Simulations of merging black holes and neutron stars may lead to a better understanding of systems that can produce gravitational waves. Compact mergers of these massive objects may be a progenitor of short-hard gamma ray bursts, which also makes them particularly interesting. While ground-based detectors such as LIGO pursue the first direct detection of gravitational waves, others are using numerical simulations within full general relativity to model these complex mergers.
As two compact objects become gravitationally bound to each other, they spiral together and eventually merge. Several groups have already perfomed simulations exploring the dependence of the merger's outcome on the mass ratio, the black hole spin, the neutron star equation of state, and the magnetic field. Instead, this work focuses on applying full general relativity to hyperbolic encounters, making it applicable to black hole - neutron star capture events that merge with large eccentricity.
Primordial binaries have no eccentricity in the LIGO frequency band; hence these new simulations are mostly relevant to star clusters and globular clusters. Star clusters at the centers of galaxies are promising sites for binary mergers. These capture binaries form with relatively small periapsis separations (point of least distance of a body from one of the foci of its elliptical orbit). Globular clusters that have undergone core collapse may also have many mergers because of their high density of compact objects.
The simulations are performed by varying the initial periapsis separation between 50 and 150 km. The black hole and neutron star have a 4:1 mass ratio and both are initially non-rotating. The outcome of the simulated mergers (disk mass, unbound material and GW signal) depends greatly on the impact parameter. In all simulations, enough energy is carried away by gravitational waves that the initial encounter results in a bound system. However, three possible behaviors are observed. (1) For the smallest values of the periapsis separation (~50-70km), a direct plunge is seen. (2) For intermediate values of the separation (70-80 km), an initial periapsis passage occurs, followed by a single elliptical orbit and then a plunge. (3) For separations greater than 87.5 km, an initial periapsis passage is followed by a long-period elliptical orbit. (For the larger separation values, the simulations are computationally limited.)
If a neutron star plunges without significant disruption, then only about 1% of the initial mass is available to form an accretion disk. However, if the neutron star is stretched into a long tidal tail, then as much as 12% of the initial mass is left to form an accretion disk. This means that the remnant disk mass can range from nearly zero to 0.3 solar masses.
The fallback rate is the rate at which material on elliptical orbits is expected to return to the accretion disk. For all simulated cases, it exhibits a t-5/3 behavior.
The total mass lost to gravitational waves varies between 0.7 and 1.7% for the various simulations.
The sensitivity to initial conditions stems partly from binary analogues of the famous zoom-whirl orbits about black holes, in which a particle alternates long excursions (zooms) with several close orbits (whirls) at approximately the radius of an unstable circular orbit. Tidal disruption precludes multiple zooms and whirls, but a narrow range of encounters leads the enhanced radiation of a whirl.
The observed variations in disk mass, unbound material and gravitational waves may help explain the diverse characteristics in gamma-ray bursts. Future simulations are ongoing, with plans to simulate variations in the neutron star equation of state and the black hole spin.