The qualitative evolution of NS-NS mergers, or indeed any compact binary merger, has long been understood, and may be divided roughly into inspiral, merger, and ringdown phases, each of which presents a distinct set of challenges for numerical modeling and detection. As a visual aid, we include a cartoon summary in Figure 2, originally intended to describe black hole–black hole (BH-BH) mergers, and attributed to Kip Thorne. Drawn before the advent of the supercomputer simulations it envisions, we note that merger waveforms for all compact binary mergers have proven to be much smoother and simpler than shown here. To adapt it to NS-NS mergers, we note that NSs are generally assumed to be essentially non-spinning, and that the “ringdown” phase may describe either a newly formed BH or a NS that survives against gravitational collapse.

Summarizing the evolution of the system through the three phases:

- After a pair of supernovae yields a relatively tight NS-NS binary, the orbital separation decays over long timescales through GW emission, a phase that takes up virtually all of the lifetime of the binary except the last few milliseconds. During the inspiral phase, binary systems may be accurately described by QE formalisms, up until the point where the gravitational radiation timescale becomes comparable to the dynamical timescale. The evolution in time is well-described by PN expansions, currently including all terms to 3PN [47], though small deviations can arise because of finite-size effects, especially at smaller separations (see Eqs. 1 – 6 for the lowest-order 2.5PN expressions for circular inspirals).
- Once the binary separation becomes no more than a few times the radii of the two NSs, binaries rapidly become unstable. The stars plunge together, following the onset of dynamical instability, and enter the merger phase, requiring full GR simulations to understand the complicated hydrodynamics that ensues. According to all simulations to date, if the NS masses are nearly equal, the merger resembles a slow collision, while if the primary is substantially more massive than the secondary the latter will be tidally disrupted during the plunge and will essentially accrete onto the primary. Since the NSs are most likely irrotational just prior to merging, there is a substantial velocity discontinuity at the surface of contact, leading to rapid production of vortices. Meanwhile, some fraction of the mass may be lost through the outer Lagrange points of the system to form a disk around the central remnant. This phase yields the maximum GW amplitude predicted by numerical simulations, but with a signal much simpler and more quasi-periodic than in the original cartoon version. GW emission during the merger encodes important information about the NS EOS, particularly the GW frequency at which the binary orbit becomes unstable (see Eq. 4) resulting in a characteristic cutoff in GW emission at those frequencies. Meanwhile, the merger itself may generate the thermal energy that eventually powers a SGRB, which occurs when the neutrinos and anti-neutrinos produced by shock-heated material annihilate around the remnant to produce high-energy photons.
- Finally, the system will eventually settle into a new, dynamically stable configuration through
a phase of ringdown, with a particular form for the GW signal that depends on the remnant’s
mass and rotational profile. If the remnant is massive enough, it will be gravitationally unstable
and collapse promptly to form a spinning BH. Otherwise it must fall into one of three classes
depending on its total mass. Should the remnant mass be less than the maximum mass
supported by the nuclear matter EOS for an isolated, non-rotating configuration, it will clearly
remain stable forever. Instead a remnant that is “supramassive”, i.e., with a mass above the
isolated stationary mass limit but below that allowed for a uniformly rotating NS (typically
, with very weak dependence on the EOS; see, e.g., [147, 70, 71], and references
therein) may become unstable. Supramassive remnants are stable against gravitational collapse
unless angular momentum losses, either via pulsar-type emission or magnetic coupling to
the outer disk, can drive the angular velocity below the critical value for stability. If the
remnant has a mass above the supramassive limit, it may fall into the hypermassive regime,
where it is supported against gravitational collapse by rapid differential rotation. Hypermassive
NS (HMNS) remnants can have significantly larger masses, depending on the EOS (see,
e.g., [31, 275, 86, 293, 114]), and will survive for timescales much longer than the dynamical
time, undergoing a wide variety of oscillation modes. They can emit GWs should a triaxial
configuration yield a significant quadrupole moment, and potentially eject mass into a disk
around the remnant. Eventually, some combination of radiation reaction and magnetic and
viscous dissipation will dampen the differential rotation and lead the HMNS to collapse to
a spinning BH, again with the possibility that it may be surrounded by a massive disk that
could eventually accrete. The energy release during HMNS collapse provides the possibility for
a “delayed” SGRB, in which the peak GW emission occurs during the initial merger event, but
the gamma-ray emission, powered by the collapse of the HMNS to a BH, occurs significantly
later.
Most calculations indicate that a geometrically thick, lower-density, gravitationally bound disk of material will surround whatever remnant is formed. Such disks, which are geometrically thick, are widely referred to as “tori” throughout the literature, though there is no clear distinction between the two terms, and we will use “disk” throughout this paper to describe generically the bound material outside a central merger remnant. Such disks are expected to heat up significantly, and much of the material will eventually accrete onto the central remnant, possibly yielding observable EM emission. Given the low densities and relatively axisymmetric configuration expected, disks are not significant GW emitters. There may be gravitationally unbound outflow from mergers as well, though dynamical simulations neither confirm nor deny this possibility yet. Such outflows, which can be the sites of exotic nuclear reactions, are frequently discussed in the context of r-process element formation, but their inherently low densities make them difficult phenomena to model numerically with high accuracy.

Living Rev. Relativity 15, (2012), 8
http://www.livingreviews.org/lrr-2012-8 |
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