Nonconformally flat initial data for binary compact objects

Kōji Uryū, François Limousin, John L. Friedman, Eric Gourgoulhon, and Masaru Shibata
Phys. Rev. D 80, 124004 – Published 2 December 2009

Abstract

A new method is described for constructing initial data for a binary neutron-star system in quasiequilibrium circular orbit. Two formulations for nonconformally flat data, waveless and near-zone helically symmetric, are introduced; in each formulation, the Einstein-Euler system, written in 3+1 form on an asymptotically flat spacelike hypersurface, is exactly solved for all metric components, including the spatially nonconformally flat potentials, and for irrotational flow. A numerical method applicable to both formulations is explained with an emphasis on the imposition of a spatial gauge condition. Results are shown for solution sequences of irrotational binary neutron-stars with matter approximated by parametrized equations of state that use a few segments of polytropic equations of state. The binding energy and total angular momentum of solution sequences computed within the conformally flat—Isenberg-Wilson-Mathews—formulation are closer to those of the third post-Newtonian (3PN) two point particles up to the closest orbits, for the more compact stars, whereas sequences resulting from the waveless/near-zone helically symmetric formulations deviate from the 3PN curve even more for the sequences with larger compactness. We think it likely that this correction reflects an overestimation in the Isenberg-Wilson-Mathews formulation as well as in the 3PN formula, by 1 cycle in the gravitational-wave phase during the last several orbits. The work suggests that imposing spatial conformal flatness results in an underestimate of the quadrupole deformation of the components of binary neutron-star systems in the last few orbits prior to merger.

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  • Received 6 August 2009

DOI:https://doi.org/10.1103/PhysRevD.80.124004

©2009 American Physical Society

Authors & Affiliations

Kōji Uryū1, François Limousin2, John L. Friedman3, Eric Gourgoulhon2, and Masaru Shibata4

  • 1Department of Physics, University of the Ryukyus, Senbaru, Nishihara, Okinawa 903-0213, Japan
  • 2Laboratoire Univers et Théories, UMR 8102 du CNRS, Observatoire de Paris, Université Paris Diderot, F-92190 Meudon, France
  • 3Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201, USA
  • 4Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

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Issue

Vol. 80, Iss. 12 — 15 December 2009

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