Returning to the questions posed in Section 6, we can now provide the current state of the field’s best answers, though this remains a very active area of research and new results will certainly continue to modify this picture.

- With regard to the final fate of the merger remnant, calculations using full GR are required, but the details of the microphysics do not seem to play a very strong role. It is now possible to determine whether or not a pair of NSs with given parameters and specified EOS will form a BH or HMNS promptly after merger, and to estimate whether a HMNS will collapse on a dynamical timescale or one of the longer dissipative timescales (see, e.g., [134]). For NS-NS binaries with sufficiently small masses, it is also possible to determine quickly whether the remnant mass is below the supramassive limit for which a NS is stabilized against collapse by uniform rotation alone, and thus would be unlikely to collapse, barring a significant amount of fallback accretion, unless pulsar emission or magnetic field coupling to the outer disk reduced the rotation rate below the critical value. This scenario likely applies only for mergers where the total system mass is relatively small [70], even taking into account the current maximum observed NS mass of [81]. Based on the wide arrays of EOS models already considered, it is entirely possible to infer the likely fate for sets of parameters and/or EOS models that have not yet been simulated, although no one has yet published a “master equation” that summarizes all of the current work into a single global form. While magnetic fields with realistic magnitudes are unlikely to affect the BH versus HMNS question [172, 117], finite-temperature effects might play a nontrivial role should NSs be sufficiently hot prior to merger [265] (and see also [209]). In the end, by the time the second generation of GW detectors make the first observations of mergers, the high-frequency shot-noise cutoff will prove to be a bigger obstacle to determining the fate of the remnant than any numerical uncertainty. A schematic diagram showing the possible final fates for a NS-NS merger along with the potential EM emission (see Figure 21 of [282]) is shown in Figure 18.
- GW emission during merger is also well-understood, though there are a few gaps that need to be filled, with full GR again a vital requirement. While the PN inspiral signal prior to merger is very well understood, finite-size tidal effects introduce complications beyond those seen in BH-BH mergers, yet the longest calculations performed to date [15] encompass fewer orbits prior to merger than the longest BH-BH runs [261]. As noted in [15] and elsewhere, longer calculations will likely appear over time, helping to refine the prediction for the NS-NS merger GW signal as the binary transitions from a PN phase into one that can only be simulated using full GR, and teasing out the NS physics encoded in the GW signal. It seems clear from the published work that the emission during the onset of the merger is well-understood, as is the very rapid decay that occurs once the remnant collapses to a BH, either promptly or following some delay. GW emission from HMNSs has been investigated widely, and there have been correlations established between properties of the initial binary and the late-stage high-frequency emission (see, e.g., [145, 117]), but given that magnetic fields, neutrino cooling, and other microphysical effects seem to be important, a great deal of work remains to be done. Perhaps more importantly, since HMNSs emit radiation at frequencies well beyond the shot-noise limit of even second-generation GW detectors, while the final inspiral occurs near peak sensitivity, it is likely that the first observations of NSs will constrain the nuclear EOS (or perhaps the quark matter EOS [35]) primarily via the detection of small finite-size effects during inspiral. Since QE calculations are computationally inexpensive compared to numerical merger simulations, there should be much more numerical data available about the inspiral stage than other phases of NS-NS mergers, which should help optimize the inferences to be drawn from future observations.
- Determining the mass of the thick disk that forms around a NS-NS merger remnant remains a very difficult challenge, since its density is much lower and harder to resolve using either grid-based or particle-based simulations. The parameterization given by Eq. 34 [240] is generally consistent with the GR calculations of other groups (see, e.g., [134]), and seems to reflect a current consensus. It is also clear that disk masses around HMNSs (up to ) are significantly larger than those forming around prompt collapses, which are limited to about .
- It is likely that several orders of magnitude more mass-energy are present in the remnant disk than is observed in EM radiation from a SGRB. Modeling the emission from the disk (and possibly a HMNS) remains extremely challenging. Neutrino leakage schemes have been applied in both approximate relativistic calculations [252, 246] and full GR [265], and a more complex flux-limited diffusion scheme has been applied to the former as a post-processing step [82], but there are no calculations that follow in detail the neutrinos as they flow outward, annihilate, and produce observable EM emission. At present, nuclear reactions are typically not followed in detail; rather, the electron fraction of the nuclear material, , is evolved, and used to calculate neutrino emission and absorption rates.
- Magnetic fields, on the other hand, are starting to be much better understood. B-fields do seem to grow quite large through winding effects, even during the limited amount of physical time that can currently be modeled numerically [6, 172, 332, 241], with some calculations indicating exponential growth rates. The resulting geometries seem likely to produce the disk/jet structure observed throughout astrophysics when magnetized objects accrete material, which span scales from stellar BHs or pre-main sequence stars all the way up to active galactic nuclei [241].
- While recent numerical simulations have strengthened the case for NS-NS mergers as SGRB progenitors, full GR calculations have not generated much support for the same events yielding significant amounts of r-process elements. Noting the standard caveat that low-density ejecta are difficult to model, and that nuclear reactions are rarely treated self-consistently, there is still tension between CF calculations producing ejecta with the proper temperatures and masses to reproduce the observed cosmic r-process abundances (see, e.g., [123]), and full GR calculations that produce almost no measurable unbound material whatsoever.

While NS-NS merger calculations have seen tremendous progress in the past decade, the future remains extremely exciting. Between the addition of more accurate and realistic physical treatments, the exploration of the full phase space of models, and the linking of numerical relativity to astrophysical observations and GW detection, there remain many unsolved problems that will be attacked over the course of the next decade and beyond.

Living Rev. Relativity 15, (2012), 8
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