Gravitational Waves from the Merger of Binary Neutron Stars in a Fully General Relativistic Simulation

Abstract

We performed 3D numerical simulations of the merger of equal-mass binary neutron stars in full general relativity using a new large-scale supercomputer. We take the typical grid size as (505, 505, 253) for (x, y, z) and the maximum grid size as (633, 633, 317). These grid numbers enable us to put the outer boundaries of the computational domain near the local wave zone and hence to calculate gravitational waveforms of good accuracy (within ∼ 10% error) for the first time. To model neutron stars, we adopt a Γ -law equation of state in the form P = (Γ − 1)ρε, where P , ρ, ε and Γ are the pressure, rest mass density, specific internal energy and adiabatic constant. It is found that gravitational waves in the merger stage have characteristic features that reflect the formed objects. In the case that a massive, transient neutron star is formed, its quasi-periodic oscillations are excited for a long duration, and this property is reflected clearly by the quasi-periodic nature of waveforms and the energy luminosity. In the case of black hole formation, the waveform and energy luminosity are likely damped after a short merger stage. However, a quasi-periodic oscillation can still be seen for a certain duration, because an oscillating transient massive object is formed during the merger. This duration depends strongly on the initial compactness of neutron stars and is reflected in the Fourier spectrum of gravitational waves. To confirm our results and to calibrate the accuracy of gravitational waveforms, we carried out a wide variety of test simulations, changing the resolution and size of the computational domain. * ) Hereafter, we refer to the stage after which the hydrodynamic interaction between two neutron stars sets in as the 'merger stage'. The stage before the merger stage is referred to as the 'early stage'.

Model waveform accuracy standards for gravitational wave data analysis

“…Therefore the appropriate minimum error requirement, including the effects of the calibration error from Eq. (48), for Initial LIGO is 4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi…”

“…Several gravitational wave detectors [1][2][3] have now achieved a high enough level of sensitivity that the first astrophysical observations are expected to occur within the next few years. The numerical relativity community has also matured to the point that several groups are now computing model gravitational waveforms for the inspiral and merger of black hole and neutron star binary systems [4][5][6][7][8][9][10][11][12][13]. Beyond the pioneering work of Mark Miller [14] and Stephen Fairhurst [15], however, little effort has gone into thinking about the question of how accurate these model waveforms need to be.…”

Differentially-rotating neutron star models with a parametrized rotation profile

“…refers to constant specific angular momentum,"v-const." is for constant linear velocity, "HMNS" is the approximate power-law of some numerical relativistic simulations with HMNS formation (e.g., Shibata & Uryū 2002;Baiotti et al 2008).…”

“…These hyper-massive neutron stars (HMNSs) remain stable over many dynamical timescales before collapsing to form a black hole (BH) (e.g. Shibata & Uryū 2002;Baiotti et al 2008). To study the effect of the centrifugal force in supporting the HMNS, most of these papers show the angular velocity profile of the merged object before the eventual collapse to form a BH.…”

Magnetohydrodynamics in full general relativity: Formulation and tests

“…As the time slicing condition, an approximate maximal slice condition K ≈ 0 is adopted following previous papers (e.g., [36]). As the spatial gauge condition, we adopt a hyperbolic gauge condition as in [37,6].…”