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Figure 1:
Cartoon showing standard formation channels for close NS-NS binaries through binary
stellar evolution. Image reproduced from [178]. |
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Figure 2:
Cartoon picture of a compact binary coalescence, drawn for a BH-BH merger but applicable
to NS-NS mergers as well (although NSs are generally assumed to be non-spinning). Image adapted
from Kip Thorne. |
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Figure 3:
Isodensity contours and velocity profile in the equatorial plane for a merger of two
equal-mass NSs with assumed to follow the APR model [3] for the NS EOS. The
hypermassive merger remnant survives until the end of the numerical simulation. Image reproduced
by permission from Figure 4 of [144], copyright by APS. |
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Figure 4:
Isodensity contours and velocity profile in the equatorial plane for a merger of two
equal-mass NSs with assumed to follow the APR model [3] for the NS EOS. With
a higher mass than the remnant shown in Figure 3, the remnant depicted here collapses promptly
to form a BH, its horizon shown by the dashed blue circle, absorbing all but 0.004% of the total rest
mass from the original system. Image reproduced by permission from Figure 5 of [144], copyright
by APS. |
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Figure 5:
Isodensity contours and velocity profile in the equatorial plane for a merger of two
unequal-mass NSs with and , with both assumed to follow the APR
model [3] for the NS EOS. In unequal-mass mergers, the lower mass NS is tidally disrupted during
the merger, forming a disk-like structure around the heavier NS. In this case, the total mass of
the remnant is sufficiently high for prompt collapse to a BH, but 0.85% of the total mass remains
outside the BH horizon at the end of the simulation, which is substantially larger than for equal-mass
mergers with prompt collapse (see Figure 4). Image reproduced by permission from Figure 6 of [144],
copyright by APS. |
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Figure 6:
Dimensionless binding energy vs. dimensionless orbital frequency , where
is the total ADM (Arnowitt–Deser–Misner) mass of the two components at infinite separation,
for two QE NS-NS sequences that assume a piecewise polytropic NS EOS. The equal-mass case
assumes for both NSs, while the unequal-mass case assumes
and . The thick curves are the numerical results, while the thin curves show the
results from the 3PN approximation. The lack of any minimum suggests that instability for these
configurations occurs at the onset of mass shedding, and not through a secular orbital instability.
Image reproduced by permission from Figure 16 of [305], copyright by AAS. |
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Figure 7:
Mass-shedding indicator vs. orbital frequency ,
where is the fluid enthalpy and the derivative is measured at the NS surface in the equatorial
plane toward the companion and toward the pole in the direction of the angular momentum vector,
for a series of QE NS-NS sequences assuming equal-mass components. Here, corresponds
to a spherical NS, while indicates the onset of mass shedding. More massive NSs are more
compact, and thus able to reach smaller separations and higher angular frequencies before mass
shedding gets underway. Image reproduced by permission from Figure 19 of [305], copyright by AAS. |
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Figure 8:
Isodensity contours for QE models of NS-NS binaries. In each case, the two NSs have
masses (left) and (right), and the center-of-mass separation is as
small as the QE numerical methods allow while able to find a convergent result. The models assume
different EOS, resulting in different central concentrations and tidal deformations. Image reproduced
by permission from Figures 9 – 12 of [305], copyright by AAS. |
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Figure 9:
Approximate energy spectrum derived from QE sequences of equal-mass
NS-NS binaries with isolated ADM masses and a EOS, but varying
compactnesses (denoted here), originally described in [303]. The diagonal lines show the
energy spectrum corresponding to a point-mass binary, as well as values with 90%, 75%, and 50%
of the power at a given frequency. Asterisks indicate the onset of mass-shedding, beyond which QE
results are no longer valid. Image reproduced by permission from Figure 2 of [98], copyright by APS. |
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Figure 10:
Type of final remnant corresponding to different EOS models. The vertical axis shows
the total mass of two NSs. The horizontal axis shows the EOSs together with the corresponding
