Binary Neutron Star Mergers

Abstract

We review the current status of studies of the coalescence of binary neutron star systems. We begin with a discussion of the formation channels of merging binaries and we discuss the most recent theoretical predictions for merger rates. Next, we turn to the quasi-equilibrium formalisms that are used to study binaries prior to the merger phase and to generate initial data for fully dynamical simulations. The quasi-equilibrium approximation has played a key role in developing our understanding of the physics of binary coalescence and, in particular, of the orbital instability processes that can drive binaries to merger at the end of their lifetimes. We then turn to the numerical techniques used in dynamical simulations, including relativistic formalisms, (magneto-)hydrodynamics, gravitational-wave extraction techniques, and nuclear microphysics treatments. This is followed by a summary of the simulations performed across the field to date, including the most recent results from both fully relativistic and microphysically detailed simulations. Finally, we discuss the likely directions for the field as we transition from the first to the second generation of gravitational-wave interferometers and while supercomputers reach the petascale frontier.

Figure 1

Cartoon showing standard formation channels for close NS-NS binaries through binary stellar evolution. Image reproduced from [178].

Figure 2

Cartoon picture of a compact binary coalescence, drawn for a BH-BH merger but applicable to NS-NS mergers as well (although NSs are generally assumed to be non-spinning). Image adapted from Kip Thorne.

Figure 3

Isodensity contours and velocity profile in the equatorial plane for a merger of two equal-mass NSs with M_ns = 1.4 M_⊙ assumed to follow the APR model [3] for the NS EOS. The hypermassive merger remnant survives until the end of the numerical simulation. Image reproduced by permission from Figure 4 of [144], copyright by APS.

Figure 4

Isodensity contours and velocity profile in the equatorial plane for a merger of two equal-mass NSs with M_ns = 1.5 M_⊙ assumed to follow the APR model [3] for the NS EOS. With a higher mass than the remnant shown in Figure 3, the remnant depicted here collapses promptly to form a BH, its horizon shown by the dashed blue circle, absorbing all but 0.004% of the total rest mass from the original system. Image reproduced by permission from Figure 5 of [144], copyright by APS.

Figure 5

Isodensity contours and velocity profile in the equatorial plane for a merger of two unequal-mass NSs with M₁ = 1.3 M_⊙ and M₂ = 1.6 M_⊙, with both assumed to follow the APR model [3] for the NS EOS. In unequal-mass mergers, the lower mass NS is tidally disrupted during the merger, forming a disk-like structure around the heavier NS. In this case, the total mass of the remnant is sufficiently high for prompt collapse to a BH, but 0.85% of the total mass remains outside the BH horizon at the end of the simulation, which is substantially larger than for equal-mass mergers with prompt collapse (see Figure 4). Image reproduced by permission from Figure 6 of [144], copyright by APS.

Figure 6

Dimensionless binding energy E_b/M₀ vs. dimensionless orbital frequency M₀Ω, where M₀ is the total ADM (Arnowitt-Deser-Misner) mass of the two components at infinite separation, for two QE NS-NS sequences that assume a piecewise polytropic NS EOS. The equal-mass case assumes M_NS = 1.35 M_⊙ for both NSs, while the unequal-mass case assumes M₁ = 1.15 M_⊙ and M₂ = 1.55 M_⊙. The thick curves are the numerical results, while the thin curves show the results from the 3PN approximation. The lack of any minimum suggests that instability for these configurations occurs at the onset of mass shedding, and not through a secular orbital instability. Image reproduced by permission from Figure 16 of [305], copyright by AAS.

Figure 7

Mass-shedding indicator vs. orbital frequency M₀Ω, where h is the fluid enthalpy and the derivative is measured at the NS surface in the equatorial plane toward the companion and toward the pole in the direction of the angular momentum vector, for a series of QE NS-NS sequences assuming equal-mass components. Here, χ = 1 corresponds to a spherical NS, while χ = 0 indicates the onset of mass shedding. More massive NSs are more compact, and thus able to reach smaller separations and higher angular frequencies before mass shedding gets underway. Image reproduced by permission from Figure 19 of [305], copyright by AAS.

Figure 8

Isodensity contours for QE models of NS-NS binaries. In each case, the two NSs have masses M₁ = 1.15 M_⊙ (left) and M₂ = 1.55 M_⊙ (right), and the center-of-mass separation is as small as the QE numerical methods allow while able to find a convergent result. The models assume different EOS, resulting in different central concentrations and tidal deformations. Image reproduced by permission from Figures 9–12 of [305], copyright by AAS.

