10.2. NS²Ms: Binary Neutron Star Mergers

Binary neutron star mergers (NS²Ms) [35] or, with a small variant: neutron star-black hole mergers [271] are probably the best candidates for GRB sources. These mergers take place because of the decay of the binary orbits due to gravitational radiation emission. A NS²M results, most likely, in a rotating black hole [276]. The process releases 5 × 10⁵³ ergs [277]. Most of this energy escapes as neutrinos and gravitational radiation, but a small fraction of this energy suffices to power a GRB. The discovery of the famous binary pulsar PSR 1913+16 [48] demonstrated that this decay is taking place [275]. The discovery of other binary pulsars, and in particular of PSR 1534+12 [278], has shown that PSR 1913+16 is not unique and that such systems are common. These observations suggest that NS²Ms take place at a rate of 10^-6 events per year per galaxy [50, 51, 52]. This rate is comparable to the simple estimate of the GRB event rate (assuming no beaming and no cosmic evolution of the rate) [56, 272, 183].

It has been suggested [279, 280] that most neutron star binaries are born with very close orbits and hence with very short lifetimes (see however, [281, 282]). If this idea is correct, then the merger rate will be much higher. This will destroy, of course, the nice agreement between the rates of GRBs and NS²Ms. Consistency can be restored if we invoke beaming, which might even be advantageous as far as the energy budget is concerned. Unfortunately, the short lifetime of those systems, which is the essence of this idea means that at any given moment of time there are only about a hundred such systems in the Galaxy (compared to about 10⁵ wider neutron star binaries).This makes it very hard to confirm or rule out this speculation. We should be extremely lucky to detect such a system.

It is not clear yet how NS²Ms form. The question is how does the system survive the second supernova event? The binary system will be disrupted it this explosion ejects more than half of its total mass. There are two competing scenarios for the formation of NS²Ms. In one scenario the first neutron star that forms sinks into the envelope of its giant companion and its motion within this envelope lead to a strong wind that carries away most of the secondary's mass. When the secondary reaches core collapse it has only a small envelope and the total mass ejected is rather small. In a second scenario the second supernova explosion is asymmetric. The asymmetric explosion gives a velocity of a few hundred km/sec to the newborn neutron star. In a fraction of the cases this velocity is in the right direction to keep the binary together. Such a binary system will have a comparable center of mass velocity [28, 283, 284, 285]. This second scenario has several advantages. First it explains both the existence of binary neutron stars and the existence of high velocity pulsars [283, 286]. Second, and more relevant to GRBs, with these kick velocities these binaries could escape from their parent galaxy, provided that this galaxy is small enough. Such escaping binaries will travel a distance of ~ 200 kpc (v / 200 km / sec) (T / 10⁹ yr) before they merge. The GRB will occur when the system is at a distance of the order of hundred kpc from the parent galaxy. Clearly there is no "no host" problem in this case [28].

While a NS²M has enough energy available to power a GRB it is not clear how the GRB is produced. A central question is, of course, how does a NS²M generate the relativistic wind required to power a GRB. Most of the binding energy (which is around 5 × 10⁵³ ergs escapes as neutrinos [277]. Eichler et al. [35] suggested that about one thousandth of these neutrinos annihilate and produce pairs that in turn produce gamma-rays via e⁺ e^- . This idea was criticized on several grounds by different authors. Jaroszynksi [288] pointed out that a large fraction of the neutrinos will be swallowed by the black hole that forms. Davies et al. [276] and Ruffert & Janka [289, 290, 291] who simulated neutron star mergers suggested that the central object won't be warm enough to produce a significant neutrino flux because the merger is nearly adiabatic [69]. The neutrinos are also emitted over a diffusion time of several seconds, too long to explain the rapid variations observed in GRB [79], but to short to explain the observed GRB durations. Wilson & Mathews [292, 293] included approximate general relativistic effects in a numerical simulation of a neutron star merger. They found that the neutron stars collapse to a single black hole before they collide with each other. This again will suppress the neutrino emission from the merger. However, the approximation that they have used has been criticized by various authors and it is not clear yet that the results are valid. Others suggested that the neutrino wind will carry too many baryons. However, it seems that the most severe problem with this model stems from the fact that the prompt neutrino burst could produce only a single smooth pulse. This explosive burst is incompatible with the internal shocks scenario.

An alternative source of energy within the NS²M is the accretion power of a disk that forms around the black hole [28, 69, 227]. Various numerical simulations of neutron star mergers [276, 289, 290, 291] find that a ~ 0.1 M forms around the central black hole. Accretion of this disk on the central black hole may take a few dozen seconds [69]. It may produce the wind needed to produce internal shocks that could produce, in turn a GRB.

How can one prove or disprove this, or any other, GRB model? Theoretical studies concerning specific details of the model can, of course, make it more or less appealing. But in view of the fact that the observed radiation emerges from a distant region which is very far from the inner "engine" I doubt if this will ever be sufficient. It seems that the only way to confirm any GRB model will be via detecting in time-coincidence another astronomical phenomenon, whose source could be identified with certainty. Unfortunately while the recent afterglow observations take us closer to this target they do not tell us what are the sources of GRBs. We still have to search for additional signals.

NS²Ms have two accompanying signals, a neutrino signal and a gravitational radiation signal. Both signals are extremely difficult to detect. The neutrino signal could be emitted by some of the other sources that are based on a core collapse. Furthermore, with present technology detection of neutrino signals from a cosmological distance is impossible. On the other hand the gravitational radiation signal has a unique characteristic form. This provides a clear prediction of coincidence that could be proved or falsified sometime in the not too distant future when suitable gravitational radiation detectors will become operational.