3.2 Qualitative numerical results

Constructing QE sequences for a given set of NS parameters requires sophisticated numerical schemes, but not supercomputer-scale resources, as we discuss in Section 4 below, focusing first on the numerical techniques used to construct QE binary data in GR, and the astrophysical information contained in the GW emission during the inspiral phase. Merger and ringdown, on the other hand, typically require large-scale numerical simulations, including some of the largest calculations performed at major supercomputer centers, as we discuss in detail Section 5 and 6 below.

To illustrate the various physical processes that occur during NS-NS mergers, we show the evolution of three different NS-NS merger simulations in Figures 3View Image, 4View Image, and 5View Image, taken from Figures 4 – 6 of [144Jump To The Next Citation Point]. In Figure 3View Image, we see the merger of two equal-mass NSs, each of mass MNS = 1.4M ⊙, described by the APR (Akmal–Pandharipande–Ravenhall) EOS [3Jump To The Next Citation Point]. In the second panel, clear evidence of “tidal lags” is visible shortly after first contact, leading to a slightly off-center collision pattern. By the third panel, an ellipsoidal HMNS has been formed, surrounded by a disk of material of lower density, which gradually relaxes to form a more equilibrated HMNS by the final panel. In Figure 4View Image, we see a merger of two slightly heavier equal-mass NSs with MNS = 1.5M ⊙. In this case, the deeper gravitational potential limits the amount of mass that goes into the disk, and once a BH is formed (with a horizon indicated by the dashed blue circle in the final panel) it accretes virtually all of the rest mass initially present in the two NSs, with only 0.004% of the total remaining outside the horizon.

View Image

Figure 3: Isodensity contours and velocity profile in the equatorial plane for a merger of two equal-mass NSs with MNS = 1.4M ⊙ assumed to follow the APR model [3Jump To The Next Citation Point] for the NS EOS. The hypermassive merger remnant survives until the end of the numerical simulation. Image reproduced by permission from Figure 4 of [144Jump To The Next Citation Point], copyright by APS.
View Image

Figure 4: Isodensity contours and velocity profile in the equatorial plane for a merger of two equal-mass NSs with MNS = 1.5M ⊙ assumed to follow the APR model [3Jump To The Next Citation Point] for the NS EOS. With a higher mass than the remnant shown in Figure 3View Image, the remnant depicted here collapses promptly to form a BH, its horizon shown by the dashed blue circle, absorbing all but 0.004% of the total rest mass from the original system. Image reproduced by permission from Figure 5 of [144Jump To The Next Citation Point], copyright by APS.

In Figure 5View Image, we see the merger of an unequal-mass binary, with masses M1 = 1.3M ⊙ and M2 = 1.6M ⊙. In this case, the heavier NS partially disrupts the lighter NS prior to merger, leading to the secondary NS being accreted onto the primary. In this case, a much more massive disk is formed and, even after a BH forms in the center of the remnant, a substantial amount of matter, representing 0.85% of the total mass, remains outside the horizon. Later accretion of this material could potentially release the energy required to power a SGRB.

View Image

Figure 5: Isodensity contours and velocity profile in the equatorial plane for a merger of two unequal-mass NSs with M1 = 1.3M ⊙ and M2 = 1.6M ⊙, with both assumed to follow the APR model [3Jump To The Next Citation Point] for the NS EOS. In unequal-mass mergers, the lower mass NS is tidally disrupted during the merger, forming a disk-like structure around the heavier NS. In this case, the total mass of the remnant is sufficiently high for prompt collapse to a BH, but 0.85% of the total mass remains outside the BH horizon at the end of the simulation, which is substantially larger than for equal-mass mergers with prompt collapse (see Figure 4View Image). Image reproduced by permission from Figure 6 of [144Jump To The Next Citation Point], copyright by APS.


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