relativistically expanding fireball or jet, which finally produces the observable gamma-ray burst, can be provided by the annihilation of neutrino-antineutrino pairs (Paczynski 1991; Mészáros & Rees 1992; Woosley 1993a) or possibly by magnetohydrodynamical processes (Blandford & Znajek 1977; Mészáros & Rees 1997). In the former case, the gravitational binding energy of accreted disk matter is tapped, in the latter case the rotational energy of the central black hole could be converted into kinetic energy of the outflow. If neutrino processes are supposed to power the gamma-ray burst phenomenon, very high neutrino luminosities are needed, of magnitude similar as those from core-collapse supernovae. The rate of neutron star mergers, however, is much smaller (by a factor of 100-10000) than the Galactic supernova rate. This practically excludes them as detectable sources of thermal neutrinos in the MeV energy range, because the signals are too faint to be measurable from extragalactic distances. Dissipative processes in the relativistic outflow, which are considered to produce the gamma-ray burst, may also lead to the generation of high-energy or even ultra high-energy neutrinos (Paczynski & Xu 1994; Waxman & Bahcall 1997, 2000). Such neutrinos might be seen in future km²-scale experiments like ICECUBE, which is currently under construction in the Antarctica. However, they do not carry much specific information about the origin of the relativistically moving particles and it is therefore not very likely that they can yield much evidence about the nature of the central engine that powers the gamma-ray burst.

Neutron-rich matter, which is ejected from the system during the dynamical phase of the merging, was suggested as a possible site for the rapid neutron capture process (r-process) to produce heavy nuclei beyond the iron group (Lattimer et al. 1974, 1976; Hilf et al. 1974; Eichler et al. 1989; Meyer 1989). This problem has gained new interest recently (Rosswog et al. 1999, 2000; Freiburghaus et al. 2000). The possible contribution to the Galactic r-process material is estimated from the gas mass that gets unbound during the violent last stages of the coalescence. The nuclear reactions in decompressed neutron star matter depend sensitively on the initial conditions (neutron excess, composition, temperature, density), the dynamical and, in particular, thermal history of the material, and the influence of beta-decays and corresponding neutrino losses. All of these issues are so far not well under control in theoretical models, and therefore hydrodynamic simulations of neutron star mergers have not (yet?) been able to yield conclusive results.

These questions have been the motivation for a large number of investigations of the spiral-in phase and the ultimate merging of neutron stars. Analytic studies and ellipsoidal treatments concentrated on the effects of viscous dissipation for the heating and the rotation of the stars (Kochanek 1992; Bildsten & Cutler 1992; Lai 1994), the final instability of the mass transfer near the tidal radius (e.g., Bildsten & Cutler 1992; Lai et al. 1994a,b; Taniguchi & Nakamura 1996; Lai & Wiseman 1996; Lombardi et al. 1997; Baumgarte 2001) and the deformed equilibrium structure and tidal lag of the binary configuration prior to the dynamical interaction (Lai & Shapiro 1995). Hydrodynamical simulations of the coalescence were performed for Newtonian gravity with SPH codes (e.g., Rasio & Shapiro 1992, 1994, 1995; Centrella & McMillan 1993; Zhuge et al. 1994, 1996; Davies et al. 1994; Rosswog et al. 1999, 2000) and with grid-based methods (e.g., Oohara & Nakamura 1990; Nakamura & Oohara 1991), partly including special treatments of the gravitational-wave emission and their back-reaction on the flow by adding the corresponding post-Newtonian terms to the equations of hydrodynamics (e.g., Ruffert et al. 1996, 1997a; Ruffert et al. 1997b). More recently progress has been achieved in a wider use of the post-Newtonian approximation (Shibata et al. 1998; Ayal et al. 2001; Faber & Rasio 2000; Faber et al. 2001) and considerable advances were made towards general relativistic treatments (Oohara & Nakamura 1999; Shibata 1999; Shibata & Uryu 2000, 2001).

