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

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 ADM mass of cold and spherical neutron stars is ≈ 2.04M⊙ and 1.80M⊙, 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 2.4M⊙ and 2.8M⊙ with the rest-mass ratio QM to be in the range 0.9 < ∼ QM ≤ 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 ∼ 2.7M⊙ and ∼ 2.5M⊙ 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 ∼ 100 Mpc. Thermal properties of the outcome formed after the merger are also analyzed to approximately estimate the neutrino emission energy.

Magnetohydrodynamics in full general relativity: Formulation and tests

“…This is indeed the case for frequently used equations of state such as Γ-law equations of state P = (Γ − 1)ρε where Γ is an adiabatic constant and hybrid equations of state for which P is written in the form P (ρ, h) (e.g., [15,7]). Thus, Eqs.…”

“…In the past several years, this field has been extensively developed (e.g., [1][2][3][4][5][6][7]) and, as a result, now it is feasible to perform accurate simulations of such general relativistic phenomena for yielding scientific results (e.g., [6][7][8][9] for our latest results). For example, with the current implementation, radiation reaction of gravitational waves in the merger of binary neutron stars can be taken into account within ∼ 1% error in an appropriate computational setting [6,7]. This fact illustrates that the numerical relativity is a robust approach for detailed theoretical study of astrophysical phenomena and gravitational waves emitted.…”

“…For example, simplified ideal equations of state have been adopted instead of realistic ones (but see [7]). Also, the effect of magnetic fields has been neglected although it could often play an important role in the astrophysical phenomena (but see [10]).…”

“…This implies that a small seed field can wind up and grow in the complex motion of the matter, resulting in a significant effect in the dynamics of the matter such as magnetically driven wind or jet and angular momentum redistribution. Specifically, in the context of the general relativistic astrophysics, the magnetic fields will play a role in the following phenomena and objects: Stellar core collapse of magnetized massive stars to a protoneutron star [11] or a black hole, stability of accretion disks (which are either non-self-gravitating or self-gravitating) around black holes and neutron stars, magnetic braking of differentially rotating neutron stars [10] which are formed after merger of binary neutron stars [6,7] and stellar core collapse [14][15][16]8,9], and magnetically induced jet around the compact objects (e.g., [17]). To clarify these phenomena, fully general relativistic MHD (GRMHD) simulation (involving dynamical spacetimes) is probably the best theoretical approach.…”

Sources of Gravitational Waves: Theory and Observations

“…A BH with an accretion disk might promptly form if M NS max < M < ∼ 3 M and the component masses are different from each other. However, if M NS max < M < ∼ 3 M and the component masses are similar, a transient object called a hypermassive NS may form [304,306]. The hypermassive NS is expected to be a non-axisymmetric ellipsoid supported against collapse by a combination of thermal pressure and differential rotation [305] and can delay BH formation for 1 ms to 1 s [305,307].…”