5.1 Overview: General relativistic (magneto-)hydrodynamics and microphysical treatments

NS-NS binaries are highly relativistic systems, numerous groups now run codes that evolve both GR metric fields and fluids self-consistently, with some groups also incorporating an ideal magnetohydrodynamic evolution scheme that assumes infinite conductivity. The codes that evolve the GR hydrodynamics or magnetohydrodynamics (GRHD and GRMHD, respectively) equations are many and varied, incorporating different spatial meshes, relativistic formalisms, and numerical techniques, and we will summarize the leading variants here. All full GR codes now make use of the significant insight gained from BH-BH merger calculations, but much work on these systems predates the three 2005 “breakthrough” papers by Pretorius [231Jump To The Next Citation Point], Goddard [22Jump To The Next Citation Point], and the group then at UT Brownsville (now at RIT) [61Jump To The Next Citation Point], with the first successful NS-NS merger calculations announced already in 1999 [287Jump To The Next Citation Point]. A list of the groups that have performed NS-NS merger calculations using full GR is presented below; note that many of these groups have also performed BH-NS simulations, as discussed in the review by Shibata and Taniguchi [284Jump To The Next Citation Point].

Of the full GR codes used to evolve NS-NS binaries, almost all are grid-based and make use of some form of adaptive mesh refinement. The one exception is the SpEC code developed by the SXS collaboration, formed originally by Caltech and Cornell, which has used a hybrid spectral-method field solver with grid-based hydrodynamics. Most make use of the BSSN formalism for evolving Einstein’s equations (see Section 5.2.1 below), while the HAD code uses the alternate Generalized Harmonic Gauge (GHG) approach. This technique is also used by the SXS collaboration and the Princeton group, who have both performed simulations of merging BH-NS binaries (see Section 6.6) but have yet to report any results on NS-NS mergers. Three groups have reported results for NS-NS mergers including MHD (HAD, Whisky, and UIUC), while the KT (Kyoto/Tokyo) group has reported magnetized evolutions of HMNS remnants (see [280] and references therein for a discussion of their work and that of other numerical relativity groups), but have yet to use that code for a NS-NS merger calculation.

While full GR codes were being developed to study NS-NS binaries, a parallel and rather independent track developed to study detailed microphysical effects in binary mergers using approximate relativistic schemes. This includes codes like that developed by the MPG group that accurately track the production of neutrinos and antineutrinos and their annihilation during a merger, as well as post-processing routines that use extensive nuclear chains to track the production of rare high-atomic number r-process elements in merger ejecta [123Jump To The Next Citation Point]. Meanwhile, the Bremen group’s SPH code includes variable-temperature physically motivated equations of state [247Jump To The Next Citation Point] and magnetohydrodynamics [233Jump To The Next Citation Point], and has been used with a multi-group flux-limited diffusion neutrino code to generate expected neutrino signatures from merger calculations [82Jump To The Next Citation Point]. A summary of groups performing NS-NS merger calculations is presented in Table 3.


Table 3: A summary of groups reporting NS-NS merger calculation results. The asterisk for the KT collaboration’s MHD column indicates that they have used an MHD-based code for other projects, but not yet for NS-NS merger simulations. Gravitational formalisms include full GR, assumed to be implemented using the BSSN decomposition except for the HAD collaborations’s GHG approach, the CF approximation, or Newtonian gravity. Microphysical treatments include physically motivated EOS models or quark-matter EOS and neutrino leakage schemes.
Abbrev. Refs. Grav. MHD Microphysics
KT [134Jump To The Next Citation Point, 144Jump To The Next Citation Point, 145Jump To The Next Citation Point, 265Jump To The Next Citation Point, 264Jump To The Next Citation Point, 287Jump To The Next Citation Point, 288Jump To The Next Citation Point] GR * Phys. EOS, ν-leakage
[285Jump To The Next Citation Point, 286Jump To The Next Citation Point, 282Jump To The Next Citation Point, 332Jump To The Next Citation Point]
HAD [7Jump To The Next Citation Point, 6Jump To The Next Citation Point] GR (GHG) Y N
Whisky [17Jump To The Next Citation Point, 18Jump To The Next Citation Point, 14Jump To The Next Citation Point, 15Jump To The Next Citation Point, 116Jump To The Next Citation Point, 117Jump To The Next Citation Point, 240Jump To The Next Citation Point, 241Jump To The Next Citation Point] GR Y N
UIUC [172Jump To The Next Citation Point] GR Y N
Jena [308Jump To The Next Citation Point] GR N N
MPG [34Jump To The Next Citation Point, 35Jump To The Next Citation Point, 33, 32Jump To The Next Citation Point, 123Jump To The Next Citation Point, 209Jump To The Next Citation Point, 208Jump To The Next Citation Point, 296Jump To The Next Citation Point] CF N Quark, Phys. EOS, ν-leakage
Bremen [82Jump To The Next Citation Point, 233Jump To The Next Citation Point, 247Jump To The Next Citation Point] Newt Y Phys. EOS , ν-leakage


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