6.6 Comparison to BH-NS merger results

While there is a history of Newtonian, quasi-relativistic, post-Newtonian, and CF gravitational formalisms being used to perform BH-NS merger simulations, their results are nearly always quantitatively, if not qualitatively, different than full GR simulations, and we focus here on the latter (see [284Jump To The Next Citation Point] for a more thorough historical review). Most of the groups that have performed full GR NS-NS merger calculations have also published results on BH-NS mergers, including Whisky (for head-on collisions) [174], KT [290Jump To The Next Citation Point, 289Jump To The Next Citation Point, 283, 332Jump To The Next Citation Point, 276, 154, 153Jump To The Next Citation Point], UIUC [91Jump To The Next Citation Point, 94, 92Jump To The Next Citation Point], HAD [66Jump To The Next Citation Point], as well as the SXS collaboration [85, 84Jump To The Next Citation Point, 108Jump To The Next Citation Point, 107] and Princeton (for elliptical mergers) [294Jump To The Next Citation Point, 88Jump To The Next Citation Point]. Summarizing the results of these works, we get a rather coherent picture, which we describe below.

The GW signal from BH-NS mergers is somewhat “cleaner” than that from NS-NS mergers, since the disruption of the NS and its accretion by the BH rapidly terminate the GW emission. In general, 3PN estimates model the signal well until tidal effects become important. The more compact the NS, the higher the dimensionless “cutoff frequency” Mtotfcut at which the GW energy spectrum plummets, with direct plunges in which the NS is swallowed whole typically yielding excess power near the frequency maximum from the final pre-merger burst. For increasingly prograde BH spins, there is more excess power over the 3PN prediction at lower frequencies, but also a lower cutoff frequency marking the plunge (see the discussion in [284]). From an observational standpoint, the deviations from point-mass form become more visible for a higher mass BH-NS system, because frequencies scale characteristically like the inverse of the total mass. The distinction is particularly important for Advanced LIGO, as systems with M ≳ 3M BH ⊙ typically yield cutoff frequencies within the advanced LIGO band at source distances of D ∼ 100 Mpc, while for lower-mass systems the cutoff occurs at or just above the upper end of the frequency band. This is significantly different than the situation for NS-NS mergers, in which the characteristic frequencies corresponding to the merger itself typically fall at frequencies above the advanced LIGO high-frequency sensitivity limit, and those corresponding to remnant oscillations in the range 2 – 4 kHz, which will prove a challenge even for third-generation GW detectors.

Disk masses for BH-NS mergers were found to be extremely small in the first calculations, all performed using non-spinning BHs [290, 289, 91], but have since been corrected to larger values once more sophisticated grid-based schemes and atmosphere treatments were added to those codes. More recent results indicate disk masses for reasonable physical parameters can be as large as 0.4M ⊙, for highly-spinning (aBH ∕M = 0.9) mergers [108Jump To The Next Citation Point], with values of 0.035 –0.05M ⊙ characterizing non-spinning models with mass ratios q ≈ 1∕5 [153]. Mass loss into a disk is suppressed by misaligned spins, especially for highly-inclined BHs, so the aligned cases should currently be interpreted as upper limits for the disk mass when alignment is varied [108]. Overall, disk masses for BH-NS merger remnants are comparable to those from NS-NS merger remnants, and may not be clearly distinguishable from them based solely on the emission properties of the disk. For BH-NS mergers with mass ratios q = 1∕3 and prograde spins of dimensionless magnitude a ∕M = 0.5 BH, the disk parameters found after a run performed with the inclusion of a finite-temperature NS EOS [84] indicated that the neutrino luminosity from the disk might be as high as 1053 erg/s. While NS-NS merger simulations have led to predictions of neutrino luminosities a few times larger than this, the result does indicate that BH-NS mergers are also plausible SGRB progenitor candidates, possibly with lower characteristic luminosities than bursts resulting from NS-NS mergers.

The role of magnetic fields in BH-NS mergers has only been investigated recently [66, 92Jump To The Next Citation Point], in simulations that apply an initially poloidal magnetic field to the NSs in the binary. Magnetic fields were found to have very little effect on the resulting GW signal and the mass accretion rate for the BH for physically reasonable magnetic field strengths, with visible divergences appearing only for 17 B ∼ 10 G [92], which is not particularly surprising. Just as in NS-NS mergers, magnetic fields play very little role during inspiral, and unlike the case of NS-NS mergers there is no opportunity to boost fields at a vortex sheet that forms when the binary makes contact, nor in a HMNS via differential rotation. While the MRI may be important in determining the thermal evolution and mass accretion rate in a post-merger disk, such effects will likely be observable primarily on longer timescales.

Just as full-GR NS-NS simulations do not indicate that such mergers are likely sources of the r-process elements we observe in the universe, BH-NS simulations in full GR make the same prediction: no detectable mass loss from the system whatsoever, at least in the calculations performed to date. The picture may change when even larger prograde spins are modeled, since this should lead to maximal disk production, or if more detailed microphysical treatments indicate that a significant wind can be generated from either a HMNS or BH disk and unbind astrophysically interesting amounts of material, but neither has been seen in the numerical results to date.

As is seen in NS-NS mergers, the pericenter distance plays a critical role in the evolution of eccentric BH-NS mergers as well. Large disk masses containing up to 0.3M ⊙, with an unbound fraction of roughly 0.15M ⊙, can occur when the periastron separation is located just outside the classical ISCO, with GW signals taking on the characteristic zoom-whirl form predicted for elliptical orbits [294]. In between pericenter passages, radial oscillations of the neutron star produce GW emission at frequencies corresponding to the f-mode for the NS as well [88].

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