6.5 Simulations including microphysics

In parallel to efforts in full GR, there has also been great progress in numerical simulations that include approximate relativistic treatments but a more detailed approach to microphysical issues. The first simulations to use a realistic EOS for NS-NS mergers were performed by Ruffert, Janka, and collaborators [253, 139Jump To The Next Citation Point, 254Jump To The Next Citation Point], who assumed the Lattimer–Swesty EOS for their Newtonian PPM-based Eulerian calculations. They were able to determine a physically meaningful temperature for NS-NS merger remnants of 30 – 50 MeV, an overall neutrino luminosity of roughly 1053 erg/s for tens of milliseconds, and a corresponding annihilation rate of 2 – 5 × 1050 erg/s given the computed annihilation efficiencies of a few parts in a thousand. This resulted in an energy loss of 2 – 4 × 1049 erg over the lifetime of the remnant [139], a value later confirmed in multigrid simulations that replaced the newly formed HMNS by a Newtonian or quasi-relativistic BH surrounded by the bound material making up a disk [251]. The temperatures in the resulting neutron-rich (Ye ≈ 0.05 –0.2) remnant were thought to be encouraging for the production of r-process elements [254], although numerical resolution of the low-density ejecta limited the ability to make quantitatively accurate estimates of its exact chemical distribution. Further calculations, some of which involved unequal-mass binaries, indicated that the temperatures and electron fractions in the ejecta were likely not sufficient to produce solar abundances of r-process elements [252Jump To The Next Citation Point], with electron fractions in particular smaller than those set by hand in the r-process production model that appears in [111, 245]. More recently, it was suggested [123Jump To The Next Citation Point] that the decompression of matter originally located in the inner crust of a NS and ejected during a merger has a nearly solar elemental distribution for heavy r-process elements (A > 140). This indicates that NS-NS mergers may be the source of the observed cosmic r-process elements should there be sufficient mass loss per merger event, − 5 Mej ∼ 3 –5 × 10 M ⊙, although these amounts have yet to be observed in full GR simulations which have often admittedly been performed using cruder microphysical treatments.

In [244], Rosswog and Davies included a detailed neutrino leakage scheme in their calculations and also adopted the Shen EOS for several calculations, finding in a later paper [248] that the gamma-ray energy release is roughly 1048 erg, in line with previous results from other groups, but noting that the values would be significantly higher if temperatures in the remnant were higher, since the neutrino luminosity scales like a very high power of the temperature. These calculations also identified NS-NS mergers as likely SGRB candidates given the favorable geometry [249], and the possibility that the MRI in a HMNS remnant could dramatically boost magnetic fields on the sub-second timescales characterizing SGRBs [250]. Rosswog and Liebendörfer [246Jump To The Next Citation Point] found that electron antineutrinos ¯νe dominate the emission, as had Ruffert and Janka [252Jump To The Next Citation Point], though the exact thermodynamic and nuclear profiles were found to be somewhat sensitive to the properties of the EOS model. More recently, using the VULCAN 2-dimensional multi-group flux-limited-diffusion radiation hydrodynamics code [173] to evaluate slices taken from SPH calculations, Dessart et al. [82Jump To The Next Citation Point] found that neutrino heating of the remnant material will eject roughly 10−4M ⊙ from the system.

Price and Rosswog [233, 247] performed the first MHD simulation of merging NS-NS binaries using an SPH code that included magnetic field effects, finding that the Kelvin–Helmholtz unstable vortices formed at the contact surface between the two NSs could boost magnetic fields rapidly up to ∼ 1017 G. These results were not seen in GRMHD simulations, where gains in the magnetic field strength generated by dynamos were limited by the swamping of the vortex sheet at the surface of contact by rapidly infalling NS material that went on to form the eventual HMNS or BH [117Jump To The Next Citation Point]. Longer-term simulations did note that shearing instabilities were able to support power-law, or perhaps even exponential, growth of the magnetic fields on longer timescales (∼ 10 s of ms), which augurs well for NS-NS mergers as the central engines of SGRBs [241Jump To The Next Citation Point].

An effort to identify potential observational differences between NSs and COs with quark-matter interiors has been led by Oechslin and collaborators. Using an SPH code with CF gravity, Oechslin et al. [210, 212] considered mergers of NSs with quark cores described by the MIT bag model [67, 102, 142], which have significantly smaller maximum masses than traditional NSs. They found the hybrid nuclear-quark EOS yielded higher ISCO frequencies for NSs with masses ≳ 1.5M ⊙ and slightly larger GW oscillation frequencies for any resulting merger remnant compared to purely hadronic EOS. Bauswein et al. [34] followed up this work by investigating whether “strangelets”, or small lumps of strange quark matter, would be ejected in sufficient amounts throughout the interstellar medium to begin the phase transition that would convert traditional hadronic NSs into strange stars. They determined that the total rate of strange matter ejection in NS-NS mergers could be as much as −8 10 M ⊙ per year per galaxy or essentially zero depending on the parameters input into the MIT bag model, with the upper values clearly detectable by orbiting magnetic spectrometers such as the AMS-02 detector that was recently installed on the International Space Station [182, 148]. Further calculations concluded that the mergers of strange stars produce a much more tenuous halo than traditional NS mergers, more rapid formation of a BH, and higher frequency ringdown emission [35Jump To The Next Citation Point], as we show in Figure 17View Image.

View Image

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 [35Jump To The Next Citation Point], copyright by APS.

Oechslin, Janka, and Marek also analyzed a wide range of EOS models using their CF SPH code, finding that matter in spiral arms was typically cold and that the dynamics of the disk formed around a post-merger BH depends on the initial temperature assumed for the pre-merger NS [209Jump To The Next Citation Point]. They also determined that the kHz GW emission peaks produced by HMNSs may help to constrain various parameters of the original NS EOS, especially its high-density behavior [208], with further updates to the prediction provided by Bauswein and Janka [32]. Most recently, Stergioulas et al. [296] studied the effect of nonlinear mode couplings in HMNS oscillations, leading to the prediction of a triplet peak of frequencies being present or low mass (MNS = 1.2– 1.35M ⊙) systems in the kHz range.

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