Astron. Astrophys. 319, 122-153 (1997)

1. Introduction

During the first two and a half years of operation, the Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (GRO) has observed 1122 cosmic gamma-ray bursts (Meegan et al. 1995a). The angular distribution of the bursts on the sky is amazingly well compatible with isotropy (e.g., Tegmark et al. 1995). There are recent claims that a tenuous indication of an association with host galaxies is present in the burst sample evaluated by Larson et al. (1996) and that a correlation with Abell clusters has been found on a 95% confidence level in the BATSE 3B catalog (Kolatt & Piran 1996). If confirmed, these would be the first hints of a correlation of gamma-ray bursts with any other astronomical population. Number counts show a deficiency of faint bursts relative to the power law expected for the brightness distribution of a homogeneous spatial distribution of standard candle sources (Fenimore 1996). This paucity of weak bursts could be caused by a truncation of the distance to very far burst sources or might be an effect due to the expansion of the universe or could be associated with an evolution of the spatial density of bursts (Bloom et al. 1996). Both observational facts, isotropy and bend in the brightness distribution, would be naturally explained if the gamma-ray bursters were situated at cosmological distances (e.g., Paczyski 1995, Hartmann et al. 1996, Kolatt & Piran 1996). Nevertheless, the assumption that they might populate an extended Galactic halo cannot be ruled out yet (Lamb 1995, Bulik & Lamb 1995), and Galactic halo models have been constructed (Podsiadlowski et al. 1995) which are able to fulfil the stringent limits set by the isotropy of the detected bursts and their inhomogeneous spatial distribution.

The distribution of measured gamma-ray burst durations exhibits a bimodal structure with peaks at about 0.5 s and about 30 s (Meegan et al. 1995a). The bursts can be as short as  ms but can also last for several 100 s with variabilities and fluctuations on a millisecond time scale (Fishman et al. 1994). The extremely short sub-ms rise times of the gamma-ray luminosities suggest that the energy sources for the bursts must be connected with very compact astrophysical objects which have a typical size of the order of 100 km. This favors neutron stars or black holes as most likely candidates for the enigmatic origin of the cosmic gamma-ray bursts.

Despite of more than 25 years of gamma-ray burst observations, there is neither a convincing identification of counterparts in any other energy range of the electromagnetic spectrum (Greiner 1995a, 1995b; Vrba 1996), nor has a generally accepted, satisfactory theoretical model been developed yet (Nemiroff 1994a, Hartmann & Woosley 1995, Woosley 1996). About 120 gamma-ray burst models have been published in the refereed literature until 1992 (Nemiroff 1994a), until 1994 there were 135 (Nemiroff 1994b), and maybe another one or two dozens have been added since.

Cosmological explanations have become increasingly popular in the more recent publications, a fair fraction of which suggests collisions of two neutron stars or mergers of binaries consisting of either two neutron stars (NS-NS) or a black hole and a neutron star (BH-NS) as possible sources of the bursts (e.g., Paczyski 1986; Goodman 1986; Eichler et al. 1989; Piran 1990; Paczyski 1991; Narayan et al. 1991, 1992; Piran et al. 1992; Mészáros & Rees 1992a, b, 1993; Woosley 1993a; Mochkovitch et al. 1993, 1995a; Hernanz et al. 1994, Katz & Canel 1995a). One of the reasons for the attractivity of these scenarios is the desired compactness of the objects, another reason is the knowledge that these events should happen and should release large amounts of energy (Dermer & Weiler 1995). The frequency of NS-NS and BH-NS mergers was estimated to be between and per year per galaxy (Narayan et al. 1991, Phinney 1991, Tutukov et al. 1992, Tutukov & Yungelson 1993, Lipunov et al. 1995) and is therefore sufficient to explain the observed burst rate which requires an event rate of about  yr^-1 per galaxy (Narayan et al. 1992). These rates per galaxy are so low that burst repetition in the same region of the sky is practically excluded which is in agreement with the observations (Lamb 1996, Meegan et al. 1995b, Brainerd et al. 1995, Efron & Petrosian 1995). If the merger rate is near the high end of the estimated range, some beaming of the gamma-ray emission might be involved, or the majority of the bursts has to be very dim and escapes detection. Beaming would also lower the energy that must be converted into gamma rays at the source in order to cause the observed fluences.

