3.1 Comparison to BH-NS mergers

Since this three-phase picture is applicable to BH-NS mergers as well, it is worthwhile to compare the two merger processes at a qualitative level to understand the key similarities and differences. Inspiral for BH-NS mergers is also well-described by PN expansions up until shortly before the merger, but the parameter space is fundamentally different. First, since BHs are heavier than NSs, the dynamics can be quite different. Also, since BHs may be rapidly-spinning (i.e., have dimensionless spin angular momenta as large as J ∕M 2 ∼ 1), spin-orbit couplings can play a very important role in the orbital dynamics of the binary, imprinting a large number of oscillation modes into the GW signal (see, e.g., [126, 57]). From a practical standpoint, the onset of instability in BH-NS mergers should be easier to detect for LIGO, Virgo, and other interferometers, since the larger mass of BH-NS binaries implies that instability occurs at lower GW frequencies (see Eq. 4View Equation, noting that the separation a at which mass-transfer begins scales roughly proportionally to the BH mass).

The onset of instability of a BH-NS binary is determined by the interplay of the binary mass-ratio, NS compactness, and BH spin, with the first of these playing the largest role (see Figures 13 – 15 of [302] and the summary in [284Jump To The Next Citation Point]). In general, systems with high BH masses and/or more compact NSs tend to reach a minimum in the binding energy as the radius increases, leading to a dynamical orbital instability that occurs near the classical innermost stable circular orbit (ISCO). In these cases, the NS plunges toward the BH before the onset of tidal disruption, and is typically “swallowed whole”. leaving behind almost no material to form a disk. The GW emission from such systems is sharply curtailed after the merger event, yielding only a low-amplitude, high-frequency, rapidly-decaying “ringdown” signal (see, e.g., [154Jump To The Next Citation Point]). Numerical calculations have shown that even in borderline cases between dynamical instability and mass-shedding the NS is essentially swallowed whole, especially in cases where the BH in either non-spinning or spinning in the retrograde direction, which pushes the ISCO out to larger radii (see, e.g., [290Jump To The Next Citation Point, 289Jump To The Next Citation Point, 283Jump To The Next Citation Point, 91Jump To The Next Citation Point, 94Jump To The Next Citation Point]).

A richer set of phenomena occurs when the BH-NS mass ratio is closer to unity, the NS is less compact, the BH has a prograde spin direction, or more generally, some combination of those factors. In such cases, the NS will reach the mass-shedding limit prior to dynamical instability, and be tidally disrupted. Unlike what was described in semi-analytic Newtonian models (see, e.g., [68, 228, 77]) and seen in some early Newtonian and quasi-relativistic simulations (see, e.g., [165, 166, 138], stable mass transfer, in which angular momentum transfer via mass-shedding halts the inspiral, has never been seen in full GR calculations, nor even in approximate GR models (see the discussion in [96]). Even so, unstable mass transfer can produce a substantial disk around the BH, though in every GR simulation to data the substantial majority of the NS matter is accreted promptly by the BH (see [284Jump To The Next Citation Point] for a detailed summary of all current results). The exact structure of the disk and its projected lifetime depend on the binary system parameters, with the binary mass ratio and spin both important in determining the disk mass and the BH spin orientation critical for determining both the disk’s vertical structure and its thermodynamic state given the shock heating that occurs during the NS disruption. In general, the mass and temperature of the post-merger disks are comparable to those seen in some NS-NS mergers, and inasmuch as either is a plausible SGRB progenitor candidate then both need to be viewed as such. To date, no calculation performed in full GR has found any bound and self-gravitating NS remnant left over after the merger, including both NS cores that survive the initial onset of mass transfer by recoiling outward (predicted for cases in which stable mass transfer was thought possible, as noted above) or those in which bound objects form through fragmentation of the circum-BH disk. Motivated by observations of wide-ranging timescales for X-ray flares in both long and short GRBs [225], the latter channel has been suggested to occur in collapsars [227] and mentioned in the context of mergers [243Jump To The Next Citation Point], possibly on longer timescales than current simulations permit. Even so, there is no analogue to the HMNS state that may result from NS-NS mergers, nor any mechanism for a delayed SGRB as provided by HMNS collapse.

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