jean marck - Academia.edu (original) (raw)

Papers by jean marck

arXiv: General Relativity and Quantum Cosmology, 1999

We present results of numerical computations of quasiequilibrium sequences of binary neutron star... more We present results of numerical computations of quasiequilibrium sequences of binary neutron stars with zero vorticity, in the general relativistic framework. The Einstein equations are solved under the assumption of a conformally flat spatial 3-metric (Wilson-Mathews approximation). The evolution of the central density of each star is monitored as the orbit shrinks in response to gravitational wave emission. For a compactification ratio M/R=0.14, the central density remains rather constant (with a slight increase, below 0.1%) before decreasing. For a higher compactification ratio M/R=0.17 (i.e. stars closer to the maximum mass configuration), a very small density increase (at most 0.3%) is observed before the decrease. This effect remains within the error induced by the conformally flat approximation. It can be thus concluded that no substantial compression of the stars is found, which would have indicated a tendency to individually collapse to black hole prior to merger. Moreover,...

The Ninth Marcel Grossmann Meeting, 2002

Approaches to Numerical Relativity

Progress of Theoretical Physics Supplement, 1999

A review is given of recent results about the computation of irrotational Darwin-Riemann configur... more A review is given of recent results about the computation of irrotational Darwin-Riemann configurations in general relativity. Such configurations are expected to represent fairly well the late stages of inspiralling binary neutron stars. *) Contrary to MacLaurin ellipsoids, which are exact solutions for rotating incompressible fluids in Newtonian gravity, Darwin ellipsoids are approximate solutions, because of the second order truncation in the expansion of the gravitational potential of the companion.

Physical Review Letters, 1999

We report on general relativistic calculations of quasiequilibrium configurations of binary neutr... more 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.

Physical Review D, 1998

A multi-domain spectral method for computing very high precision 3-D stellar models is presented.... more A multi-domain spectral method for computing very high precision 3-D 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 reveals to be of the order of 10 −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.

Physical Review D, 1997

A general relativistic version of the Euler equation for perfect uid hydrodynamics is applied to ... more A general relativistic version of the Euler equation for perfect uid hydrodynamics is applied to a system of two neutron stars orbiting each other. In the quasi-equilibrium phase of the evolution of this system, a rst integral of motion can be derived for certain velocity elds of the neutron star uid including the (academic) case of co-rotation with respect to the orbital motion (synchronized binaries) and the realistic case of counter-rotation with respect to the orbital motion. The velocity eld leading to this latter conguration can be computed by solving three-dimensional vector and scalar Poisson equations.

Physical Review D, 2001

We study equilibrium sequences of close binary systems composed of identical polytropic stars in ... more We study equilibrium sequences of close binary systems composed of identical polytropic stars in Newtonian gravity. The solving method is a multi-domain spectral method which we have recently developed. An improvement is introduced here for accurate computations of binary systems with stiff equation of state (γ > 2). The computations are performed for both cases of synchronized and irrotational binary systems with adiabatic indices γ = 3, 2.5, 2.25, 2 and 1.8. It is found that the turning points of total energy along a constant-mass sequence appear only for γ ≥ 1.8 for synchronized binary systems and γ ≥ 2.3 for irrotational ones. In the synchronized case, the equilibrium sequences terminate by the contact between the two stars. On the other hand, for irrotational binaries, it is found that the sequences terminate at a mass shedding limit which corresponds to a detached configuration.

Journal of Computational Physics, 1990

The present numerical method for solving three-dimensional PDFs in a sphere subject to various bo... more The present numerical method for solving three-dimensional PDFs in a sphere subject to various boundary conditions was developed with a view to the characterization of the gravitational-collapse process for a star which ends in either the formation of a supernova or a black hole, with subsequent gravitational radiation emissions. Attention is given to the application of a spectral analysis-based numerical method to the solution of three-dimensional waveequations, as well as to the solutions of gas-dynamics equations for various pertinent cases.

Journal of Computational Physics, 1991

A high-accuracy numerical technique is presented which employs two moving grids, respectively bef... more A high-accuracy numerical technique is presented which employs two moving grids, respectively before and after the shock formation, to solve 1D Euler equations that are coupled with the transport equations for the entropy and the chemical abundances in cases with and without shock formation. Chebychev polynomial series are used to expand quantities on both sides of the matching point, and Rankine-Hugoniot conditions are used to ascertain the shock velocity after shock formation. Illustrative results are presented.

Physical Review D, 1994

We calculate the gravitational radiation produced by the merger and coalescence of inspiraling bi... more We calculate the gravitational radiation produced by the merger and coalescence of inspiraling binary neutron stars using 3-dimensional numerical simulations. The stars are modeled as polytropes and start out in the pointmass limit at wide separation. The hydrodynamic integration is performed using smooth particle hydrodynamics (SPH) with Newtonian gravity, and the gravitational radiation is calculated using the quadrupole approximation. We h a v e run several simulations, varying both the neutron star radius and the equation of state. The resulting gravitational wave energy spectra dE=df are rich in information about the hydrodynamics of merger and coalescence. In particular, our results demonstrate that detailed information on both GM=Rc 2 and the equation of state can in principle be extracted from the spectrum.