2.2 Current parameter space surveyed

Only a small parameter space has been surveyed for the study of quasi-equilibrium sequences. We classify the study by seven parameters in Table 1:

(1)
The EOS of the NS
(2)
The spatial background metric &tidle;γij and the extrinsic curvature K

The notation of “CF” means the conformally-flat condition γ&tidle;ij = fij, and that of “M” denotes the maximal slicing K = 0.

The notation of “KS” means the Kerr–Schild metric. In this case, the extrinsic curvature K is also set to that derived from the Kerr–Schild metric.

(3)
The state of the fluid flow in the NS

The notation of “Co” means a corotating NS, and that of “Ir” denotes an irrotational NS.

(4)
The method to handle the BH, i.e., the excision or the puncture

The notation of “Pu” means the puncture approach, and that of “Ex” denotes the excision approach.

(5)
The BH spin a
(6)
The compactness of the NS 𝒞
(7)
The mass ratio Q

Because all the papers published so far employed the Γ = 2 polytrope for the EOS, we do not include the EOS in Table 1.


Table 1: Summary for the study of quasi-equilibrium sequences.
(1) (2) (3) (4) (5) (6) (7)
Taniguchi et al. (2006) [208] KS Ir Ex 0 0.088 5
Taniguchi et al. (2007) [209Jump To The Next Citation Point] CF,M Ir Ex 0 0.088, 0.145 1, 2, 3, 5, 10
Taniguchi et al. (2008) [210Jump To The Next Citation Point] CF,M Ir Ex 0 0.109, 0.120, 0.132, 1 ∼ 9
          0.145, 0.160, 0.178
Grandclément CF,M Ir Ex 0 0.075, 0.100, 0.125, 5
(2006) [82Jump To The Next Citation Point], (2007) [83Jump To The Next Citation Point]         0.150
Shibata & Uryū (2006) [202Jump To The Next Citation Point] CF,M Co Pu 0 0.139 2.47
Shibata & Uryū (2007) [203Jump To The Next Citation Point] CF,M Co Pu 0 0.139, 0.148 2.47, 3.08
Kyutoku et al. (2009) [106Jump To The Next Citation Point] CF,M Ir Pu 0 0.132, 0.145, 0.160 1, 3, 5
  CF,M Ir Ex 0 0.144 1
Foucart et al. (2008) [75Jump To The Next Citation Point] KS Ir Ex 0 0.144 1
  KS Ir Ex –0.5 0.144 1

As found in Table 1, the surveyed parameter space is quite narrow, in particular for the EOS of the NS and the BH spin; complete sequences with a ⁄= 0 have not yet been derived, and moreover, BH-NS binaries in quasi-equilibrium in which the BH spin takes a high value > 0.9 or the BH spin and orbital angular momentum vector misalign have not been studied yet. These are issues left for the future. For the initial data of the merger simulation, a slightly wider parameter space has been employed. We will summarize this in Section 3.1.1.


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