Since the detected gamma-ray bursts appear to be isotropically distributed and do not visibly trace the large-scale structure of luminous matter in the universe, in particular, are not concentrated towards the supergalactic plane like nearby galaxies, constraints on the distance scale to cosmological bursts can be placed. From the BATSE 3B catalog Quashnock (1996) infers that the comoving distance to the "edge" of the burst distribution is greater than 630  Mpc and the nearest bursts are farther than 40  Mpc (at the 95% confidence level), the median distance to the nearest burst being 170  Mpc (h is the Hubble constant in units of 100 km/s/Mpc). From the absence of anisotropies in supergalactic coordinates, Hartmann et al. (1996) conclude that the minimum sampling distance is 200  Mpc, and Kolatt & Piran (1996) find for their accurate position sub-sample members locations within 600  Mpc. In case of isotropic emission, standard candle non-evolving burst sources at these cosmological distances must release -ray energies of the order of  erg (Woods & Loeb 1994, Quashnock 1996).

This energy is about 0.1-0.2% of the rest-mass energy of one solar mass or roughly 1% of the gravitational binding energy set free when two 1.5  neutron stars merge. A large part of the energy released during the merging, i.e., up to more than 10% of , is carried away by gravitational waves, the exact value depending on the nuclear equation of state and thus on the compactness of the neutron stars and of the merged object (see Ruffert et al. 1996 and references therein). A similar amount of energy could be radiated away in neutrinos which are abundantly produced when the matter of the coalescing and merging stars is heated up to very high temperatures by tidal forces, friction, and viscous dissipation of kinetic energy in shocks (Eichler et al. 1989, Narayan et al. 1992, Harding 1994). The duration of the neutrino emission, the neutrino luminosity, and the total energy radiated in neutrinos will be determined by the structure and dynamical evolution of the merger, by the thermodynamical conditions in the merging stars, and by the lifetime of the merged object before it collapses into a black hole or before the surrounding material is swallowed by the black hole. Gravitational waves as well as neutrinos from these very distant sources cannot be measured with current experiments, but detectors are planned or built for gravitational waves (LIGO, VIRGO, GEO600; see, e.g., Thorne 1992) and are envisioned for neutrinos (a kilometer-scale neutrino telescope with 1 km³ of instrumented volume; see Weiler et al. 1994, Halzen & Jaczko 1996, Halzen 1996), which might be lucky to catch the death throes of massive binaries in the not too distant future.

Due to the very high opacity of neutron star matter, high energy photons cannot be emitted by the merging object directly, unless the very outer layers are heated to sufficiently high temperatures. Even if they were radiating with luminosities substantially above the Eddington limit (Duncan et al. 1986), NS-NS or NS-BH mergers at cosmological distances would still be far too faint to be visible from Earth. However, if only a tiny fraction (less than 1%) of the potentially emitted neutrinos and antineutrinos annihilate in the vicinity of the merger (Goodman et al. 1987, Cooperstein et al. 1987) and create a fireball of electron-positron pairs and photons (Cavallo & Rees 1978), an intense outburst of gamma-radiation can be produced with an overall power output exceeding the Eddington luminosity by up to 15 orders of magnitude and energetic enough to account for a cosmological gamma-ray burst (Eichler et al. 1989).

Relativistic expansion of the pair-photon plasma and the final escape of high energy gamma-radiation with the observed non-thermal spectrum (e.g., Band 1993) from an optically thin fireball can only occur if the baryon load of the radiation-pressure ejected shells is sufficiently small, i.e., the contamination with baryons must be below a certain limit (Goodman 1986, Paczyski 1986). If the admixture of baryons is too large, highly relativistic outflow velocities will be impeded through conversion of radiation energy to kinetic energy and the flow will remain optically thick, leading to a degradation of the photons to the UV range (Paczyski 1990, Shemi & Piran 1990). In order to suppress pair production and to make the fireball optically thin to its own photons, the Lorentz factor of the emitting region must obey (Fenimore et al. 1993, Mészáros et al. 1993). The bulk Lorentz factor is related with the ratio of total energy to (baryon) rest mass energy: where is the fraction of the total energy in the fireball that ends up as observed energy in -rays, . Therefore a lower limit for places an upper bound on the amount of baryonic mass M released in the explosive event or being present as ambient gas near the burst source, . Based on the empirical data from the first BATSE catalog (169 bursts), Woods & Loeb (1994) deduce a mean minimum Lorentz factor of about 500, corresponding to an average maximum baryon load of for gamma-ray burst events at cosmological distances. Recent introductory reviews and summaries of the properties of fireballs in the context of cosmological models of gamma-ray bursts were given by Dermer & Weiler (1995), Mészáros (1995), and Piran (1995, 1996).

