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Merger of binary neutron stars with realistic equations of state in full general relativity

Masaru Shibata¹, Keisuke Taniguchi², and Kōji Uryū³

¹Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153-8902, Japan
²Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
³Astrophysical Sector, SISSA, via Beirut 2/4, Trieste 34013, Italy

Phys. Rev. D 71, 084021 – Published 18 April, 2005

DOI: https://doi.org/10.1103/PhysRevD.71.084021

Abstract

We present numerical results of three-dimensional simulations for the merger of binary neutron stars in full general relativity. Hybrid equations of state are adopted to mimic realistic nuclear equations of state. In this approach, we divide the equations of state into two parts as $P = P_{cold} + P_{th}$ . $P_{cold}$ is the cold part for which we assign a fitting formula for realistic equations of state of cold nuclear matter slightly modifying the formula developed by Haensel and Potekhin. We adopt the SLy and FPS equations of state for which the maximum allowed Arnowitt-Deser-Misner (ADM) mass of cold and spherical neutron stars is $\approx 2.04 M_{⊙}$ and $1.80 M_{⊙}$ , respectively. $P_{th}$ denotes the thermal part which is written as $P_{th} = (Γ_{th} - 1) ρ (ε - ε_{cold})$ , where $ρ$ , $ε$ , $ε_{cold}$ , and $Γ_{th}$ are the baryon rest-mass density, total specific internal energy, specific internal energy of the cold part, and the adiabatic constant, respectively. Simulations are performed for binary neutron stars of the total ADM mass in the range between $2.4 M_{⊙}$ and $2.8 M_{⊙}$ with the rest-mass ratio $Q_{M}$ to be in the range $0.9 ≲ Q_{M} \leq 1$ . It is found that if the total ADM mass of the system is larger than a threshold $M_{thr}$ , a black hole is promptly formed in the merger irrespective of the mass ratios. In the other case, the outcome is a hypermassive neutron star of a large ellipticity, which results from the large adiabatic index of the realistic equations of state adopted. The value of $M_{thr}$ depends on the equation of state: $M_{thr} \sim 2.7 M_{⊙}$ and $\sim 2.5 M_{⊙}$ for the SLy and FPS equations of state, respectively. Gravitational waves are computed in terms of a gauge-invariant wave extraction technique. In the formation of the hypermassive neutron star, quasiperiodic gravitational waves of a large amplitude and of frequency between 3 and 4 kHz are emitted. The estimated emission time scale is $≲ 100 ms$ , after which the hypermassive neutron star collapses to a black hole. Because of the long emission time, the effective amplitude may be large enough to be detected by advanced laser interferometric gravitational wave detectors if the distance to the source is smaller than $\sim 100 Mpc$ . Thermal properties of the outcome formed after the merger are also analyzed to approximately estimate the neutrino emission energy.

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Merger of binary neutron stars with realistic equations of state in full general relativity

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