On 2017 August 17, the gravitational-wave event GW170817 was observed by the Advanced LIGO and Virgo detectors, and the gamma-ray burst (GRB) GRB 170817A was observed independently by the Fermi Gamma-ray Burst Monitor, and the Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory. The probability of the near-simultaneous temporal and spatial observation of GRB 170817A and GW170817 occurring by chance is $5.0\times {10}^{-8}$. We therefore confirm binary neutron star mergers as a progenitor of short GRBs. The association of GW170817 and GRB 170817A provides new insight into fundamental physics and the origin of short GRBs. We use the observed time delay of $(+1.74\pm 0.05)\,{\rm{s}}$ between GRB 170817A and GW170817 to: (i) constrain the difference between the speed of gravity and the speed of light to be between $-3\times {10}^{-15}$ and $+7\times {10}^{-16}$ times the speed of light, (ii) place new bounds on the violation of Lorentz invariance, (iii) present a new test of the equivalence principle by constraining the Shapiro delay between gravitational and electromagnetic radiation. We also use the time delay to constrain the size and bulk Lorentz factor of the region emitting the gamma-rays. GRB 170817A is the closest short GRB with a known distance, but is between 2 and 6 orders of magnitude less energetic than other bursts with measured redshift. A new generation of gamma-ray detectors, and subthreshold searches in existing detectors, will be essential to detect similar short bursts at greater distances. Finally, we predict a joint detection rate for the Fermi Gamma-ray Burst Monitor and the Advanced LIGO and Virgo detectors of 0.1–1.4 per year during the 2018–2019 observing run and 0.3–1.7 per year at design sensitivity.

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Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A

The article reviews the current status of a theoretical approach to the problem of the emission of gravitational waves by isolated systems in the context of general relativity. Part A of the article deals with general post-Newtonian sources. The exterior field of the source is investigated by means of a combination of analytic post-Minkowskian and multipolar approximations. The physical observables in the far-zone of the source are described by a specific set of radiative multipole moments. By matching the exterior solution to the metric of the postNewtonian source in the near-zone we obtain the explicit expressions of the source multipole moments. The relationships between the radiative and source moments involve many nonlinear multipole interactions, among them those associated with the tails (and tails-of-tails) of gravitational waves. Part B of the article is devoted to the application to compact binary systems. We present the equations of binary motion, and the associated Lagrangian and Hamiltonian, at the third post-Newtonian (3PN) order beyond the Newtonian acceleration. The gravitational-wave energy flux, taking consistently into account the relativistic corrections in the binary moments as well as the various tail eects, is derived through 3.5PN order with respect to the quadrupole formalism. The binary’s orbital phase, whose prior knowledge is crucial for searching and analyzing the signals from inspiralling compact binaries, is deduced from an energy balance argument.

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Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries.

Neutron Stars 1: Equation of State and Structure

When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

On Continued Gravitational Contraction

The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.

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Physics of Neutron Star Crusts

We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the precoalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational. The latter state is technically more complicated to treat than the former one (synchronized binary), but is expected to represent fairly well the late evolutionary stages of a binary neutron star system. As regards the gravitational field, an approximation of general relativity is used, which amounts to solving five of the ten Einstein equations (conformally flat spatial metric). The obtained system of partial differential equations is solved by means of a multidomain spectral method. Two spherical coordinate systems are introduced, one centered on each star; this results in a precise description of the stellar interiors. Thanks to the multidomain approach, this high precision is extended to the strong field regions. The computational domain covers the whole space so that exact boundary conditions are set to infinity. Extensive tests of the numerical code are performed, including comparisons with recent analytical solutions. Finally a constant baryon number sequence (evolutionary sequence) is presented in detail for a polytropic equation of state with $\ensuremath{\gamma}=2.$

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: Method and tests

A multidomain spectral method for computing very high precision three-dimensional stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g., the star's surface). In addition, a regularization procedure is introduced to deal with the infinite derivatives on the boundary that may appear in the density field when stiff equations of state are used. Consequently all the physical fields are smooth functions on each domain and the spectral method is absolutely free of any Gibbs phenomenon, which yields to a very high precision. The power of this method is demonstrated by direct comparison with analytical solutions such as MacLaurin spheroids and Roche ellipsoids. The relative numerical error is revealed to be of the order of ${10}^{\ensuremath{-}10}.$ This approach has been developed for the study of relativistic inspiralling binaries. It may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too.

Numerical approach for high precision 3D relativistic star models

A new set of equations and a new numerical method for computing stationary axisymmetric rapidly rotating star models within general relativity is presented. The source term of the gravitational field is not restricted to a perfect fluid one but represents the most general one, including anisotropic stresses, permitted under the assumptions of stationarity, axisymmetry and absence of meridional currents. This allows us to derive the equations governing the equilibrium of rotating neutron stars with strong magnetic fields in a self-consistent and fully relativistic way. As regards the numerics, the improvement lies in the exact computation of the metric in the whole space outside the star, thanks to a numerical grid which extends to infinity (due to a suitable compactification of the space external to the star)

Axisymmetric rotating relativistic bodies: a new numerical approach for exact' solutions

We report on general relativistic calculations of quasiequilibrium configurations of binary neutron stars in circular orbits with zero vorticity. These configurations are expected to represent realistic situations as opposed to corotating configurations. The Einstein equations are solved under the assumption of a conformally flat spatial 3-metric (Wilson-Mathews approximation). The velocity field inside the stars is computed by solving an elliptical equation for the velocity scalar potential. Results are presented for sequences of constant baryon number (evolutionary sequences). Although the central density decreases much less with the binary separation than in the corotating case, it still decreases. Thus, no tendency is found for the stars to individually collapse to black hole prior to merger.

Numerical Models of Irrotational Binary Neutron Stars in General Relativity

We present spectral methods developed in our group to solve three-dimensional partial differential equations. The emphasis is put on equations arising from astrophysical problems in the framework of general relativity.

J.-A. Marck

Papers

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: Method and tests

Numerical approach for high precision 3D relativistic star models

Axisymmetric rotating relativistic bodies: a new numerical approach for exact' solutions

Numerical Models of Irrotational Binary Neutron Stars in General Relativity

Spectral methods in general relativistic astrophysics