1.5 Non-relativistic simulation for the merger

The other important task is to clarify the evolution process in the last inspiral and merger phases. For this purpose, the numerical simulation is the unique approach because (at least) non-linear hydrodynamics including related physics has to be solved. The merger process of BH-NS binaries was first studied in the framework of Newtonian or pseudo-Newtonian gravity by several groups [95Jump To The Next Citation Point, 124Jump To The Next Citation Point, 123Jump To The Next Citation Point, 121Jump To The Next Citation Point, 122Jump To The Next Citation Point, 171Jump To The Next Citation Point, 169Jump To The Next Citation Point, 174Jump To The Next Citation Point]. These works have qualitatively clarified the tidal disruption process, the subsequent formation process of a BH-disk system, properties of the remnant accretion disk, gravitational waveforms emitted during the merger, and a fraction of matter ejected from the system. Earlier work [95Jump To The Next Citation Point, 124, 123, 121, 122, 171Jump To The Next Citation Point] was performed modeling BH by a point mass of Newtonian gravity. Because of the absence of the ISCO around the point mass in Newtonian gravity, the gravity in the vicinity of the BH was even qualitatively different from that in reality. They conclude that the NS might be tidally disrupted even in an orbit very close to the BH (well inside a radius of 2 6GMBH ∕c, which is unrealistic), and consequently, a massive remnant disk with mass larger than 0.1M ⊙ might be formed around the BH, irrespective of the mass ratio and the internal velocity field of the NS. In subsequent work [169Jump To The Next Citation Point, 174Jump To The Next Citation Point], the general-relativistic gravity of the BH was partly mimicked employing the Paczyński–Wiita potential for the point mass [152]. In this work, it was found that massive disk formation with mass larger than 0.1M ⊙ was possible only for a binary system composed of a low-mass BH or of a spinning BH for the case that the BH mass is not low [174Jump To The Next Citation Point]. These properties are qualitatively in agreement with those derived in recent fully general-relativistic simulations, and thus, for qualitatively or semi-qualitatively understanding the nature of the BH-NS merger, the pseudo-Newtonian simulation is shown to be helpful. In recent years, approximately general relativistic simulations were also performed by two groups [64, 65, 164]. The derived qualitative features in the merger of BH-NS binaries agree with those from pseudo-Newtonian studies as well as by the general relativistic studies described in Section 3.

Simulations in [95Jump To The Next Citation Point] were carried out incorporating detailed microphysical processes such as finite-temperature EOS and neutrino emission employing a neutrino leakage scheme. The neutrino luminosity from the BH-disk system formed in their simulations was found to be 1053 – 1054 ergs/s for the first 10 – 20 ms after the formation of the disks. This was the result for the case in which a hot and massive disk (of temperature ≳ 10 MeV and mass 0.2– 0.7M ⊙) is formed. The high neutrino luminosity is encouraging for driving a SGRB via neutrino-antineutrino pair annihilation process. As remarked upon above, the massive disk formation in their model parameters would unlikely if general relativistic effects had been correctly taken into account. The high temperature also does not agree with a latest fully general relativistic result in which the simulation was performed with a similar EOS [57Jump To The Next Citation Point]. However, the results of [95Jump To The Next Citation Point] suggested for the first time that if such a massive disk was indeed formed, the resulting BH-disk system was a promising candidate for the central engine of SGRB. Also, their technique for handling the neutrino emission process becomes a useful guideline for detailed numerical studies in full general relativity (e.g., [183Jump To The Next Citation Point, 185Jump To The Next Citation Point]).

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