Figure 9

Approximate energy spectrum dE_GW/df derived from QE sequences of equal-mass NS-NS binaries with isolated ADM masses M_NS = 1.35 M_⊙ and a Γ = 2 EOS, but varying compactnesses (denoted M/R here), originally described in [303]. The diagonal lines show the energy spectrum corresponding to a point-mass binary, as well as values with 90%, 75%, and 50% of the power at a given frequency. Asterisks indicate the onset of mass-shedding, beyond which QE results are no longer valid. Image reproduced by permission from Figure 2 of [98], copyright by APS.

Figure 10

Type of final remnant corresponding to different EOS models. The vertical axis shows the total mass of two NSs. The horizontal axis shows the EOSs together with the corresponding NS radii for M_NS = 1.4 M_⊙. Image reproduced by permission from Figure 3 of [134], copyright by APS.

Figure 11

Evolution of the total rest mass M_tot of the remnant disk (outside the BH horizon) normalized to the initial value for NS-NS mergers using a Γ = 2 polytropic EOS with differing mass ratios and total masses. The order of magnitude of the mass fraction in the disk can be read off the logarithmic mass scale on the vertical axis. The curves referring to different models have been shifted in time to coincide at t_coll. Image reproduced by permisison from Figure 5 of [240], copyright by IOP.

Figure 12

Fluid density isocontours and magnetic field distribution (in a plane slightly above the equator) immediately after first contact for a magnetized merger simulation. The cavities at both trailing edges are attributed to magnetic pressure inducing buoyancy. Image reproduced by permission from Figure 1 of [6], copyright by APS.

Figure 13

Evolution of the density in a NS-NS merger, with magnetic field lines superposed. The first panel shows the binary shortly after contact, while the second shows the short-lived HMNS remnant shortly before it collapses. In the latter two panels, a BH has already formed, and the disk around it winds up the magnetic field to a poloidal geometry of extremely large strength, ∼ 10¹⁵ G, with an half-opening angle of 30°, consistent with theoretical SGRB models. Image reproduced by permission from Figure 1 of [241], copyright by AAS.

Figure 14

Dimensionless GW strain Dh/m₀, where D is the distance to the source and m₀ the total mass of the binary, versus time for four different NS-NS merger calculations. The different merger types become apparent in the post-merger GW signal, clearly indicating how BH formation rapidly drives the GW signal down to negligible amplitudes. Image reproduced by permission from Figures 5 and 6 of [134], copyright by APS.

Figure 15

Effective strain at a distance of 100 Mpc shown as a function of the GW frequency (solid red curve) for the same four merger calculations depicted in Figure 14. Post-merger quasi-periodic oscillations are seen as broad peaks in the GW spectrum at frequencies f_GW = 2–4 kHz. The blue curve shows the Taylor T4 result, which represents a particular method of deducing the signal from a 3PN evolution. The thick green dashed curve and orange dot-dashed curves depict the sensitivities of the second-generation Advanced LIGO and LCGT (Large Scale Cryogenic Gravitational Wave Telescope) detectors, respectively, while the maroon dashed curve shows the sensitivity of a hypothetical third-generation Einstein Telescope. Image reproduced by permission from Figures 5 and 6 of [134], copyright by APS.

Figure 16

Comparison between numerical waveforms, shown as a solid black line, and semi-analytic NNLO EOB waveforms, shown as a red dashed line (top panel). The top panels show the real parts of the EOB and numerical relativity waveforms, and the middle panels display the corresponding phase differences between waveforms generated with the two methods. There is excellent agreement between with the numerical waveform almost up to the time of the merger as shown by the match of the orbital frequencies (bottom panel). Image reproduced by permission from Figure 14 of [15], copyright by APS.

Figure 17

Evolution of a binary strange star merger performed using a CF SPH evolution. The “spiral arms” representing mass loss through the outer Lagrange points of the system are substantially narrower than those typically seen in CF calculations of NS-NS mergers with typical nuclear EOS models. Image reproduced by permission from Figure 4 of [35], copyright by APS.

Figure 18

Summary of potential outcomes from NS-NS mergers. Here, M_thr is the threshold mass (given the EOS) for collapse of a HMNS to a BH, and Q_m is the binary mass ratio. ‘Small’, ‘massive’, and ‘heavy’ disks imply total disk masses M_disk ≪ 0.01 M_⊙, 0.01 M_⊙ ≲ M_disk ≲ 0.03 M_⊙, and M_disk ≳ 0.05 M_⊙, respectively. ‘B-field’ and ‘J-transport’ indicate potential mechanisms for the HMNS to eventually lose its differential rotation support and collapse: magnetic damping and angular momentum transport outward into the disk. Spheroids are likely formed only for the APR and other stiff EOS models that can support remnants with relatively low rotational kinetic energies against collapse. Image reproduced by permission from [282], copyright by APS.