![]() ![]() There is a third possibility, in which stable mass transfer occurs after the onset of mass shedding of the NS by the BH tidal field. The final fate of BH-NS binaries is classified into two categories a NS is tidally disrupted by its companion BH before it is swallowed by the BH or a NS is simply swallowed by its companion BH in the final phase. To elucidate whether the merger of BH-NS binaries could be a promising source for the progenitor of the central engine, numerical-relativity simulations are required (see also Section 1.3). The second fact is that BH-NS binaries may be some of the progenitors of the central engine of gamma-ray bursts with short time duration ≲2s (SGRB), for which the source is still unknown. This has motivated PN and numerical-relativity studies as well as two-body approximate general relativistic studies (e.g., ) for the coalescing compact binaries. To detect gravitational waves and to extract physical information from the gravitational-wave signal, theoretical templates must be prepared. The detection rate of BH-NS binaries will be ∼ 0.5–50 events per year for the advanced detectors such as advanced-LIGO. The frequency for the late inspiral orbits is just within the frequency-band sensitivity for the advanced gravitational-wave detectors, ∼ 10–3000 kHz, and the amplitude of ∼ 10 −22 is high enough that the signal of gravitational waves may be detected. ![]() Where μ is the reduced mass of the binary defined by M BH M NS/ m 0, and D is the distance to the source. In particular, the following two facts have recently enhanced the motivation for the study of BH-NS binaries: First, BH-NS binaries in close orbits are among the most promising sources for the large laser-interferometric gravitational-wave detectors, such as LIGO, VIRGO, LCGT, and Einstein Telescope : The frequency and amplitude of gravitational waves near the last orbit are estimated to give This implies that coalescence is likely to occur frequently in the Hubble volume, and therefore, the evolution process and the final fate of BH-NS binaries deserve a detailed theoretical study. ![]() In addition, coalescence in elliptic galaxies could contribute to the total coalescence rate of the universe by a significant fraction. However, many of statistical studies based on the stellar evolution synthesis suggest that the coalescence will occur by 1–10% as frequently as that of NS-NS binaries in our galaxy and hence in the normal spiral galaxies (every ∼ 10 6–10 7 years). This implies that a numerical study in the framework of general relativity is required for precisely understanding the final evolution phase of BH-NS binaries.īH-NS binaries have not been observed yet even in our galaxy in contrast to NS-NS binaries. In particular, in the merger phase and subsequent remnant-formation phase, the dynamics of the system depends strongly on the structure of the NS (the radius and density profile, or its equation of state hereafter EOS) and the BH spin, as well as on general relativistic gravity. In addition, the adiabatic approximation for the orbital evolution becomes worse, because the gravitational-radiation-reaction time scale is as short as the orbital period the ratio of τ GW to the orbital period, P orb, is approximately written asĪnd thus, for the orbit close to the last one with r ∼ 6 Gm 0/ c 2, τ GW is comparable to P orb. On the other hand, throughout the late inspiral to the merger phases, the orbital evolution process depends significantly on their finite-size effects and the resulting modification on the interaction between the two objects. The evolution through the inspiral phase is well understood within the post-Newtonian (PN) approximation. In most of the inspiral phase during which the binary separation gradually decreases due to the gravitational radiation reaction, two compact objects are well approximated by two point masses in an adiabatic orbit, because their radii are much smaller than the orbital separation (finite-size effects, such as tidal deformation, are negligible) and also the gravitational-radiation-reaction time scale is much longer than the orbital period (cf. Thus, if the initial semi-major axis is smaller than ∼ 10 7 km, the BH and NS merge within the Hubble time scale after a substantial emission of gravitational waves. The lifetime for a binary of elliptic orbits with the semi-major axis r is shorter than τ Gw. G is the gravitational constant and c the speed of light, respectively. Where r, M BH, and M NS are the orbital separation, masses of the BH and NS, respectively, and m 0 = M BH + M NS. ![]()
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