Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998tx19.confe.495t&link_type=abstract
Abstracts of the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.:
Astronomy and Astrophysics
Astrophysics
Scientific paper
First post-Newtonian (PN) hydrostatic equations for an irrotational fluid are solved for an incompressible binary system. The 1PN configurations are expressed as a deformation of the Newtonian irrotational Darwin-Riemann ellipsoid using Lagrangian displacement vectors. It is found that the angular velocity of the binary system at the innermost stable circular orbit in the unit of sqrt{GMast/aast^3} has almost the same value as in the Newtonian order when increasing the compactness parameter GMast/c^2 aast in which Mast and aast denote the mass and the radius of a star. We also investigate the validity of an ellipsoidal approximation, in which the 1PN solution is obtained assuming an ellipsoidal figure. It is found that the ellipsoidal approximation gives fairly accurate results. However, if we neglect the velocity potential of the 1PN order, the results change their feature regardless of the shape of the star.
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