NS radii for . Image reproduced by permission from Figure 3 of [134], copyright by
APS. |
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Figure 11:
Evolution of the total rest mass of the remnant disk (outside the BH horizon)
normalized to the initial value for NS-NS mergers using a polytropic EOS with differing
mass ratios and total masses. The order of magnitude of the mass fraction in the disk can be read
off the logarithmic mass scale on the vertical axis. The curves referring to different models have
been shifted in time to coincide at . Image reproduced by permisison from Figure 5 of [240],
copyright by IOP. |
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Figure 12:
Fluid density isocontours and magnetic field distribution (in a plane slightly above
the equator) immediately after first contact for a magnetized merger simulation. The cavities at
both trailing edges are attributed to magnetic pressure inducing buoyancy. Image reproduced by
permission from Figure 1 of [6], copyright by APS. |
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Figure 13:
Evolution of the density in a NS-NS merger, with magnetic field lines superposed. The first
panel shows the binary shortly after contact, while the second shows the short-lived HMNS remnant
shortly before it collapses. In the latter two panels, a BH has already formed, and the disk around it
winds up the magnetic field to a poloidal geometry of extremely large strength, 1015 G, with an
half-opening angle of 30°, consistent with theoretical SGRB models. Image reproduced by permission
from Figure 1 of [241], copyright by AAS. |
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Figure 14:
Dimensionless GW strain , where is the distance to the source and
the total mass of the binary, versus time for four different NS-NS merger calculations. The different
merger types become apparent in the post-merger GW signal, clearly indicating how BH formation
rapidly drives the GW signal down to negligible amplitudes. Image reproduced by permission from
Figures 5 and 6 of [134], copyright by APS. |
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Figure 15:
Effective strain at a distance of 100 Mpc shown as a function of the GW frequency (solid
red curve) for the same four merger calculations depicted in Figure 14. Post-merger quasi-periodic
oscillations are seen as broad peaks in the GW spectrum at frequencies = 2 – 4 kHz.
The blue curve shows the Taylor T4 result, which represents a particular method of deducing
the signal from a 3PN evolution. The thick green dashed curve and orange dot-dashed curves
depict the sensitivities of the second-generation Advanced LIGO and LCGT (Large Scale Cryogenic
Gravitational Wave Telescope) detectors, respectively, while the maroon dashed curve shows the
sensitivity of a hypothetical third-generation Einstein Telescope. Image reproduced by permission
from Figures 5 and 6 of [134], copyright by APS. |
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Figure 16:
Comparison between numerical waveforms, shown as a solid black line, and semi-analytic
NNLO EOB waveforms, shown as a red dashed line (top panel). The top panels show the real parts
of the EOB and numerical relativity waveforms, and the middle panels display the corresponding
phase differences between waveforms generated with the two methods. There is excellent agreement
between with the numerical waveform almost up to the time of the merger as shown by the match
of the orbital frequencies (bottom panel). Image reproduced by permission from Figure 14 of [15],
copyright by APS. |
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Figure 17:
Evolution of a binary strange star merger performed using a CF SPH evolution. The
“spiral arms” representing mass loss through the outer Lagrange points of the system are substantially
narrower than those typically seen in CF calculations of NS-NS mergers with typical nuclear EOS
models. Image reproduced by permission from Figure 4 of [35], copyright by APS. |
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Figure 18:
Summary of potential outcomes from NS-NS mergers. Here, is the
threshold mass (given the EOS) for collapse of a HMNS to a BH, and is the binary
mass ratio. ‘Small’, ‘massive’, and ‘heavy’ disks imply total disk masses ,
, and , respectively. ‘B-field’ and ‘J-transport’
indicate potential mechanisms for the HMNS to eventually lose its differential rotation support and
collapse: magnetic damping and angular momentum transport outward into the disk. Spheroids are
likely formed only for the APR and other stiff EOS models that can support remnants with relatively
low rotational kinetic energies against collapse. Image reproduced by permission from [282], copyright
by APS. |