For the quasi-equilibrium sequences numerically derived so far, we mainly review those in , because it is the only systematic study. In particular, we highlight a curve of the critical mass ratio, which separates BH-NS binaries that encounter an ISCO before reaching mass shedding, and vice versa, as a function of the compactness of the NS. The result is shown in Equation (104) and in Figure 9. Such a critical curve clearly classifies the possible final fate of BH-NS binaries, which depends on the ratio and the compactness of the NS for a given EOS of NS and BH spin.
As seen in Table 1, the parameter space surveyed so far is quite narrow. A systematic study of quasi-equilibrium sequences has been done only for binaries composed of a non-spinning BH and an irrotational NS with polytropic EOS. It is desirable that the remaining parameter space is systematically surveyed near the future. Systematic numerical results for such a study will be quite helpful for predicting the final fate of BH-NS binaries and for checking the results derived in numerical simulations. Specifically, it is necessary to study in detail quasi-equilibrium sequences of binaries composed of a spinning BH and a NS with an EOS other than single polytrope.
Living Rev. Relativity 14, (2011), 6
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