The limits for the baryon load in the fireball set by observational requirements are very stringent and the baryonic pollution of the pair-photon plasma is a major concern for gamma-ray burst models based on mergers of massive binary stars. In order to obtain -annihilation in a baryon-poor region around the merger, anisotropies of the merger geometry are considered to be essential (Narayan et al. 1992; Mészáros & Rees 1992a, b; Woosley 1993a; Mochkovitch 1993, 1995a; Hernanz 1994). The hope is that centrifugal forces can keep a region near the rotation axis of the merging NS-NS or NS-BH system relatively baryon free and that the neutrino-driven mass loss from an accretion disk or torus formed after the merging of the binary will leave a "clean" funnel along the axis of symmetry where -annihilation can create collimated jets expanding relativistically in both axis directions. Also, general relativistic bending of the and trajectories and -annihilation inside the innermost stable orbit for massive particles around the accreting black hole have been suggested to be potentially helpful. Secondary processes could lead to the reconversion of baryonic kinetic energy, e.g. by external shock interactions of the expanding fireball in the ambient interstellar medium or pre-ejected gas (Rees & Mészáros 1992; Mészáros & Rees 1992a, 1993; Sari & Piran 1995) or by internal shock interactions of shells having different speeds within the expanding fireball (Narayan et al. 1992, Paczyski & Xu 1994, Rees & Mészáros 1994, Mochkovitch et al. 1995b). Even more complex physics like the upscattering of interstellar photons of a local thermal radiation field by collisions with electrons in the ultrarelativistic wind (Shemi 1994) or highly amplified magnetic fields (Mészáros & Rees 1992a, Usov 1992, Smolsky & Usov 1996) might be important in determining the temporal and spectral structure of the observable gamma-ray burst. In fact, such secondary processes may be crucial to produce the detected very high energy photons with energies of up to more than 1 GeV (Hurley et al. 1994, Teegarden 1995).

In this work we shall not deal with the possibly very complex and complicated processes that are involved in the formation of the finally observable gamma-ray signature. Instead, our interest will be concentrated on the hydrodynamical modelling of the last stages of the coalescence of binary neutron stars employing an elaborate equation of state for neutron star matter with the aim to compute the neutrino emission from the merger. The results of our models will allow us to calculate the efficiency of -annihilation and the energy deposition in the vicinity of the merging stars. After dozens of papers that suggest and refer to the annihilation of pairs from merging compact binaries as the energy source of cosmological gamma-ray bursts, we shall try to put this hypothesis to a quantitative test. We shall investigate the questions whether the neutrino emission from the tidally heated neutron stars just prior to merging (Mészáros & Rees 1992b), during the dynamical phase of the merging or collision (Narayan et al. 1992, Mészáros & Rees 1992b, Dermer & Weiler 1995, Katz & Canel 1995a) or after the merging when a hot accretion disk or torus has possibly formed around a central black hole (Woosley 1993a, Mochkovitch et al. 1993), is sufficiently luminous and lasting to yield the energy required for gamma-ray bursts at cosmological distances. Also, our simulations will provide information about how much mass might remain in an accretion disk or torus and about the thermodynamcial conditions in this disk matter. These aspects might have interesting implications for the possible contributions of NS-NS and NS-BH mergers to the nucleosynthesis of heavy elements.

The paper is organized as follows. In Sect.  2 the computational method and initial conditions for our simulations are described and the hydrodynamical evolution of the merger is shortly summarized from the results given in detail by Ruffert et al. 1996 (Paper I). In Sect.  3 the results for the neutrino emission and thermodynamical evolution of the merger will be presented. Section  4 deals with the neutrino-antineutrino annihilation and contains information about the numerical evaluation (Sect.  4.1), about the numerical results (Sect.  4.2), and about an analytical model which was developed to estimate the neutrino emission and annihilation for an accretion torus around a black hole (Sect.  4.3). In Sect.  5 the results will be discussed concerning their implications for heavy element nucleosynthesis and for gamma-ray bursts, and Sect.  6 contains a summary and conclusions.

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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