Many of the results later confirmed using relativistic QE sequences were originally derived in Newtonian
and PN calculations, particularly as explicit extensions of Chandrasekhar’s body of work (see [65]).
Chandrasekhar’s studies of incompressible fluids were first extended to compressible binaries by Lai, Rasio,
and Shapiro [156, 155, 158
, 157
, 159
], who used an energy variational method with an ellipsoidal
treatment for polytropic NSs. They established, among other results, the magnitude of the rapid inspiral
velocity near the dynamical stability limit [156], the existence of a critical polytropic index (
)
separating binary sequences undergoing the two different terminal instabilities [155
], the role
played by the NS spin and viscosity and magnitude of finite-size effects in relation to 1PN
terms [158
, 157
], and the development of tidal lag angles as the binary approaches merger [159
]. They also
determined that for most reasonable EOS models and non-extreme mass ratios, as would pertain to
NS-NS mergers, an energy minimum is inevitably reached before the onset of mass transfer
through Roche lobe overflow. The general results found in those works were later confirmed
by [201
], who used a SCF technique [131, 132], finding similar locations for instability points as
a function of the adiabatic index of polytropes, but a small positive offset in the radius at
which instability occurred. Similar results were also found by [311, 312
], but with a slight
modification in the total system energy and decrease in the orbital frequency at the onset of
instability.
The first PN ellipsoidal treatments were developed by Shibata and collaborators using self-consistent
fields [270, 269, 279
, 281
, 299] and by Lombardi, Rasio, and Shapiro [177
]. Both groups found that the
nonlinear gravitational effects imply a decrease in the orbital separation (increase in the orbital frequency)
at the instability point for more compact NS. This result reflects a fairly universal principle in relativistic
binary simulations: as gravitational formalisms incorporate more relativistic effects, moving from Newtonian
gravity to 1PN and on to CF approximations and finally full GR, the strength of the gravitational
interaction inevitably becomes stronger. The effects seen in fully dynamical calculations will be discussed in
Section 6, below.
The first fully relativistic CTS QE data for synchronized NS-NS binaries were constructed by
Baumgarte et al. [26, 25], using a grid-based elliptic solver. Their results demonstrated that the maximum
allowed mass of NSs in close binaries was larger than that of isolated NSs with the same (polytropic) EOS,
clearly disfavoring the “star-crushing” scenario that had been suggested by [327
, 187
] using a similar
CTS formalism (but see also the error in these latter works addressed in [104
], discussed in
Section 6.3 below). Baumgarte et al. also identified how varying the NS radius affects the ISCO
frequency, and thus might be constrained by GW observations. Using a multigrid method, Miller et
al. [192
] showed that while conformal flatness remained valid until relatively near the ISCO, the
assumption of syncronized rotation broke down much earlier. Usui et al. [319
] used the Green’s
function approach with a slightly different formalism to compute relativistic sequences and
determined that the CTS conditions were valid up until extremely relativistic binaries were
considered.
The first relativistic models of physically realistic irrotational NS-NS binaries were constructed by the
Meudon group [51] using the Lorene multi-domain pseudo-spectral method code. Since then, the Meudon
group and collaborators have constructed a wide array of NS-NS initial data, including polytropic NS
models [125, 303
, 304
], as well as physically motivated NS EOS models [36
] or quark matter
condensates [170
]. Irrotational models have also been constructed by Uryū and collaborators [313
, 317
]
for use in dynamical calculations, and nuclear/quark matter configurations have been generated by Oechslin
and collaborators [212
, 209
]. A large compilation of QE CTS sequences constructed using physically
motivated EOS models including FPS (Friedman–Pandharipande) [222], SLy (Skyrme Lyon) [83
], and
APR [3
] models, along with piecewise polytropes designed to model more general potential cases
(see [237
]), was published in [305
].
The most extensive set of results calculated using the waveless/near-zone helical symmetry condition
appear in [316], with equal-mass NS-NS binary models constructed for the FPS, Sly, and APR EOS in
addition to
polytropes. Results spanning all of these QE techniques are summarized in
Table 2.
Author | Ref. | Grav. | Method | EOS | Compactness | Mass ratio | Spin |
Lai | [155] | Newt. | Ellips. | ![]() |
N/A | 1.0 | Syn. |
Lai | [158] | Newt. | Ellips. | ![]() |
N/A | 1.0 | Syn./Irr. |
Lai | [157] | Newt. | Ellips. | ![]() |
N/A | 0.2 – 1.0 | Syn./Irr. |
New | [201![]() |
Newt. | SCF | ![]() |
N/A | 1.0 | Syn. |
Uryū | [312] | Newt. | SCF | ![]() |
N/A | 1.0 | Irr. |
Shibata | [270] | PN | Grid | ![]() |
![]() |
1.0 | Syn. |
Shibata | [279] | PN | Grid | ![]() |
![]() |
1.0 | Syn. |
Shibata | [281] | PN | Ellips. | ![]() |
![]() |
1.0 | Syn. |
Lombardi | [177] | PN | Ellips. | ![]() |
![]() |
1.0 | Syn./Irr. |
Baumgarte | [25] | CTS | Multigrid | ![]() |
![]() |
1.0 | Syn. |
Usui | [319] | Mod. CTS | Green’s | ![]() |
![]() |
1.0 | Syn. |
Uryū | [313![]() |
CTS | Green’s | ![]() |
![]() |
1.0 | Syn./Irr. |
Uryū | [317] | CTS | Green’s | ![]() |
![]() |
1.0 | Irr. |
Bonazzola | [51] | CTS | Spectral | ![]() |
![]() |
1.0 | Syn/Irr. |
Taniguchi | [303![]() |
CTS | Spectral | ![]() |
![]() |
0.9 – 1.0 | Syn./Irr. |
Taniguchi | [304] | CTS | Spectral | ![]() |
![]() |
0.83 – 1.0 | Syn./Irr. |
Miller | [192![]() |
CTS | Multigrid | ![]() |
![]() |
1.0 | Syn. |
Bejger | [36] | CTS | Spectral | Phys. | ![]() |
1.0 | Irr. |
Limousin | [170] | CTS | Spectral | Quark | ![]() |
1.0 | Syn./Irr. |
Oechslin | [212![]() |
CTS | SPH | Quark | ![]() |
1.0 | Irr. |
Taniguchi | [305] | CTS | Spectral | Physical | ![]() |
0.7 – 1.0 | Irr. |
Uryū | [316] | WL/NHS | Multipatch | ![]() |
![]() |
1.0 | Irr. |
http://www.livingreviews.org/lrr-2012-8 |
Living Rev. Relativity 15, (2012), 8
![]() This work is licensed under a Creative Commons License. E-mail us: |