6 Dynamical Calculations

NS-NS merger simulations address a broad set of questions, which can be roughly summarized as follows (note the same questions apply to BH-NS mergers as well):

  1. What is the final fate of the system, assuming a given set of initial parameters? Do we get a prompt collapse to a BH or the formation of a HMNS supported against collapse by differential rotation? Other outcomes are disfavored, at least for pre-merger NSs with masses M ≳ 1.4M NS ⊙ since the supramassive limit is at most 20% larger than that of a non-rotating NS [70Jump To The Next Citation Point, 71], and even for the stiffest EOS these values are typically less than 2.8M ⊙.
  2. What is the GW signal from the merger, and how does it inform us about the initial pre-merger parameters of the system?
  3. What fraction of the system mass is left in a disk around the central BH or HMNS? While deriving exact EM emission profiles from a hydrodynamical configuration remains a challenge for the future, minimum conditions that would allow for the energy release observed in SGRBs have been established based on scaling arguments.
  4. What is the neutrino and EM emission from the system, in both the time and energy domains? Obviously, the answer to this question and those that follow depend critically on the answers above.
  5. What role do B-fields play in the GW, EM, and neutrino emission, and how does that tie in with other models suspected of having the same disk/jet geometry and gamma-ray emission like active galactic nuclei, pre-main sequence stars, etc.?
  6. Do mergers produce a cosmologically significant quantity of r-process elements, or do those likely get produced by other astrophysical events instead?

The influence of the gravitational formalism used in a numerical simulation on the answer one finds for the questions above differs item by item. Determining the final fate of a merging system is highly dependent on the gravitational formalism; NS-NS merger remnants only undergo collapse in quasi-relativistic and fully GR schemes. Moreover, orbital dynamics at separations comparable to the ISCO and even somewhat larger depend strongly on the gravitational scheme. In particular, mass loss rates into a disk are often suppressed by orders of magnitude in GR calculations when compared to CF simulations, and even more so in comparison to PN and Newtonian calculations. EM emission profiles from a disk are difficult to calculate accurately without the use of full GR for this reason. On the other hand, while GR is required to calculate the exact GW signal from a merger, even early Newtonian simulations predicted many of the qualitative GW emission features correctly, and PN and CF schemes yielded results with some degree of quantitative accuracy about the full wavetrain. B-fields have only begun to be explored, but it already seems clear that they will affect the hydrodynamical evolution primarily after the merger in cases where differential rotation in a HMNS or disk winds up magnetic field strengths up to energy equipartition levels, vastly stronger than those found in pre-merger NSs. For such configurations, non-relativistic calculations can often reproduce the basic physical scenario but full GR is required to properly understand the underlying dynamics. Finally, the production of r-process elements, which depends sensitively on the thermodynamic evolution of the merger, seems to generally disfavor binary mergers as a significant source of the observed stellar abundances since the temperature and thus the electron fraction of the fluid remains too small [252Jump To The Next Citation Point], regardless of the nature of the gravitational treatment used in the calculations. This picture may need to be revised if significant mass loss occurs from the hot accretion disk that forms around the central post-merger object, possibly due to energy release from the r-process itself, but numerical calculations do not currently predict sufficient mass loss to match observations [297]. We will address each of these topics in greater detail in the sections below.

Since the first NS-NS merger calculations, there have been two main directions for improvements: more accurate relativistic gravitation, resulting in the current codes that operate using a self-consistent fully GR approach, and the addition of microphysical effects, which now include treatments of magnetic fields and neutrino/EM radiation. Noting that several of the following developments overlapped in time, e.g., the first full GR simulations by Shibata and Uryū [287Jump To The Next Citation Point] are coincident with the first PN SPH calculations, and predate the first CF SPH calculations, we consider in turn the original Newtonian calculations, those performed using approximate relativistic schemes, the calculations performed using full GR, and finally those that have included more advanced microphysical treatments.

 6.1 Quasi-equilibrium and semi-analytic methods vs fully dynamical results
 6.2 Early dynamical calculations
 6.3 Approximate relativistic schemes
 6.4 Full GR calculations
  6.4.1 HMNS and BH remnant properties
  6.4.2 Magnetized NS-NS mergers
  6.4.3 GW emission
  6.4.4 Binary eccentricity
 6.5 Simulations including microphysics
 6.6 Comparison to BH-NS merger results

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