Accurate evolutions of inspiralling neutron-star binaries: prompt and delayed collapse to black hole (0804.0594v3)

Abstract: Binary neutron-star (BNS) systems represent primary sources for the gravitational-wave (GW) detectors. We present a systematic investigation in full GR of the dynamics and GW emission from BNS which inspiral and merge, producing a black hole (BH) surrounded by a torus. Our results represent the state of the art from several points of view: (i) We use HRSC methods for the hydrodynamics equations and high-order finite-differencing techniques for the Einstein equations; (ii) We employ AMR techniques with "moving boxes"; (iii) We use as initial data BNSs in irrotational quasi-circular orbits; (iv) We exploit the isolated-horizon formalism to measure the properties of the BHs produced in the merger; (v) Finally, we use two approaches, based either on gauge-invariant perturbations or on Weyl scalars, to calculate the GWs. These techniques allow us to perform accurate evolutions on timescales never reported before (ie ~30 ms) and to provide the first complete description of the inspiral and merger of a BNS leading to the prompt or delayed formation of a BH and to its ringdown. We consider either a polytropic or an ideal fluid EOS and show that already with this idealized EOSs a very interesting phenomenology emerges. In particular, we show that while high-mass binaries lead to the prompt formation of a rapidly rotating BH surrounded by a dense torus, lower-mass binaries give rise to a differentially rotating NS, which undergoes large oscillations and emits large amounts of GWs. Eventually, also the NS collapses to a rotating BH surrounded by a torus. Finally, we also show that the use of a non-isentropic EOS leads to significantly different evolutions, giving rise to a delayed collapse also with high-mass binaries, as well as to a more intense emission of GWs and to a geometrically thicker torus.

• The paper presents high-fidelity numerical simulations that accurately capture the inspiral and merger dynamics of neutron-star binaries using advanced relativistic hydrodynamics techniques.
• The paper finds that merger outcomes—from prompt black hole formation to delayed collapse of a hypermassive neutron star—strongly depend on the neutron star equation of state.
• The paper identifies distinct gravitational-wave signatures, including inspiral chirps and post-merger oscillations, which offer actionable insights for current and next-generation detectors.

Overview of Numerical Simulations of Neutron-Star Binary Coalescence

This paper presents a comprehensive numerical simulation paper on the dynamics and gravitational-wave (GW) emission of inspiralling binary neutron stars (NSs) within the framework of full general relativity. The simulations focus on the fate of these systems as they merge into either a black hole (BH) promptly or after a delay. Key to these studies is the implementation of advanced techniques in relativistic hydrodynamics and numerical relativity, including high-resolution shock-capturing schemes, adaptive mesh refinement (AMR), and the extraction of gravitational waves through both the Newman-Penrose formalism and gauge-invariant perturbative methods.

The paper investigates equal-mass NS binaries with initial configurations in quasi-circular orbits, employing different equations of state (EOSs): an isentropic polytropic EOS and a non-isentropic ideal-fluid EOS. These EOSs represent extreme forms of neutron star matter, where the former forbids the formation of shocks, thus simulating a scenario without thermal effects from shocks, whereas the latter allows shock heating to influence post-merger outcomes.

Results and Discussion

1. Pre-Merger Dynamics: The pre-merger dynamics encapsulated an inspiral phase lasting from two to five orbits (depending on the initial separation), after which the NSs merged. The dynamics included observable effects such as tidal distortions and eccentricities primarily introduced by the initial gauge conditions.
2. Post-Merger Outcomes: The immediate progeny of the merger varied significantly depending on the mass and EOS:
   • High-mass binaries with a polytropic EOS underwent a rapid collapse to a BH following the merger, producing a high-density torus around the BH. These simulations uncovered quick post-merger dynamics exemplifying the distinct signatures in GW signals.
   • Low-mass binaries, in contrast, formed a long-lived hypermassive neutron star (HMNS) that subsequently collapsed to a BH, characterized by significant emission of gravitational waves from non-axisymmetric instabilities.
   • The use of a non-isentropic EOS delayed the collapse to a BH, attributed to thermal pressure support from shock heating, which increased the stellar temperature and reduced compactness.
3. Gravitational-Wave Signatures: The GW signals were categorized by inspiral-induced chirps followed by complex post-merger oscillations:
   • The waveforms exhibited characteristic damped oscillations linked to the real and imaginary components of the Weyl scalar or perturbation variables.
   • The post-merger GW spectrum varied with the EOS: with peaks correlating to bar-mode instabilities and the GW emission of stabilized HMNSs.
   • Signal-to-Noise Ratios (SNRs) calculated for different detectors emphasized that while current detectors could marginally detect such signals, advanced detectors will significantly enhance detectability prospects.
4. Hydrodynamical Instabilities: The formation of a shear layer during the merger drives a Kelvin-Helmholtz instability, leading to complex small-scale vorticity patterns captured by the AMR system. This hydrodynamic behavior might have implications for the amplification of magnetic fields in realistic astrophysical conditions.
5. Implications and Future Directions: This paper underscores the pivotal role of the EOS and initial configurations on the coalescence and post-merger dynamics of NS binaries. The accurate representation of these effects via high-fidelity simulations offers rich insight into the physics of neutron stars and GW astrophysics. Moving forward, it suggests the necessity of incorporating more realistic EOSs and magnetic fields, as well as achieving even longer simulated inspiral sequences for more conclusive high-frequency GW spectrum predictions.

Conclusion

The research presented in this paper represents a significant step forward in understanding the complex dynamics of neutron-star binaries, from their inspiral through post-merger phenomenology, all within a comprehensive relativistic framework. The resulting insights deliver important constraints on the EOS of dense matter and lay the groundwork for interpreting future observations from gravitational-wave detectors, thus offering a novel perspective on the behavior of dense stellar objects and their GW emissions.