A spectacular result was obtained by Mathews & Wilson (1997, and references therein) who found that relativistic effects lead to a compression of the two neutron stars during the late stages of the spiral-in and therefore to their gravitational collapse to black holes prior to the merging. This effect contradicts Newtonian models where tidal stretching reduces the density of the stars as they get closer. Analytic considerations confirm the Newtonian behavior also for the post-Newtonian case (Thorne 1998; Baumgarte et al. 2000,b), and more recent simulations by the Wilson group (Marronetti et al. 1999) as well as general relativistic hydrodynamic models by other groups (Bonazzola et al. 1999; Shibata et al. 1998) were not able to reproduce the result of Mathews & Wilson (1997). The latter was recognized to be due to an error in the approximation scheme to full general relativity (Flanagan 1999). In any case, pre-merging collapse of the neutron stars is a speculative option only if the nuclear equation of state is extraordinarily soft and the neutron stars are already very close to the maximum mass for stable single neutron stars.

The majority of the simulations by other groups was done with simple microphysics, in particular with a polytropic law $P = K\rho^\Gamma$ for the equation of state (EoS) of the neutron star matter. This is a fair approach when one is mainly interested in the calculation of the gravitational-wave emission, which is associated with the motion of the bulk of the mass. It offers the advantage that the influence of the stiffness of the EoS, which determines the mass-radius relation of the neutron stars and the amount of compression which occurs during the final plunge, can be easily studied by choosing different values for the adiabatic index $\Gamma$ .

Several years ago we started to compute merger models with a more elaborate treatment of the EoS of the neutron star matter, using the physical description by Lattimer & Swesty (1991), which enabled us to follow the thermodynamics of the gas and to include a treatment of the neutrino production and emission from the heated neutron stars (Ruffert et al. 1996, 1997a; Ruffert & Janka 1998, 1999; Janka et al. 1999). Our main aims were the investigation of the relevance for gamma-ray burst scenarios, in particular for those where the neutrino emission had been suggested to provide the energy for the relativistic gamma-ray burst fireball via neutrino-antineutrino annihilation. Also the amount of mass ejection during the dynamical interaction and the properties of the ejected matter depend on the EoS, which cannot be descibed by one simple polytropic law in both the low-density and high-density regimes.

After publication of our first papers (Ruffert et al. 1996, 1997a), we changed our code considerably and, in particular, we improved many features which had influence on the results of our simulations. For example, we introduced nested grids to get a higher resolution of the neutron stars and at the same time to use a larger computational volume. In addition, we extended the EoS table to higher temperatures and lower densities. The latter allowed us to reduce the density of the dilute medium that has to be assumed around the neutron stars on the Eulerian grid. Since the heat capacity of cold, degenerate matter is very small, minor numerical noise in the internal energy had induced larger errors in the temperature. We therefore also implemented an entropy equation, because the entropy is numerically less problematic for calculating the temperature. Besides these improvements, we also covered a wider range of scenarios, e.g., added models with opposite directions of the neutron star spins and with different neutron star masses as well as different mass ratios.

All of our later publications referred to data of models which were computed with the improved version of the code. So did the simulations of the black hole accretion in Ruffert & Janka (1999) start from an initial model of the new generation of calculations, and also in the tables of Janka et al. (1999) data of new neutron star merger models were listed. So far, however, we published only very specific aspects of these new models and did not present our results in detail. This is the purpose of the present publication.

In Sect. 2 we will give a technical description of the code changes and improvements, in Sect. 3 a list of computed models, in Sect. 4 we shall present the main results for the new models, and in Sect. 5 we shall discuss the implications and draw conclusions.

$\begin{figure*} \includegraphics[width=14cm,clip]{gridsrr.eps}\raisebox{8cm}{\parbox[t]{3.3cm}{ } } \end{figure*}$

Figure 1: Illustration of four levels of nested grids in two (instead of three) spatial dimensions, each level with 64 cells in every direction, covering a computational volume with side length of 328 $\,$ km. The innermost two grid levels are enlarged and the initial positions of the two neutron stars in the orbital plane are indicated.